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BOUOHT-WIT-H THE l*iCO*lE OF THE

•SAGE lENDOVl^ENT FUND

THE <GiFT OF

IHENRY W. SAGE

1891

Cornell University Library
ArY794

Collected papers on acoustics

3 1924 022 547 024

The original of this book is in
the Cornell University Library.

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the United States on the use of the text.

http://www.archive.org/details/cu31924022547024

COLLECTED PAPERS
ON ACOUSTICS

yi/t»Jt/L0LMJI. i^>AB-&u««w-v

COLLECTED PAPERS
ON ACOUSTICS

WALLACE CLEMENT SABINE

LATE HOIXIS PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY
IN HARVARD UNIVERSITY

CAMBRIDGE
HARVARD UNIVERSITY PRESS

LONDON : HUMPHREY MILFORD
Oxford Univbbsitt Press

1922

PREFACE

1 HIS volume aims to contain all the important contributions to the
subject of acoustics from the pen of the late Professor W. C. Sabine.
The greater part of these papers appeared in a number of different
architectural journals and were therefore addressed to a changing
audience, little acquainted with physical science, and to whose mem-
bers the subject was altogether novel. Under these circumstances a
certain amount of repetition was not only unavoidable, but desirable.
Little attempt has been made to reduce this repetition but in one
case an omission seemed wise. The material contained in the author's
earliest papers on acoustics, which appeared in the Proceedings of
the American Institute of Architects in 1898, is repeated almost
completely in the paper which forms the first chapter of this volume;
it has, therefore, been omitted from this collection with the exception
of a few extracts which have been inserted as footnotes in the first
chapter.

No apology is made for the preservation of the paper from the
Proceedings of the Franklin Institute, for, though much of the ma-
terial therein is to be found in the earlier chapters of this volume, the
article is valuable as a summary, and as such it is recommended
to the reader who desires to obtain a general view of the subject.

In addition to the papers already in print at the time of the
author's death the only available material consisted of the manu-
scripts of two articles, one on Echoes, the other on Whispering Gal-
leries, and the full notes on four of the lectures on acoustics delivered
at the Sorbonne in the spring of 1917. Of this material, the first
paper was discarded as being too fragmentary; the second, after
some slight omissions and corrections in the text made necessary by
the loss of a few of the illustrations, forms Chapter 11 of this volume;
an abstract of so much of the substance of the lecture notes as had
not already appeared in print has been made, of which part is to be
found in the form of an Appendix and part is contained in some of the
following paragraphs.

The reader may often be puzzled by reference to works about to be
published but of which no trace is to be found in this volume. It is

vi PREFACE

a melancholy fact that these papers were either never written or else
were destroyed by their author; no trace of them can be found. The
extent of the labors of which no adequate record remains may best be
judged from the following extracts taken from the notes on the Paris
lectures just mentioned.

" On the one hand we have the problem (Reverberation) which we
have been discussing up to the present moment, and on the other
the whole question of the transmission of sound from one room to
another, through the walls, the doors, the ceiling and the floors; and
the telephonic transmission, if I may so call it, through the length of
the structure. It is five years ago since this second problem was first
attacked and though the research is certainly not complete, some
ground has been covered. A quantitatively exact method has been
established and the transmission of sound through about twenty
different kinds of partitions has been determined.

" For example : Transmission of sound through four kinds of doors
has been studied; two of oak, two of pine, one of each kind was
paneled and was relatively thin and light; one of each kind was very
heavy, nearly four centimetres thick; through four kinds of windows,
one of plate glass, one with common panes, one double with an air
space of two centimetres between, one with small panes set in lead
such as one sees in churches; through brick walls with plaster on both
sides; through walls of tile similarly plastered; through walls of a
character not common in France and which we call gypsum block;
through plaster on lath; through about ten different kinds of sound
insulators, patented, and sold in quantities representing hundreds of
thousands of dollars each year, yet practically without value, since
one can easily converse through six thicknesses of these substances
and talk in a low tone through three, while a single thickness is that
ordinarily employed. The behavior of an air space has been studied,
the effect of the thickness of this air space, and the result of filling
the space with sand, saw-dust and asbestos. In spite of all this, the
research is far from complete and many other forms of construction
must be investigated before it will be possible to publish the results ;
these determinations must be made with the greatest exactness as
very important interests are involved. . . .

PREFACE vii

" The research is particularly laborious because resonance has a
special importance in a great number of forms of construction. It is a
much greater factor in transmission than in absorption.

" I shall not enlarge on this subject here for two reasons : first, I
believe that it is not of special interest, at least, in its present state,
and second, because it is not proper to present a formal discussion of
this subject while the research is still unfinished."

The last paragraph is characteristic. The severity of the criti-
cism which Professor Sabine always applied to his own productions
increased with time, and it is to this extreme self-criticism and re-
pression that we must ascribe the loss of much invaluable, scientific
material.

Thanks are due to The American Institute of Architects and to
the editors of The American Architect, The Brickbuilder, The En-
gineering Record, and The Journal of the Franklin Institute, for
permission to reprint the articles which originally appeared in their
respective Journals.

The Editor is also greatly obliged to Dr. Paul Sabine and Mr. Clif-
ford M. Swan for a great deal of valuable material, and to Mr. Frank
Chouteau Brown for his assistance in seeing the book through the
press. He is particularly indebted to his colleague Professor F. A.
Saunders for his invaluable aid in all matters touching the correct
presentation of the material of this volume.

Theodore Lyman
jefferson physical laboratory

Hahvard- University
June, 1921

CONTENTS

PAGE

1. Reverberation 3

[The American Architect, 1900]

2. The Accuracy of Musical Taste in Regard to Architectural

Acoustics. The Variation in Reverberation with Variation in
Pitch 69

[Proceedings of the American Academy of Arts and Sciences, Vol. xm. No. 2, June,
1906]

3. Melody and the Origin of the Musical Scale 107

[Vice-Presidential Address, Section B, American Association for the Advancement
of Science, Chicago, 1907]

4. Effects of Air Currents and of Temperature 117

[Engineering Record, June, 1910]

5. Sense of Loudness 129

[Contributions from the Jefferson Physical Laboratory, Vol. viii, 1910]

6. The Correction of Acoustical Difficulties 131

[The Architectural Quarterly of Harvard University, March, 1912]

7. Theatre Acoustics 163

[The American Architect, Vol. civ, p. 257]

8. Building Material and Musical Pitch w 199

The Brickbuilder, Vol. xxiii. No. 1, January, 1914]

9. Architectural Acoustics 219

[Journal of the Franklin Institute, January, 1915]

10. Insulation Sound 237

[The Brickbuilder, Vol. xxiv. No. 2, February, 1915]

11. Whispering Galleries 255

Appendix 277

On the Measurement of the Intensity of Sound and on the Reaction of the Room
upon the Sound

COLLECTED PAPERS
ON ACOUSTICS

REVERBERATION^

INTRODUCTION

1 HE following investigation was not undertaken at first by choice,
but devolved on the writer ia 1895 through instructions from the
Corporation of Harvard University to propose changes for remedy-
ing the acoustical difficulties in the lecture-room of the Fogg Art
Museum, a building that had just been completed. About two years
were spent in experimenting on this room, and permanent changes
were then made. Almost immediately afterward it became certain
that a new Boston Music Hall would be erected, and the questions
arising in the consideration of its plans forced a not unwelcome con-
tinuance of the general investigation.

No one can appreciate the condition of architectural acoustics —
the science of sound as applied to buildings — who has not with a
pressing case in hand sought through the scattered literature for
some safe guidance. Responsibility in a large and irretrievable ex-
penditure of money compels a careful consideration, and emphasizes
the meagerness and inconsistency of the current suggestions. Thus
the most definite and often repeated statements are such as the
following, that the dimensions of a room should be in the ratio

2 : 3 : 5, or according to some writers, 1:1:2, and others, 2 : 3 : 4;
it is probable that the basis of these suggestions is the ratios of the
harmonic intervals in music, but the connection is untraced and re-
mote. Moreover, such advice is rather difficult to apply; should one
measure the length to the back or to the front of the galleries, to the
back or the front of the stage recess? Few rooms have a flat roof,
where should the height be measured.'' One writer, who had seen the
Mormon Temple, recommended that all auditoriums be elliptical.
Sanders Theatre is by far the best auditorium in Cambridge and is
semicircular in general shape, but with a recess that makes it almost
anything; and, on the other hand, the lecture-room in the Fogg Art

1 The American Architect and The Engineering Record, 1900.
8

4 REVERBERATION

Museum is also semicircular, indeed was modeled after Sanders
Theatre, and it was the worst. But Sanders Theatre is in wood and
the Fogg lecture-room is plaster on tile; one seizes on this only to be
immediately reminded that Sayles Hall in Providence is largely
lined with wood and is bad. Curiously enough, each suggestion is
advanced as if it alone were sufficient. As examples of remedies,
may be cited the placing of vases about the room for the sake of
resonance, wrongly supposed to have been the object of the vases in
Greek theatres, and the stretching of wires, even now a frequent
though useless device.

The problem is necessarily complex, and each room presents many
conditions, each of which contributes to the result in a greater or less
degree according to circumstances. To take justly into account these
varied conditions, the solution of the problem should be quantitative,
not merely qualitative; and to reach its highest usefulness It should
be such that its application can precede, not follow, the construction
of the building.

In order that hearing may be good in any auditorium, it is neces-
sary that the sound should be sufficiently loud; that the simultane-
ous components of a complex sound should maintain their proper
relative intensities; and that the successive sounds in rapidly mov-
ing articulation, either of speech or music, should be clear and dis-
tinct, free from each other and from extraneous noises. These three
are the necessary, as they are the entirely sufficient, conditions for
good hearing. The architectural problem is, correspondingly, three-
fold, and in this introductory paper an attempt will be made to
sketch and define briefly the subject on this basis of classification.
Within the three fields thus defined is comprised without exception
the whole of architectural acoustics.

1. Loudness. — Starting with the simplest conceivable auditorimn
— a level and open plain, with the ground bare and hard, a single
person for an audience — it is clear that the soimd spreads in a hemi-
spherical wave diminishing in intensity as it increases in size, pro-
portionally. If, instead of being bare, the ground is occupied by a
large audience, the sound diminishes in intensity even more rapidly,
being now absorbed. The upper part of the sound-wave escapes un-
affected, but the lower edge — the only part that is of service to an

INTRODUCTION 5

audience on a plain — is rapidly lost. The first and most obvious
improvement is to raise the speaker above the level of the audience;
the second is to raise the seats at the rear; and the third is to place a
wall behind the speaker. The result is most attractively illustrated
in the Greek theatre. These changes being made, still all the sound
rising at any considerable angle is lost through the opening above,
and only part of the speaker's efforts serve the audience. When to
this auditorium a roof is added the average intensity of sound
throughout the room is greatly increased, especially that of sustained
tones; and the intensity of sound at the front and the rear is more
nearly equalized. If, in addition, galleries be constructed in order to
elevate the distant part of the audience and bring it nearer to the
front, we have the general form of the modern auditorium. The
problem of calculating the loudness at different parts of such an audi-
torium is, obviously, complex, but it is perfectly determinate, and as
soon as the reflecting and absorbing power of the audience and of the
various wall-surfaces are known it can be solved approximately.
Under this head will be considered the effect of sounding-boards, the
relative merits of different materials used as reflectors, the refrac-
tion of sound, and the influence of the variable temperature of
the air through the heating and ventilating of the room, and similar
subjects.

2. Distortion of Complex Sounds: Interference and Resonance. —
In discussing the subject of loudness the direct and reflected sounds
have been spoken of as if always re enforcing each other when they
come together. A moment's consideration of the nature of sound
will show that, as a matter of fact, it is entirely possible for them to
oppose each other. The sounding body in its forward motion sends
off a wave of condensation, which is immediately followed through
the air by a wave of rarefaction produced by the vibrating body as
it moves back. These two waves of opposite character taken to-
gether constitute a sound-wave. The source continuing to vibrate,
these waves follow each other in a train. Bearing in mind this alter-
nating character of sound, it is evident that should the sound travel-
ing by different paths — by reflection from different walls — come
together again, the paths being equal in length, condensation will
arrive at the same time as condensation, and reenforce it, and rare-

6 REVERBERATION

faction will, similarly, reenforce rarefaction. But should one path
be a little shorter than the other, rarefaction by one and condensa-
tion by the other may arrive at the same time, and at this point
there will be comparative silence. The whole room may be mapped
out into regions in which the sound is loud and regions in which it
is feeble. When there are many reflecting surfaces the interference
is much more complex. When the note changes in pitch the inter-
ference system is entirely altered in character. A single incident
will serve to illustrate this point. There is a room in the Jefferson
Physical Laboratory, known as the constant-temperature room,
that has been of the utmost service throughout these experiments.
It is in the center of one wing of the building, is entirely under
ground, even below the level of the basement of the building, has
separate foundations and double walls, each wall being very thick
and of brick in cement. It was originally designed for investiga-
tions in heat requiring constant temperature, and its peculiar loca-
tion and construction were for this purpose. As it was not so in
use, however, it was turned over to these experiments in sound, and
a room more suitable could not be designed. From its location and
construction it is extremely quiet. Without windows, its walls,
floor, and ceiling — all of solid masonry — are smooth and un-
broken. The single door to the room is plain and flush with the
wall. The dimensions of the room are, on the floor, 4.27 X 6.10
meters; its height at the walls is 2.54 meters, but the ceiling is
slightly arched, giving a height at the center of 3.17 meters. This
room is here described at length because it will be frequently re-
ferred to, particularly in this matter of interference of sound. While
working in this room with a treble c gemshorn organ pipe blown by
a steady wind-pressure, it was observed that the pitch of the pipe
apparently changed an octave when the observer straightened up
in his chair from a position in which he was leaning forward. The
explanation is this : The organ pipe did not give a single pure note,
but gave a fundamental treble c accompanied by several overtones,
of which the strongest was in this case the octave above. Each note
in the whole complex sound had its own interference system, which,
as long as the sound remained constant, remained fixed in position.
It so happened that at these two points the region of silence for one

INTRODUCTION 7

note coincided with the region of reenforcement in the other, and
vice versa. Thus the observer in one position heard the fundamental
note, and in the other, the first overtone. The change was exceed-
ingly striking, and as the notes remained constant, the experiment
could be tried again and again. With a little search it was possible
to find other points in the room at which the same phenomenon
appeared, but generally in less perfection. The distortion of the
relative intensities of the components of a chord that may thus be
produced is evident. Practically almost every sound of the voice
in speech and song, and of instrumental music, even single-part
music so-called, is more or less complex, and, therefore, subject to
this distortion. It will be necessary, later, to show under what cir-
cumstances this phenomenon is a formidable danger, and how it
may be guarded against, and under what circumstances it is negli-
gible. It is evident from the above occurrence that it may be a most
serious matter, for in this room two persons side by side can talk
together with but little comfort, most of the difficulty being caused
by the interference of sound.

There is another phenomenon, in its occurrence allied to inter-
ference, but in nature distinct — the phenomenon of resonance.
Both, however, occasion the same evil — the distortion of that nice
adjustment of the relative intensities of the components of the
complex sounds that constitute speech and music. The phenome-
non of interference just discussed merely alters the distribution of
sound in the room, causing the intensity of any one pure sustained
note to be above or below the average intensity at near points.
Resonance, on the other hand, alters the total amount of sound in
the whole room and always increases it. This phenomenon is
noticeable at times in using the voice in a small room, or even in
particular locations in a large room. Perhaps its occurrence is most
easily observed in setting up a large church organ, where the pipes
must be readjusted for the particular space in which the organ is to
stand, no matter with how much care the organ may have been
assembled and adjusted before leaving the factory. The general
phenomenon of resonance is of very wide occurrence, not merely in
acoustics but in more gross mechanics as well, as the vibration of a
bridge to a properly timed tread, or the excessive rolling of a boat

8 REVERBERATION

in certain seas. The principle is the same in all cases. The follow-
ing conception is an easy one to grasp, and is closely analogous to
acoustical resonance: If the palm of the hand be placed on the
center of the surface of water in a large basin or tank and quickly
depressed and raised once it will cause a wave to spread, which,
reflected at the edge of the water, will return, in part at least, to
the hand. If, just as the wave reaches the hand, the hand repeats
its motion with the same force, it will reenforce the wave traveling
over the water. Thus reenforced, the wave goes out stronger than
before and returns again. By continued repetition of the motion
of the hand so timed as to reenforce the wave as it returns, the wave
gets to be very strong. Instead of restraining the hand each time
until the wave traveling to and fro returns to it, one may so time
the motion of the hand as to have several equal waves following
each other over the water, and the hand each time reenforcing the
wave that is passing. This, obviously, can be done by dividing the
interval of time between the successive motions of the hand by any
whole number whatever, and moving the hand with the frequency
thus defined. The result will be a strong reenforcement of the waves.
If, however, the motions of the hand be not so timed, it is obvious
that the reenforcement will not be perfect, and, in fact, it is possible
to so time it as exactly to oppose the returning waves. The appli-
cation of this reasoning to the phenomenon of sound, where the air
takes the place of the water and the sounding body that of the hand,
needs little additional explanation. Some notes of a complex sound
are reenforced, some are not, and thus the quality is altered. This
phenomenon enters in two forms in the architectural problem : there
may be either resonance of the air in the room or resonance of the
walls, and the two cases must receive separate discussion; their
effects are totally different.

The word "resonance" has been used loosely as synonymous
with "reverberation," and even with "echo," and is so given in
some of the more voluminous but less exact popular dictionaries.
In scientific literature the term has received a very definite and
precise application to the phenomenon, wherever it may occur, of
the growth of a vibratory motion of an elastic body under periodic
forces timed to its natural rates of vibration. A word having this

INTRODUCTION 9

significance is necessary; and it is very desirable that the term
should riot, even popularly, by meaning many things, cease to mean
anything exactly.

3. Confusion: Reverberation, Echo and Extraneous Sounds. —
Sound, being energy, once produced in a confined space, will con-
tinue until it is either transmitted by the boundary walls, or is
transformed into some other kind of energy, generally heat. This
process of decay is called absorption. Thus, in the lecture-room of
Harvard University, in which, and in behalf of which, this investi-
gation was begun, the rate of absorption was so small that a word
spoken in an ordinary tone of voice was audible for five and a half
seconds afterwards. During this time even a very deliberate
speaker would have uttered the twelve or fifteen succeeding sylla-
bles. Thus the successive enunciations blended into a loud sound,
through which and above which it was necessary to hear and dis-
tinguish the orderly progression of the speech. Across the room
this could not be done; even near the speaker it could be done only
with an effort wearisome in the extreme if long maintained. With
an audience fiUing the room the conditions were not so bad, but
still not tolerable. This may be regarded, if one so chooses, as a
process of multiple reflection from walls, from ceiling and from floor,
first from one and then another, losing a little at each reflection
until ultimately inaudible. This phenomenon will be called re-
verberation, including as a special case the echo. It must be ob-
served, however, that, in general, reverberation results in a mass of
sound filling the whole room and incapable of analysis into its dis-
tinct reflections. It is thus more difficult to recognize and impossible
to locate. The term echo will be reserved for that particular case
in which a short, sharp sound is distinctly repeated by reflection,
either once from a single surface, or several times from two or more
surfaces. In the general case of reverberation we are only concerned
with the rate of decay of the sound. In the special case of the echo
we are concerned not merely with its intensity, but with the interval
of time elapsing between the initial sound and the moment it
reaches the observer. In the room mentioned as the occasion of
this investigation, no discrete echo was distinctly perceptible, and
the case will serve excellently as an illustration of the more general

10 REVERBERATION

type of reverberation. After preliminary gropings/ first in the
literature and then with several optical devices for measuring the
intensity of sound, both were abandoned, the latter for reasons that
will be explained later. Instead, the rate of decay was measured by
measuring what was inversely proportional to it — the duration of
audibility of the reverberation, or, as it will be called here, the dura-
tion of audibility of the residual sound. These experiments may be
explained to advantage even in this introductory paper, for they
will give more clearly than would abstract discussion an idea of the
nature of reverberation. Broadly considered, there are two, and
only two, variables in a room — shape including size, and materials
including furnishings. In designing an auditorium an architect can
give consideration to both; in repair work for bad acoustical con-
ditions it is generally impracticable to change the shape, and only
variations in materials and furnishings are allowable. This was,
therefore, the line of work in this case. It was evident that, other
things being equal, the rate at which the reverberation would dis-
appear was proportional to the rate at which the sound was ab-
sorbed. The first work, therefore, was to determine the relative
absorbing power of various substances. With an organ pipe as a
constant source of sound, and a suitable chronograph for recording,
the duration of audibility of a sound after the source had ceased in
this room when empty was found to be 5.62 seconds. All the cush-
ions from the seats in Sanders Theatre were then brought over and
stored in the lobby. On bringing into the lecture-room a number
of cushions having a total length of 8.2 meters, the duration of
audibility fell to 5.33 seconds. On bringing in 17 meters the sound
in the room after the organ pipe ceased was audible for but 4.94

' The first method for determining the rate of decay of the sound, and therefore the amount
of absorption, was by means of a sensitive manometric gas flame measured by a micrometer
telescope. Later, photographing the flame was tried; but both methods were abandoned, for
they both showed, what the unaided ear could perceive, that the sound as observed at any
point in the room died away in a fluctuating manner, passing through maxima and minima.
Moreover, they showed what the unaided ear had not detected, but immediately afterward
did recognize, that the sound was often more intense immediately after the source ceased than
before. All this was interesting, but it rendered impossible any accurate interpretation of the
results obtained by these or similar methods. It was then found that the ear itself aided by
a suitable electrical chronograph for recording the duration or audibility of the residual sound
gave a surprisingly sensitive and accurate method of measurement. Proc. American Institute
of Architects, p. 35, 1898.

INTRODUCTION 11

seconds. Evidently, the cushions were strong absorbents and
rapidly improving the room, at least to the extent of diminishing the
reverberation. The result was interesting and the process was con-
tinued. Little by little the cushions were brought into the room,
and each time the duration of audibility was measured. When all
the seats (436 in number) were covered, the sound was audible for
2.03 seconds. Then the aisles were covered, and then the platform.
Still there were more cushions — almost half as many more. These
were brought into the room, a few at a time, as before, and draped
on a scaffolding that had been erected around the room, the dura-
tion of the sound being recorded each time. Finally, when all the
cushions from a theatre seating nearly fifteen hundred persons were
placed in the room — covering the seats, the aisles, the platform,
the rear wall to the ceiling — the duration of audibility of the resid-
ual sound was 1.14 seconds. This experiment, requiring, of course,
several nights' work, having been completed, all the cushions were
removed and the room was in readiness for the test of other absorb-
ents. It was evident that a standard of comparison had been
established. Curtains of cheniUe, 1.1 meters wide and 17 meters in
total length, were draped in the room. The duration of audibility
was then 4.51 seconds. Turning to the data that had just been
collected it appeared that this amount of chenille was equivalent to
30 meters of Sanders Theatre cushions. Oriental rugs, Herez,
Demirjik, and Hindoostanee, were tested in a similar manner; as
were also cretonne cloth, canvas, and hair felt. Similar experi-
ments, but in a smaller room, determined the absorbing power of
a man and of a woman, always by determining the number of run-
ning meters of Sanders Theatre cushions that would produce the
same effect. This process of comparing two absorbents by actually
substituting one for the other is laborious, and it is given here only
to show the first steps in the development of a method that will be
expanded in the following papers.

In this lecture-room felt was finally placed permanently on par-
ticular walls, and the room was rendered not excellent, but entirely
serviceable, and it has been used for the past three years without
serious complaint. It is not intended to discuss this particular case
in the introductory paper, because such discussion would be prema-

12 REVERBERATION

ture and logically incomplete. It is mentioned here merely to illus-
trate concretely the subject of reverberation, and its dependence on
absorption. It would be a mistake to suppose that an absorbent is
always desirable, or even when desirable that its position is a matter
of no consequence.^

While the logical order of considering the conditions contributing
to or interfering with distinct hearing would be that employed above,
it so happens that exactly the reverse order is preferable from an
experimental standpoint. By taking up the subject of reverberation
first it is possible to determine the coefl&cients of absorption and
reflection of various kinds of wall surface, of furniture and draperies,
and of an audience. The investigation of reverberation is now, after
five years of experimental work, completed, and an account will be
rendered in the following papers. Some data have also been secured
on the other topics and will be published as soon as rounded into
definite form.

This paper may be regarded as introductory to the general sub-
ject of architectural acoustics, and immediately introductory to a
series of articles dealing with the subject of reverberation, in which
the general line of procedure will be, briefly, as follows : The absorb-
ing power of wall-surfaces will be determined, and the law according
to which the reverberation of a room depends on its volume will be
demonstrated. The absolute rate of decay of the residual sound in
a number of rooms, and in the same room under different conditions,
will then be determined. In the fifth paper a more exact analysis

• There is no simple treatment that can cure all cases. There may be inadequate absorption
and prolonged residual sound; in this case absorbing material should be added in the proper
places. On the other hand, there may be excessive absorption by the nearer parts of the hall
and by the nearer audience and the sound may not penetrate to the greater distances. Ob-
viously the treatment should not be the same. There is such a room belonging to the Uni-
versity, known locally as Sever 35. It is low and long. Across its ceiling are now stretched
hundreds of wires and many yards of cloth. The former has the merit of being harmless, the
latter is like bleeding a patient suffering from a chill. In general, should the sound seem
smothered or too faint, it is because the sound is either imperfectly distributed to the audience,
or is lost in waste places. The first may occur in a very low and long room, the second in one
with a very high ceiUng. The first can be remedied only slightly at best, the latter can be im-
proved by the use of reflectors behind and above the speaker. On the other hand, should the
sound be loud but confused, due to a perceptible prolongation, the difficulty arises from there
being reflecting surfaces either too far distant or improperiy inclined. Proc. American Insti-
tute of Architects, p. 39, 1898.

ABSORBING POWER OF WALL-SURFACES 13

will be given, and it will be shown that, by very different lines of
attack, starting from different data, the same numerical results are
secured. Tables will be given of the absorbing power of various
wall-surfaces, of furniture, of an audience, and of all the materials
ordinarily found in any quantity in an auditorium. Finally, in
illustration of the calculation of reverberation in advance of con-
struction, will be cited the new Boston Music Hall, the most interest-
ing case that has arisen.

ABSORBING POWER OF WALL-SURFACES

In the introductory article the problem was divided into considera-
tions of loudness, of distortion, and of confusion of sounds. Con-
fusion may arise from extraneous disturbing sounds — street noises
and the noise of ventilating fans — or from the prolongation of the
otherwise discrete sounds of music or the voice into the succeeding
sounds. The latter phenomenon, known as reverberation, results
in what may be called, with accuracy and suggestiveness, residual
sound. The duration of this residual sound was shown to depend
on the amount of absorbing material inside the room, and also, of
course, on the absorbing and transmitting power of the walls; and
a method was outlined for determining the absorbing power of the
former in terms of the absorbing power of some material chosen as
a standard and used in a preliminary calibration. A moment's con-
sideration demonstrates that this method, which is of the general
type known as a "substitution method," while effective in the de-
termination of the absorbing power of furniture and corrective
material, and, in general, of anything that can be brought into or
removed from a room, is insuflScient for determinating the absorb-
ing power of wall-surfaces. This, the absorbing power of wall-
surfaces, is the subject of the present paper; and as the method of
determination is an extension of the above work, and finds its justi-
fication in the striking consistency of the results of the observations,
a more elaborate description of the experimental method is desirable.
A proof of the accuracy of every step taken is especially necessary
in a subject concerning which theory has been so largely uncon-
trolled speculation.

14 REVERBERATION

Early in the investigation it was found that measurements of
the length of time during which a sound was audible after the source
had ceased gave promising results whose larger inconsistencies could
be traced du-ectly to the distraction of outside noises. On repeating
the work during the most quiet part of the night, between half-past
twelve and five, and using refined recording apparatus, the minor
irregularities, due to relaxed attention or other personal variations,
were surprisingly small. To secure accuracy, however, it was neces-
sary to suspend work on the approach of a street car within two
blocks, or on the passing of a train a mile distant. In Cambridge
these interruptions were not serious; in Boston and in New York
it was necessary to snatch observations in very brief intervals of
quiet. In every case a single determination of the duration of the
residual sound was based on the average of a large number of
observations.

An organ pipe, of the gemshorn stop, an octave above middle c
(512 vibration frequency) was used as the source of sound in some
preliminary experiments, and has been retained in subsequent work
in the absence of any good reason for changing. The wind supply
from a double tank, water-sealed and noiseless, was turned on and
off the organ pipe by an electro-pneumatic valve, designed by Mr.
George S. Hutchings, and similar to that used in his large church
organs. The electric current controlling the valve also controlled
the chronograph, and was made and broken by a key in the hands
of the observer from any part of the room. The chronograph em-
ployed in the later experiments, after the more usual patterns had
been tried and discarded, was of special design, and answered well
the requirements of the work — perfect noiselessness, portability,
and capacity to measure intervals of time from a half second to ten
seconds with considerable accuracy. It is shown in the adjacent
diagram. The current whose cessation stopped the sounding of the
organ pipe also gave the initial record on the chronograph, and the
only duty of the observer was to make the record when the sound
ceased to be audible.

While the supreme test of the investigation lies in the consistency
and simplicity of the whole solution as outlined later, three pre-
liminary criteria are found in (1) the agreement of the observations

ABSORBING POWER OF WALI^SURPACES 15

obtained at one sitting, (2) the agreement of the results obtained
on different nights and after the lapse of months, or even years, by
the same observer under similar conditions, and (3) the agreement
of independent determinations by different observers. The first
can best be discussed, of course, by the recognized physical methods
for examining the accuracy of an extended series of observations;

Fig. 1. ChroDograph, battery, and air reservoir, the latter surmounted
by the electro-pneumatic valve and organ pipe.

and the result of such examination is as follows : Each determination
being the mean of about twenty observations under conditions such
that the audible duration of the residual sound was 4 seconds, the
average deviation of the single observations from the mean was .11
seconds, and the maximum deviation was .31. The computed
"probable error" of a single determination was about .02 seconds;
as a matter of fact, the average deviation of ten determinations
from the mean of the ten was .03 seconds, and the maximum devi-

16 REVERBERATION

ation was .05. The reason for this accuracy \dll be discussed in a
subsequent paper. The probable error of the mean, thus calculated
from the deviations of the single observations, covers only those
variable errors as likely to increase as to decrease the final result.
Fixed instrumental errors, and the constant errors commonly re-
ferred to by the term "personal factors " are not in this way exposed.
They were, however, repeatedly tested for by comparison with a
clock beating seconds, and were very satisfactorily shown not to
amount to more than .02 seconds in their cumulative effect. Three
types of chronographs, and three kinds of valves between the organ
pipe and the wind chest were used in the gradual development of
the experiment, and all gave for the same room very nearly the same
final results. The later instruments were, of course, better and more
accurate.

The second criterion mentioned above is abundantly satisfied by
the experiments. Observations taken every second or third night
for two months in the lecture-room of the Fogg Art Museum gave
practically the same results, varying from 5.45 to 5.62 with a mean
value of 5.57 seconds, a result, moreover, that was again obtained
after the lapse of one and then of three years. Equally satisfactory
agreement was obtained at the beginning and at the end of three
years in Sanders Theatre, and in the constant-temperature room
of the Physical Laboratory.

Two gentlemen, who were already somewhat skilled in physical
observation, Mr. Gifford LeClear and Mr. E. D. Densmore, gave
the necessary time to test the third point. After several nights'
practice their results differed but slightly, being .08 seconds and
.10 seconds longer than those obtained by the writer, the total
diu-ation of the sound being 4 seconds. This agreement, showing
that the results are probably very nearly those that would be ob-
tained by any auditor of normal hearing, gives to them additional
interest. It should be stated, however, that the final development
of the subject will adapt it with perfect generality to either normal
or abnormal acuteness of hearing.

Almost the first step in the investigation was to estabhsh the
following three fundamentally important facts. Later work has
proved these fundamental facts far more accurately, but the original

ABSORBING POWER OF WALL-SURFACES

experiments are here given as being those upon which the conclu-
sions were based.

The duration of audibility of the residual sound is nearly the same
in all parts of an auditorium. — Early in the investigation an ex-
periment to test this point was made in Steinert Hall, in Boston.
The source of sound remaining on the platform at the point marked

Fig. 2. Steinert Hall, Boston : position of air reservoir
and organ pipe at 0; positions of observer 1-8.

in the diagram, observations were made in succession at the points
marked 1 to 8, with the results shown in the table:

Station Duration Station Duration

1 2.12 5 2.23

2 2.17 6 2.27

3 2.23 7 2.20

4 2.20 8 2.26

On first inspection these results seem to indicate that the duration
of audibility is very slightly greater at a distance from the source,
and it would be easy to explain this on the theory that at a distance
the ear is less exhausted by the rather loud noise while the pipe is
sounding; but, as a matter of fact, this is not the case, and the

REVERBERATION

variations there shown are within the hmits of accuracy of the
apparatus employed and the skill attained thus early m the in-
vestigation. Numerous later experiments, more accurate, but not
especially directed to this point, have verified the above general
statement quite conclusively.

The duration of audibility is nearly independent of the position of
the source. — The observer remaining at the point marked in the

diagram of the large lecture-room
of the JeflFerson Physical Labora-
tory, the organ pipe and wind chest
were moved from station to sta-
tion, as indicated by the numbers
1 to 6, with the results shown in
the table:

Duration

3.90

4.00

3.90

3.98

3.95

3.96

Fig. 3. Lecture-room, Jefferson Physical
Laboratory: position of observer at 0;
positions of air reservoir and organ pipe
1-6.

The efficiency of an absorbent in
reducing the duration of the residual
sound is, under ordinary circum-
stances, nearly independent of its
position. — Fifty meters of cretonne cloth draped on a scaffolding
under the rather low ceiling at the back of the lecture-room of
the Fogg Museum, as shown in the next diagram, reduced the
audible duration of the residual sound by very nearly the same
amount, regardless of the section in which it hung, as shown in the
following table, the initial duration being 5.57 seconds:

Section
1. .

Duration

. 4.88

. 4.83

. 4.92

. 4.85

In some later experiments five and a half times as much cretonne
draped on the scaffolding reduced the audible duration of the

ABSORBING POWER OF WALL-SURFACES

residual sound to 3.25 seconds; and when hung fully exposed in
the high dome-like ceiling, gave 3.29 seconds, confirming the above
statement.

These facts, simple when proved, were by no means self-evident
so long as the problem was one of reverberation, that is, of succes.
sive reflection of sound from wall to
wall. They indicated that, at least with
reference to auditoriums of not too
great dimensions, another point of view
would be more suggestive, that of re-
garding the whole as an energy problem
in which the source is at the organ
pipe and the decay at the walls and
at the contained absorbing material.
The above results, then, all point to
the evident, but perhaps not appreci-
ated, fact that the dispersion of sound
between all parts of a hall is very rapid
in comparison with the total time re-
quired for its complete absorption, and
that in a very short time after the
soiu-ce has ceased the intensity of the
residual sound, except for the phenom-
enon of interference to be considered
later, is very nearly the same every-
where in the room.

This much being determined, the
investigation was continued in the fol-
lowing manner: Cushions from San-
ders Theatre were transferred to the
lobby of the lecture-room of the Fogg
Museum; a very few were brought into the room and spread along
the front row of seats; the duration of audibility of the residual
sound, diminished by the introduction of this additional absorbent,
was determined, and the total length of cushion was measured. The
next row of seats was then covered in the same manner and the two
observations made — length of cushion and duration of residual

Fig. 4. Lecture-room, Fogg Art
Museum: position of observer at
0; positions of absorbent at 1-4,
and in the dome.

20 REVERBERATION

sound. This was repeated till cushions covered all the seats. This
work was at first undertaken solely with the intention of determin-
ing the relative merits of different absorbing materials that might
be placed in the room as a corrective for excessive residual sound,
and the account of this application is given in the introductory
paper. A subsequent study of these and similar results obtained in
many other rooms has shown their applicability to the accurate
determination of the absorbing power of wall-surfaces. This appli-
cation may be shown in a purely analytical manner, but the expo-
sition is greatly helped by a graphical representation. The manner
in which the duration of the residual sound in the Fogg lecture-
room is dependent on the amount of absorbing material present is
shown in the following table:

LeDEth Duration of

of CnsLion Besidual Soimd

in Meters in Seconds

5.61

8 5.33

17 4.94

28 4.56

44 4.21

63 3.94

83 3.49

104 3.33

128 3.00

145 2.85

162 2.64

189 2.36

213 2.33

242 2.22

This table, represented graphically in the conventional manner —
length of cushion plotted horizontally and duration of soimd verti-
cally — gives pomts through which the curve may be drawn in the
accompanymg diagram. To discover the law from this curve we
represent the lengths of cushion by x, and the corresponding dura-
tions of sound, the vertical distances to the curve, by t. If we now
seek the formula connecting x and t that most nearly expresses the
relationship represented by the above curve, we find it to be
{a -\- x)t = h, which is the familiar formula of a rectangular hyper-
bola with its origin displaced along the axis of x, one of its asymp-
totes, by an amount a. To make this formula most closely fit our

ABSORBING POWER OF WALIr-SURFACES

curve we must, in this case, give to the constant, a, the numerical
value, 146, and to h the value, 813. The accuracy with which the
formula represents the curve may be seen by comparing the dura-
tions calculated by the formula with those determined from the
curve; they nowhere differ by more than .04 of a second, and have,
on an average, a difference of only .02 of a second. This is entirely
satisfactory, for the calculated points fall off from the curve by
scarcely the breadth of the pen point with which it was drawn.

The determination of the absorbing power of the wall-surface
depends on the interpretation of the constant, a. In the formula.

Fig. 5.

40 eo 80 100 120 140 160 180 200 220 240 260 280 300

Length of cushions in meters

Curve showing the relation of the duration of the residual
sound to the added absorbing material.

the position of a, indicating that x is to be added to it, suggests
that X and a are of a like nature, and that a is a measure of the
absorbing power of the bare room; in order to determine the curve
this was increased by the introduction of the cushions. This is
even better shown by the diagram in which the portion of the curve
experimentally determined is fitted into the curve as a whole, and
a and x are indicated. Thus, the absorbing power of the room — ■
the walls, partly plaster on stone, partly plaster on wire lath, the
windows, the skylight, the floor — was equivalent to 146 running
meters of Sanders Theatre cushions.

The last statement shows the necessity for two subsidiary in-
vestigations. The first, to express the results in some more perma-
nent, more universally available, and, if possible, more absolute

22 REVERBERATION

unit than the cushions; the other, to apportion the total absorbing
power among the various components of the structure.

The transformation of results from one system of units to an-
other necessitates a careful study of both systems. Some early
experiments in which the cushions were placed with one edge pushed
against the backs of the settees gave results whose anomalous
character suggested that, perhaps, their absorbing power depended
not merely on the amount present but also on the area of the sur-
face exposed. It was then recalled that about two years before,
at the beginning of an evening's work, the first lot of cushions

Cushions

Fig. 6. Curve 5 plotted as part of its corresponding rectangular
hyperbola. The solid part was determined experimentally;
the displacement of this to the right measm-es the absorbing
power of the walls of the room.

brought into the room were placed on the floor, side by side, with
edges touching, but that after a few observations had been taken
the cushions were scattered about the room, and the work was
repeated. This was done not at all to uncover the edges, but in
the primitive uncertainty as to whether near cushions would draw
from each other's supply of sound, as it were, and thus diminish
each other's efficiency. No further thought was then given to these
discarded observations until recalled by the above-mentioned dis-
crepancy. They were sought out from the notes of that period,
and it was found that, as suspected, the absorbing power of the
cushions when touching edges was less than when separated. Eight
cushions had been used, and, therefore, fourteen edges had been

ABSORBING POWER OF WALI^SURFACES 23

touching. A record was found of the length and the breadth of
the cushions used, and, assuming that the absorbing power was
proportional to the area exposed, it was possible to calculate their
thickness by comparing the audible duration of the residual sound
in the two sets of observations; it was thus calculated to be 7.4
centimeters. On stacking up the same cushions and measuring
their total thickness, the average thickness was found to be 7.2
centimeters, in very close agreement with the thickness estimated
from their absorption of sound. Therefore, the measurements of
the cushions should be, not in running meters of cushion, but in
square meters of exposed surface.

For the purposes of the present investigation, it is wholly un-
necessary to distinguish between the transformation of the energy
of the sound into heat and its transmission into outside space.
Both shall be called absorption. The former is the special accom-
plishment of cushions, the latter of open windows. It is obvious,
however, that if both cushions and windows are to be classed as
absorbents, the open window, because the more universally acces-
sible and the more permanent, is the better unit. The cushions, on
the other hand, are by far the more convenient in practice, for it
is possible only on very rare occasions to work accurately with the
windows open, not at all in summer on account of night noises —
the noise of crickets and other insects — and in the winter only
when there is but the slightest wind; and further, but few rooms
have sufficient window surface to produce the desired absorption.
It is necessary, therefore, to work with cushions, but to express the
results in open- window units.

Turning now to the unit into which the results are to be trans-
formed, an especially quiet winter night was taken to determine
whether the absorbing power of open windows is proportional to
the area. A test of the absorbing power of seven windows, each
1.10 meters wide, when opened .20, .40, and .80 meter, gave results
that are plotted in the diagram. The points, by falling in a straight
line, show that, at least for moderate breadths, the absorbing
power of open windows, as of cushions, is accurately proportional
to the area. Experiments in several rooms especially convenient
for the purpose determined the absorbing power of the cushions to

REVERBERATION

be .80 of that of an equal area of open windows. These cushions
were of hair, covered with canvas and light damask. "Elastic
Felt" cushions having been used during an investigation in a New
York church, it was necessary on returning to Cambridge to deter-
mine their absorbing power. This was accomplished through the
courtesy of the manufacturers, Messrs. Sperry & Beale, of New
York, and the absorbing power was found to be .73 of open-window

I 6

S 4
< 3

.10 .20 JO .40 .50 .60 .70 .80 .90 LOO 1.10 L20 LSO 1.40 LEO

Open window

Fig. 7. The absorbing power of open windows plotted against the
areas of the openings, showing them to be proportional.

units — an interesting figure, since these cushions are of frequent
use and of standard character.

Hereafter all results, though ordinarily obtained by means of
cushions, will be expressed in terms of the absorbing power of open
windows — a unit as permanent, universally accessible, and as
nearly absolute as possible. In these units the total absorbing
power of the walls, ceiling, floor, windows and chairs in the lecture-
room of the Fogg Museum is 75.5.

Next in order is the apportionment of the total absorbing power
among the various components of the structure. Let Sx be the area
of the plaster on tile, and Oi its absorbing power per square meter;
Si and ai the corresponding values for the plaster on wire lath; S3
and as for window surface, etc. Then

fli «i + 02 S2 + a% S3 + 04 Si, etc. = 75.5,
«i, Si, S3, etc., are known, and Ui, at, as, etc. — the coeflBcients of
absorption — are unknown, and are being sought. Similar equa-

APPROXIMATE SOLUTION

tions may be obtained for other rooms in which the proportions
of wall-surface of the various kinds are greatly different, until there
are as many equations as there are unknown quantities. It is then
possible by elimination to determine the absorbing power of the
various materials used in construction.

Through the kindness of Professor Goodale, an excellent oppor-
tunity for securing some fundamentally interesting data was
afforded by the new Botanical Laboratory and Greenhouse recently
given to the University. These rooms — the oflSce, the laboratory
and the greenhouse — were exclusively finished in hard-pine sheath-
ing, glass, and cement; the three rooms, fortunately, combined the
three materials in very different proportions. They and the con-
stant-temperature room in the Physical Laboratory — the latter
being almost wholly of brick and cement — gave the following
data:

Area of
Hard Pine

Sheathing

Area of Glass

Area of Brick

and Cement

Combined

Absorbing

Power

Office

127.0

84.8

12.7

3.1

124

8.37

5.14

Greenhouse

Constant-temperature room

4.64
3.08

This table gives for the three components the following coefficients
of absorption: hard pine sheathing .058, glass .024, brick set in
cement .023.

APPROXIMATE SOLUTION

In the preceding paper it was shown that the duration of the
residual sound in a particular room was proportional inversely to
the absorbing power of the bounding walls and the contained
material, the law being expressed closely by the formula (a + x)t
= k, the formula of a displaced rectangular hyperbola. In the
present paper it is proposed to show that this formula is general,
and applicable to any room; that in adapting it to different rooms
it is only necessary to change the value of the constant of inverse
proportionality k; that k is in turn proportional to the volume of

REVERBERATION

the room, being equal to about .171V in the present experiments,
but dependent on the initial intensity of the sound; and finally,
that by substituting the value of k thus determined, and also the

S s

?v,

■^

==;

::--^

■^

*=—

"~^

~-~

-7-

-==

=*3

. .

J!!;;;;

-~~

^~~~"

—

2 3 4 5 6 7 8 9^ icr 11 12 13 14 15

Length of cushions in meters

Fig. 8. Curves showing the relation of the duration of the residual
sound to the added absorbing material, — rooms 1 to 7.

O 10 20 30 M SO 60 70 80 90 100 110 120 130 140 150

Length of cushions in meters

Pig. 9. Curves showing the relation of the duration of the residual
sound to the added absorbing material, — rooms 8 to 12.

value of a, the absorbing power of the walls, and of x, the absorbing
power of the furniture and audience, it is possible to calculate in
advance of construction the duration of audibility of the residual
sound.

APPROXIMATE SOLUTION

The truth of the first proposition — the general appUcabiUty
of the hyperboHc law of inverse proportionality — can be satis-
factorily shown by a condensed statement of the results obtained
from data collected early in the investigation. These observations
were made in rooms varying ejctremely in size and shape, from a
small committee-room to a theatre having a seating capacity for
nearly fifteen hundred. Figures 8 and 9 give the curves experi-
mentally determined, the duration of audibility of the residual

9
8
7
6
5
4
3
2

:ii

1 \

\ \
\ \

\ \

!V.'.

Ill \'

\ \

'^^

ii'

^"■'^

.^^

'~V

"•

-12

"-.

^9.

^10.

-11-

—~

. ^

-^s?

'r---

--.

^.__

"■

-—

~z~

1"-V

—.":

~ -"'"■.-.

3.===

:^=V=

■-0=i

irW^

rriV

fvii?

■€?_^

FC-C-ii

■;-:-:-

10 20 30 40 50 60 70 80 90 100 110 120 130 1«0 160
120 180 240 300 360 420
540 7Z0 900 1080 1360

Total absorbing material

Fig. 10. The curves of Figs. 8 and 9 entered as parts of their corre-
sponding rectangular hyperbolas. Three scales are employed for
the volumes, by groups 1-7, 8-11, and 12.

sound being plotted against running meters of cushions. Two
diagrams are given in order to employ a smaller scale for the larger
rooms, this scale being one-tenth the other; and even in this way
there is shown but one-quarter of the curve actually obtained in
rooms numbered 11 and 12, the Fogg Art Museum lecture-room
and Sanders Theatre. In Fig. 10 each curve is entered as a part
of its corresponding hyperbola referred to its asymptotes as axes.
In this case three scales are employed in order to show the details
more clearly, the results obtained in rooms 1 to 7 on one scale, 8 to
11 on another, and 12 on a third, the three scales being proportional
to one, three and nine. The continuous portions of the curves
show the parts determined experimentally. Even with the scale

28 REVERBERATION

thus changed only a very small portion of the experimentally de-
termined parts of curves 11 and 12 are shown. Figures 11 to 16,
inclusive, all drawn to the same scale, show the great variation in
size and shape of the rooms tested; and the accompanying notes
give for each the maximum departure and average departure of the
curve, experimentally determined, from the nearest true hyperbola.
1. Committee-room, University Hall; plaster on wood lath,
wood dado; volimae, 65 cubic meters; original duration of residual
sound before the introduction of any cushions, 2.82 seconds; maxi-

Ban

a\ — irTi( — II

5 6 7

Fig. 11. 1. Committee-room. 2. Laboratory, Botanic Gardens. 3. Office,
Botanic Gardens. 4. Recorder's Office. 5. Greenhouse. 6. Dean's
Room. 7. Clerk's Room.

mum departure of experimentally determined curve from the nearest
hyperbola, .09 second; average departure, .03 second.

2. Laboratory, Botanic Gardens of Harvard University; hard
pine walls and ceiling, cement floor; volume, 82 cubic meters;
original duration of the residual sound, 2.39 seconds; maximum
departure from hyperbola, .09 second; average departure, .02
second.

3. Office, Botanic Gardens; hard pine walls, ceihng and floor;
volume, 99 cubic meters; original duration of residual sound, 1.91
seconds; maximum departure from hyperbola, .01 second; average
departure, .00 second.

4. Recorder's Office, University Hall; plaster on wood lath,
wood dado; volume, 102 cubic meters; original duration of residual
sound, 3.68 seconds; maximum departure from hyperbola, .10
second; average departure, .04 second.

APPROXIMATE SOLUTION

5. Greenhouse, Botanic Gardens; glass roof and sides, cement
floor; volume, 134 cubic meters; original duration of residual

Fig. 12. Faculty-room.

sound, 4.40 seconds; maximum departure from hyperbola, .08
second; average departure, .03 second.

6. Dean's Room, University Hall; plaster on wood lath, wood
dado; volume, 166 cubic meters; original duration of residual

Fig. 13. Lecture-room.

sound, 3.38 seconds; maximum departure from hyperbola, .06
second; average departure, .01 second.

7. Clerk's Room, University Hall; plaster on wood lath, wood
dado; volume, 221 cubic meters; original duration of residual

0Q □ □ Q
a o D a

Fig. 14, Laboratory.

sound, 4.10 seconds; maximum departure from hyperbola, .10
second; average departure, .02 second.

REVERBERATION

8. Faculty-room, University Hall; plaster on wood lath, wood
dado; volume, 1,480 cubic meters; original duration of residual
sound, 7.04 seconds; maximum departure from hyperbola, .18
second; average departure, .08 second.

9. Lecture-room, Room 1, Jefferson Physical Laboratory;
brick walls, plaster on wood lath ceiling; furnished; volume,
1,630 cubic meters; original duration of residual sound, 3.91

Fig. 15. Lecture-room.

seconds; maximum departure from hyperbola, .10 second; average
departiu-e, .04 second.

10. Large Laboratory, Room 41, Jefferson Physical Laboratory;
brick walls, plaster on wood lath ceiling; furnished; volume,
1,960 cubic meters; original duration of residual sound, 3.40 seconds;
maximum departure from hyperbola, .03 second; average depar-
ture, .01 second.

11. Lecture-room, Fogg Art Museum; plaster on tile walls,
plaster on wire-lath ceiling; volume, 2,740 cubic meters; original
duration of residual sound, 5.61 seconds; maximum departure from
hyperbola, .04 second; average departure, .02 second. The ex-
periments in this room were carried so far that the original duration
of residual sound of 5.61 seconds was reduced to .75 second.

12. Sanders Theatre; plaster on wood lath, but with a great
deal of hard-wood sheathing used in the interior finish; volume,
9,300 cubic meters; original duration of residual sound, 3.42

APPROXIMATE SOLUTION

seconds; maximum departure from hyperbola, .07 second; average
departure, .02 second.

It thus appears that the hyperbolic law of inverse proportion-
ality holds under extremely diverse conditions in regard to the size,
shape and material of the room. And as the cushions used in the
calibration were placed about quite at random, it also appears that
in rooms small or large, with high or low ceiling, with flat or curved

Fig. 16. Sanders Theatre.

walls or ceiling, even in rooms with galleries, the cushions, wherever
placed — out from under the gallery, under, or in the gallery ^ —
are nearly equally efficacious as absorbents. This merely means,
however, that the efficacy of an absorbent is independent of its
position when the problem under consideration is that of reverbera-
tion, and that the sound, dispersed by regular and irregular reflec-
tion and by diffraction, is of nearly the same intensity at all parts of
the room soon after the source has ceased; and it will be the object
of a subsequent paper to show that in respect to the initial distri-
bution of the sound, and also in respect to discrete echoes, the posi-
tion of the absorbent is a matter of prime importance.

REVERBERATION

Having shown that the hyperbolic law is a general one, interest
centers in the parameter, k, the constant for any one room, but vary-
ing from room to room, as the following table shows :

Boom

Volume

Absorbing rower of
Walls, etc., = a

Parameter h

4.76

13.6

4.65

11.1

8.08

15.4

102

5.91

21.8

134

5.87

25.8

166

7.50

25.4

221

10.6

43.5

1,480

34.5

243.0

1,630

69.0

270.0

1,960

101.0

345.0

2,740

75.0

425.0

9,300

465.0

1,590.0

1. Committee-room, University Hall. . .

2. Laboratory, Botanic Gardens

3. OflSce, Botanic Gardens

4. Recorder's OflBce

5. Greenhouse, Botanic Gardens

6. Dean's Room

7. Clerk's Room

8. Faculty-room

9. Lecture-room, Jefiferson Physical Lab-

oratory, 1

10. Laboratory, Jefferson Physical Lab-

oratory, 41

11. Fogg Lecture-room

12. Sanders Theatre

The values of the absorbing power, a, and the parameter, k, are

here expressed, not in terms of the cushions actually used ia the

experiments, but in terms of the open-window units, shown to be

preferable in the preceding article.

In the diagram. Figure 17, the values of k are plotted against the

corresponding volumes of the rooms; here again three different

scales are employed in order to magnify the results obtained in the

smaller rooms. The resulting straight line shows that the value of

k is proportional to the volume of the room, and it is to be observed

that the largest room was nearly one hundred and fifty times larger

than the smallest. By measurements of the coordinates of the line,

k
or by averaging the results found in calculating — for all the rooms

it appears that k = .17iy. The physical significance of this nu-
merical magnitude .171 will be explained later.

This simple relationship between the value of k and the volume
of the room — the rooms tested varying so greatly in size and
shape — affords additional proof, by a rather delicate test, of the
accuracy of the method of experimenting, for it shows that the ex-

APPROXIMATE SOLUTION

perimentally determined curves approximate not merely to hyper-
bolas but to a systematic family of hyperbolas. It also furnishes a
more pleasing prospect, for the laborious handling of cushions will
be unnecessary. A single experiment in a room and a knowledge of
the volume of the room will furnish suJBBcient data for the calcula-
tion of the absorbing power of its components. Conversely, a
knowledge of the volume of a room and of the coefficients of absorp-
tion of its various components, including the audience for which it
is designed, will enable one to calculate in advance of construction
the duration of audibility of the residual sound, which measures

ISO

i^n

9000

IMOo

12600

S 100

•>y

H 50

1200 U

00 841

DO 8000

3600

"4100

4
1

olun

les c

fro

Dms

Fig. 17. The parameter, h, plotted against the volumes of the
rooms, showing the two proportional.

that acoustical property of a room commonly called reverberation.
Therefore, this phase of the problem is solved to a first approxi-
mation.

The explanation of the fact that h is proportional to Y is found
in the following reasoning. Consider two rooms, constructed of
exactly the same materials, similar in relative proportions, but one
larger than the other. The rooms being empty, x, the absorbing
power of the contained material, is zero, and we have a' t' = ¥
and a" t" = h". Since the rooms are constructed of the same
materials the coefficients of absorption are the same, so that a' and
a" are proportional to the surfaces of the rooms, that is, to the squares

34 REVERBERATION

of the linear dimensions. Also, the residual sound is diminished a
certain percentage at each reflection, and the more frequent these
reflections are the shorter is the duration of its audibility; whence
t' and t" are inversely proportional to the frequency of the reflec-
tions, and hence directly proportional to the linear dimensions.
Therefore, ¥ and h", which are equal to a' t' and a" t", are propor-
tional to the cubes of the linear dimensions, and hence to the
volumes of the rooms.

Further, when the shape of the room varies, the volume remain-
ing the same, the number of reflections per second will vary. There-
fore, fc is a function not merely of the volume, but also of the shape
of the room. But that it is only a slightly varying function, com-
paratively, of the shape of the room for practical cases, is shown by
the fact that the points fall so near the straight line that averages

h
the values of the ratio — •

The value of k is also a function of the initial intensity of the
sound; but the consideration of this element will be taken up in a
following paper.

RATE OF DECAY OF RESIDUAL SOUND

In a subsequent discussion of the interference of sound it will be
shown by photographs that the residual sound at any one point
in the room as it dies away passes through maxima and minima,
in many cases beginning to rise in intensity immediately after the
source has ceased; and that these maxima and minima succeed
each other in a far from simple manner as the interference system
shifts. On this account it is quite impossible to use any of the nu-
merous direct methods of measuring sound in experiments on rever-
beration. Or, rather, if such methods were used the results would
be a mass of data extremely difficult to interpret. It was for this
reason that attempts in this direction were abandoned early in the
investigation, and the method already described adopted. In
addition to the fact that this method only is feasible, it has the
advantage of making the measurements directly in terms of those
units with which one is here concerned — the minimum audible

RATE OF DECAY OF RESIDUAL SOUND

intensity. It is now proposed to extend this method to the deter-
mination of the rate of decay of the average intensity of sound in
the room, and to the determination of the intensity of the initial
sound, and thence to the determination of the mean free path be-
tween reflections, — all in preparation for the more exact solution
of the problem.

The first careful experiment on the absolute rate of decay was
in the lecture-room of the Boston Public Library, a large room.

5 8

f-v

— 1

Mil

IMUM

UOIBL

E INTCNIITV

'"--

—

■--.

-4-.

'"^-

-K-

'■" —

-J—

■-

-h-

8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.C 9.7 9.8 9.9 10.

Time in seconds

Fig. 18. Decay of sound in the lecture-room of the Boston Public
Library from the initial sound of one, two, three, and four organ
pipes, showing only the last second.

finished, with the exception of the platform, in material of very
slight absorbing power — tile ceiling, plaster on tile walls, and
polished cement fioor.^ The reverberation was very great, 8.69
seconds. On the platform were placed four organ pipes, all of the
same pitch, each on its own tank or wind supply, and each having
its own electro-pneumatic valve. All these valves, however, were
connected to one chronograph, key, and battery, so that one, two,
three, or all the pipes, might be started and stopped at once, and
when less than four were in use any desired combination could be
made. One pipe was sounded and the duration of audibility of the
residual sound determined, of course, as always in these experi-
ments, by repeated observations. The experiment was then made

' Terrazzo cement floor.

36 REVERBERATION

with two organ pipes instead of one; then with three pipes; and,
finally, with four. The whole series was then repeated, but begin-
ning with a different pipe and combining different pipes for the two
and three pipe sets. In this way the series was repeated four times,
the combinations being so made that each pipe was given an equal
weight in the determination of the duration of audibility of the
residual sound under the four different conditions. It is safe to
assume that with experiments conducted in this manner the average
initial intensities of the sound with one, two, three, and four pipes
were to each other as one, two, three and four. The corresponding
durations of audibility shall be called U, U, ta and h. The following
results were obtained:

ti = 8.69 seconds h — h = -45 second

U = 9.14 " h-ti = .67 "

ta = 9.36 " U-ti = .86 "
U = 9.55 "

It is first to be observed that the difference for one and two organ
pipes, .45, is, within two-hundredths of a second, half that for one
and four organ pipes, .86. This suggests that the difference is
proportional to the logarithm of the initial intensity; and further
inspection shows that the intermediate result with three organ
pipes, .67, is even more nearly, in fact well within a hundredth of
a second, proportional to the logarithm of three. This reenforces
the very natural conception that however much the residual sound
at any one point in the room may fiuctuate, passing through max-
ima and minima, the average intensity of sound in the room dies
away logarithmically. Thus, if one plots the last part of the residual
sound — that which remains after eight seconds have elapsed —
on the assumption that the intensity of the sound at any instant is
proportional to the initial intensity, the result will be as shown in
the diagram. Fig. 18. The point at which the diminishing sound
crosses the line of minimum audibility in each of the four cases is
known, the corresponding ordinates of the other curves being
multiples or submultiples in proportion to the initial intensity.
The results are obviously logarithmic.

Let /i be the average intensity of the steady sound in the room
when the single organ pipe is sounding, i the intensity at any instant

BATE OF DECAY OF RESIDUAL SOUND 37

during the decay, say t seconds after the pipe has ceased, then

will be the rate of decay of the sound, and since the absorption

of sound is proportional to the intensity

di , .

= Ai, where A is the constant of proportionality,

the ratio of the rate of decay of the residual sound to the intensity

at the instant.

— log^ i-\- C = At,

a result that is in accord with the above experiments. The con-
stant of integration C may be determined by the fact that when t is
zero i is equal to 7i; whence

C = laQf. 7i, and the above equation becomes
loQe — = At.

At the instant of minimum audibility t is equal to ti, the whole
duration of the residual sound, and i is equal to i', — as the inten-
sity of the least audible sound will hereafter be denoted. Therefore

%e -T, = Atl.

This applied to the experiment with two, three and four pipes gives
similar equations of the form

where n is the number of organ pipes in use. By the elimination of
77 from these equations by pairing the first with each of the others,

A = ^ = 1.54,

ti — ti

A^^-£S^ = 1.61,
ti — ti

^(average) = 1.59,

where A is the ratio between the rate of decay and the average
intensity at any instant.

REVERBERATION

7 ^1

It is possible also to determine the initial intensity, 7i, in terms
of the minimum audible intensity, i' .

Ati,

h = i' logi'^ Ah = i' logi^ (1.59 X 8.69) = 1,000,000 i'.

With this value of the initial intensity it is possible to calculate
the intensity i of the residual sound at any instant during the decay,
by the formula log, I, - log, i = At,

and the result when plotted is shown in Figure 19, the unit of in-
tensity being minimum audibility.

A practical trial early in the year had shown that it would be
impossible to use this lecture-room as an auditorium, and the ex-

_^
m

900

000

800;,000

1 700,000

\600,00(

\ !
1500,000

\ 1 1
\ 400,000

\ 1
\ 300,000

200,000

-I
5

\ioo,oo«

2 3

10 It 12 U U 15

4 5 6 7 8 9

Time in seconds

Fig. 19. Decay of sound in the lecture-room of the Boston Public
Library beginning immediately after the cessation of one organ
pipe.

periments described above, with others, were in anticipation of
changes designed to remedy the difficulty. Hair felt, in consider-
able quantities, was placed on the rear wall. The experiments with
the four organ pipes were then repeated and the following results
were obtained :

ti = 3.65 <2 - <i = .20 .-. A = 3.41

U = 3.85 t3-ti = .31 .-. A = 3.54

<3 = 3.96 U- h = .42 .-. A = 3.29

U = 4.07
7i = 250,000 i'

A = 3.41 (average)

RATE OF DECAY OF RESIDUAL SOUND 39

A few nights later the apparatus was moved down to the attend-
ant's reception-room near the main entrance — a small room but
similar in proportions to the lecture-room. Here a careful experi-
ment extending over several nights was carried on, and it gave the
following results :

U = 4.01 <2 - <i = .19 .-. A = 3.65

h = 4.20 h-ti = .28 .-. A = 3.90

is = 4.29 U-ti = .37 .-. A = 3.75

U = 4.38 A = 3.76 (average)

h = 3,800,000 i'

The first interest lies in an attempt to connect the rate of decay,
obtained by means of the four organ pipe experiments, with the
absolute coeflScient of absorption of the walls, obtained by the
experiments with the open and closed windows; and to this end
recourse will be had to what shall here be called "the mean free
path between reflections." The residual sound in its process of
decay travels across the room from wall to wall, or ceiling, or floor,
in all conceivable directions; some paths are the whole length of
the room, some even longer, from one corner to the opposite, but
in the main the free path between reflections is less, becoming even
infinitesimally small at an angle or a corner. Between the two or
three hundred reflections that occur during its audibility the residual
sound establishes an average distance between reflections that de-
pends merely on the dimensions of the room, and may be called
"its mean free path."

.171 V

is the absorbing power of the room, measured in open- window units.
Let

s = surface.

V = volume.

A = rate of decay of the sound.

V = velocity of sound, 342 m. per second at 20 degrees C.
p = length of the mean free path between reflections.

Whence - = the average number of reflections per second, and
- is the fraction absorbed at each reflection, — = ^>

and V =
path, p.

REVERBERATION

av
'As

v.YJl V
As ti

whence may be calculated the mean free

Boston Public Library Lecture-room, bare . . .

with felt
" " " Attendant's Room

2,140.0

63.8

1.59
3.41
3.76

1,160

108

8.69
3.65
4.01

7.8
8.8

2.27

The length of the mean free path in the lecture-room, bare or
draped, ought to be the same, for the felt was placed out from
the wall at a distance imperceptibly small in comparison with the
dimensions of the room; but 7.8 and 8.8 differ more than the
experimental errors justify. Again, the attendant's room had very
nearly the same relative proportions as the lecture-room (about
2 : 3 : 6), but each linear dimension reduced in the ratio 3.22 : 1.
The mean free path, obviously, should be in the same ratio; but
when the mean free path in the attendant's room, 2.27, is multiplied
by 3.22 it gives 7.35, departing again from the other values, 7.8 and
8.8, more than experimental errors justify. The explanation of
this is to be found in the fact that the initial intensity of the sound
in the rooms for the determination of 1% was not the same but had
the values respectively, 1,000,000 i', 250,000 i' and 3,800,000 i'.
Since U has been shown proportional to the logarithms of the initial
intensities, these three numbers, 7.8, 8.8 and 7.35, may be corrected
in an obvious manner, and reduced to the comparable values they
would have had if the initial intensity had been the same in all
three cases. The results of this reduction are 7.8, 8.0 and 8.0, a
satisfactory agreement.

The length of the mean free path is, therefore, as was to be ex-
pected, proportional to the linear dimensions of the room, and such
a comparison is interesting. There is no more reason, however, for
comparing it with one dimension than another. Moreover, most
rooms in regard to which the inquiry might be made are too irregular
in shape to admit of any one actual distance being taken as standard.
Thus, in a semicircular room, still more in a horseshoe-shaped room
such as the common theatre, it is indeterminable what should be

RATE OF DECAY OF RESIDUAL SOUND 41

called the breadth or what the length. On account, therefore, of
the complicated nature of practical conditions one is forced to the
adoption of an ideal dimension, the cube root of the volume, F^'^^ the
length of one side of a cubical room of the same capacity. The above

data give as the ratio of -^ the value, .62.

yi/s

It now becomes possible to present the subject by exact analysis,
and free from approximations; but before doing so it will be well to
review from this new standpoint that which has aheady been done.

It was obvious from the beginning, even in deducing the hyper-
bolic law, that some account should be taken of the reduction in
the initial intensity of the sound as more and more absorbing
material was brought into the room, even when the source of sound
remained unchanged. Thus each succeeding value of the duration
of the residual sound was less as more and more absorbing material
was brought into the room, not merely because the rate of decay
was greater, but also because the initial intensity was less. Had the
initial intensity in some way been kept up to the same value through-
out the series, the resulting ciurve would have been an exact hyper-
bola. As it was, however, the curve sloped a little more rapidly on
account of the additional reduction in the duration arising from the
reduction in initial intensity of the sound. At the time, there was
no way to make allowance for this. That it was a very small error,
however, is shown by the fact that the departures from the true
hyperbola that were tabulated are so small.

Turning now to the parameter, h, it is evident that this also was
an approximation, though a close one. In the first place, as just
explained, the experimental curve of calibration sloped a little more
rapidly than the true hyperbola. It follows that the nearest hyper-
bola fitting the actual experimental results was always of a little
too small parameter. Further, k depended not merely on the uni-
formity of the initial intensity during the calibration of the room,
but also on the absolute value of this intensity. Thus, h = ah, and
ti is in turn proportional to the logarithm of the initial intensity.
Therefore in order to fully define k we must adopt some standard of
initial intensity. For this purpose we shall hereafter take as the

42 REVERBERATION

standard condition in initial intensity, / = 1,000,000 i', {I = 10® i'),
where i' is the minimum audible intensity, as this is the nearest
round number to the average intensity prevailing during these ex-
periments. If, therefore, during the preceding experiments the
initial intensity was above the standard, the value deduced for k
would be a little high, if below standard, a little low. This variation
of the parameter, k, would be slight ordinarily, for k is proportional
to the logarithm, not directly to the value of the initial intensity.
Slight ordinarily, but not always. Attention was first directed to
its practical importance early in the whole investigation by an ex-
periment in the dining-room of Memorial Hall — a very large room
of 17,000 cubic meters capacity. During some experiments in Sanders
Theatre the organ pipe was moved across to this dining-room, and
an experiment begim. The reverberation was of very short diu-ation,
although it wtfuld have been long had the initial intensity been
standard, for in rooms constructed of similar materials the rever-
beration is approximately proportional to the cube roots of the
volumes. There was no opportunity to carry the experiment farther
than to observe the fact that the duration was surprisingly short,
for the frightened appearance of the women from the sleeping-
rooms at the top of the hall put an end to the experiment. Finally,
^ is a function not merely of the volume but also of the shape of the
room; that is to say, of the mean free path, as has aheady been
explained.

It was early recognized that with a constant source the average
intensity of the sound in different rooms varies with variations in
size and construction, and that proper allowance should be made
therefor. The above results call renewed attention to this, and
point the way. In the following paper the more exact analysis will
be given and applied.

EXACT SOLUTION 43

EXACT SOLUTION

The present paper will carry forward the more exact analysis pro-
posed in the last paper.

For the sake of reference the nomenclature so far introduced is
here tabulated.

t = time after the source has ceased up to any instant whatever during

the decay of the sound.

t', t", t'" = duration of the residual sound, the accents indicating a changed

condition in the room such as the introduction or removal of
some absorbent, the presence of an audience, or the opening of
a window.

h, <2, . . . <n = whole duration of the residual sound, the subscripts indicating the
number of organ pipes used.

T = duration of the residual sound in a room when the initial intensity

has been standard.

i = intensity of the residual sound at any instant.

i' = intensity of minimum audibility.

Zi, /2, . . . Zn = intensity of sound in the room just as the organ pipe or pipes stop,
the subscripts indicating number of pipes.

I = standard initial intensity arbitrarily adopted, I = 1,000,000 i'.

w = absorbing power of the open windows, minus their absorbing

power when closed = area (1 — .024).

a = absorbing power of the room.

ai, 02, ... On = coefficients of absorption of the various components of the wall-
surface.

s = area of wall (and floor) surface in square meters.

*i, «2, • • ■ *n = area of the various components of the wall-surface.

V = volume of the room in cubic meters.
k = hyperbolic parameter of any room.

K = ratio of the parameter to the volume, aT = h = KV.

A = rate of decay of the sound.

p = length of mean free path between reflections.

V = velocity of sound, 342 m. per second at 20° C.

Let E denote the rate of emission of energy from the single
organ pipe.

^ = the average interval of time between reflections.

?.E = amount of energy emitted during this interval.

- E ( 1 — - ) = amount of energy left after the first reflection.

- J5 ( 1 — - ) = amount of energy left after the second reflection, etc.

V \ s/

44 REVERBERATION

If the organ pipe continues to sound, the energy in the room con-
tinues to accumulate, at first rapidly, afterwards more and more
slowly, and finally reaches a practically steady condition. Two
points are here interesting, — the time required for the sound to
reach a practically steady condition (for in the experiments the
organ pipes ought to be soimded at least this long), and second, the
intensity of the sound in the steady and final condition. At any
instant, the total energy in the room is that of the sound just issuing
from the pipe, not having suffered any reflection, plus the energy of
that which has suffered one reflection, that which has suffered two,
that which has suffered three, and so on back to that which first
issued from the pipe, as :

f4'+('-=)+('-F) + (>-.-)'+ ■■•(-;)"]■

where n is the number of reflections suffered by the sound that first
issued from the pipe, and is equal to the length of time the pipe was
blown divided by the average interval of time between reflections.
The above series, which is an ordinary geometric progression, may
be written*

Pe y-^- ; (1)

is by nature positive and less than unity. If n is very large or if
( 1 — - j is small this may be written

^ = the total energy in the room in the steady condition. (2)

is the average intensity of sound in the room as the organ pipe
stops. Substituting in this equation the values of a and p already
found,

, a = -y-' (4)

va vKV

EXACT SOLUTION 45

, J vKV T Es E ,^-

wehave ^' = ^ATKV- vV ^ AV' ^^^

Also
whence

h = log7 Ah, (7)

E^VA log7 Ah, (8)

where the unit of energy is the energy of minimum audibility in a
cubic meter of air.

It remains to determine K and a. To this end the four organ
pipe experiments must be made in a room with the windows closed
and with them open, and the values of A' and A" determined. The
following analysis then becomes available:

a = —, and a + w = —<

whence

a + w T
For standard conditions in regard to initial intensity

A' r = A" T" = log^ I = log^ (W) = 13.8,

Substituting these values.

whence

and

T" A' ^ ^, 13.8

values,

a A' „ aT' a 13.8

a + w~ A"' V ~ A'V

A'w
"- A"-A''

(9)

13.8w

(10)

Or if K has been determined (9) may be written

A'KV ,,,,

a useful form of the equation.

From equation (1) and (2) we may calculate the rate of growth
of sound in the room as it approaches the final steady condition.

46 REVERBERATION

Thus, dividing (1) by (2), the result, 1 — ( 1 - -j , gives the in-
tensity at any instant n- seconds after the sound has started, in

terms of the final steady intensity. Of all the rooms so far experi-
mented on, the growth of the sound was slowest in the lecture-room
of the Boston Public Library in its unfurnished condition. For this

room - = .037, and f = 8.0 meters. The following table shows the
s

growth of the sound in this room, and the corresponding number of

reflections which the sound that first issued from the pipe had

undergone.

Lectube-hoom, Boston Public Libraky

Time

Average
Intensity

Time

Average
Intensity

.02

.04

.69

.68

.11

.17

.92

.78

.23

.31

1.15

.85

.34

.43

100

2.30

.98

.46

.53

150

3.45

.997

1.00

It thus appears that in this particular room the organ pipe must
sound for about three seconds in order that the average intensity
of the sound may get within ninety-nine per cent of its final steady
value. As throughout this work we are concerned only with the
logarithm of the initial intensity, ninety-nine per cent of the steady
condition is abundantly near. This consideration — the necessary
length of time the organ pipe should sound — is carefully regarded
throughout these experiments. It varies from room to room, being
greater in large rooms, and less in rooms of great absorbing power.

To determine the value of E, the rate of emission of sound by
the pipe, formula (8), E = VA log^ ^^i, is available. It is here to
be observed that as this involves the antilogarithm of Ati these
quantities must be determined with the greatest possible accuracy.
The first essential to this end is the choice of an appropriate room.
Without giving the argument in detail here, it leads to this, that
the best rooms in which to experiment are those that are large in
volume and have little absorbing power. In fact, for this purpose,
small rooms are almost useless, but the accuracy of the result in-

EXACT SOLUTION 47

creases rapidly with an increase in size or a decrease in absorbing
power. On this account the lecture-room of the Boston Public
Library in its unfurnished condition was by far the best for this
determination of all the available rooms. Inserting the numerical
magnitudes obtained in this room in the equation,

E = VAlogl^Ati = 2,140 X 1.59 log^^ (1.59 X 8.69) = 3,400,000,000.

If the observations in the same room after the introduction of the
felt, already referred to, are used in the equation the resulting value
of E is 3,200,000,000. The agreement between the two is merely
fortunate, for the second conditions were very inferior to the first,
and but little reliance should be placed on it. In fact, in both re-
sults the second figures, 4 and 2, are doubtful, and the round num-
ber, 3,000,000,000, will be used. It is sufficiently accurate.

The next equation of interest is that giving the value of K,
number (10). It contains the expression. A" — A', the difference be-
tween the rates of decay with the windows open and with them closed;
^"and ^'depend linearly on the difference in duration of the residual
sound with four organ pipes and with one, and as both sets of dif-
ferences are at best small, it is evident that these experiments also
must be conducted with the utmost care and under the best con-
ditions. The best conditions would be in rooms that are large, that
have small absorbing power, and that afford window area sufficient
to about double the absorbing power of the room. Practically this
would be in large rooms that are of tile, brick, or cement walls,
ceiling and floor, and have an available window area equal to about
one-thirtieth of the total area.

The lobby of the Fogg Art Museum, although rather small, best
satisfied the desired conditions. Sixteen organ pipes were used,
arranged four on each air tank and, therefore, near together. Thus
arranged, the sixteen pipes had 7.6 times the intensity of one, as
determined by a subsequent experiment in the Physical Laboratory.
The following results were obtained:

^ log, 7.6 ^ log, 7.6 ^
t'le - t\ 5.<ii,Q - 4.59

_ log, 7.6
and ^ - 3.43-3.00 ^■''

48 REVERBERATION

^ 13.8w ^ 13.8 X 1.85 ^
F(^"-'^') 96X1.7 ■ ■

Here, however, it is easy to show by trial that errors of only one-
hundredth of a second in the four determinations of the duration
of the residual sound would, if additive, give a total error of twenty
per cent in the result.

It is impossible, especially with open windows, to time with an
accuracy of more than one-hundTedth of a second, and, therefore,
this formula,

13.8w

Z =

ViA" - A')

while analytically exact and attractive in its simplicity, is practi-
cally unserviceable on account of the sensitive manner in which the
observations enter into the calculations.

The following analysis, however, results in an equation much
more forbidding in appearance, it is true, but vastly better practi-
cally, for it involves the data of difficult determination only logarith-
mically, and then only as part of a comparatively small correcting
term. For the room with the windows closed:
A' t\ = log, I\;

and for standard conditions in regard to initial intensity
A' T' = log, I,

whence

r =t\-^,hgj-j;

T'a = KV,
hence

KV =t\a-j,log,^;

and similar steps for the same room with the windows open give
KV = fi (a + w) - ^„ log, — -

Multiplying the first of the last two equations by t"i, and the
second by t'l,

„ 1 I ,>,>f,(afij I'x (g -f- w)t\ , I\W

By equation (5)
and similarly

EXACT SOLUTION 49

a _ sp

A'~ v'

a -\- w _ sj)

A" ~ 7"

Substituting these values in the above equation,

(12)

As an illustration of the application of the last equation, the

case of the lobby of the Fogg Art Museum is here worked out at

length.

t\ = 4.59

<"i = 3.00

F = 96 cu. m.

s = 125 sq. m.

w = 1.86

.171 V
a = — - — = 3.58 as a first approximation
1 1

p = 2.8

Z'l = £^ = 8.8 XlO«i'

vaV

I"i= , ^\„ = 5.8 XlO^i'
v\a-Yw) V

Substituting these values in the above equation,

K = -^ [25.7 + 1.02 (6.53 - 8.1)] = .169 - .010 = .159,

where the term .169 is the value of K that would be deduced dis-
regarding the initial intensity of the sound, — .010 is the correction
for this, and .159 is the corrected value of K. The magnitude as
well as the sign of this correction depends on the intensity of the
source of sound, the size of the room and the material of which it
is constructed, and the area of the windows opened. This is illus-
trated in the following table, which is derived from a recalculation
of all the rooms in which the open-window experiment has been
tried, and which exhibits a fairly large range in these respects:

REVERBERATION

Boom

I'l

Uncor-
rected

Correc-
tion

Lobby Foes Museum

202

1,630

1,960

8,800,000
67,000,000

1,700,000
390,000
300,000

1.86
1.86
5.10
12.0
14.6

.169
.191
.164
.150
.137

-.010
-.027
+.005
+ .017
+.024

.159

Lobby Fogg Museum, 16 pipes . . .
Jefferson Physical Laboratory 15 .
Jefferson Physical Laboratory 1 . .
Jefferson Physical Laboratory 41 .

.164
.169
.167
.161

Average value of K = .164

The value, K = .164, having been adopted, interest next turns
to the determination of the absorbing power, a, of a room. For this
purpose we have choice of three equations, two of which have
aheady been deduced, (9) and (11),

a =

and

a =

A'KV

13.8

and a third equation may be obtained as follows :
It has been shoAvn that

va I

and

T'a = KV.

Therefore

at\-?^logJ-^ = KV,
V 1

and

°4(^''+?'-t)

(13)

Of these three equations the first, (9), for reasons already pointed
out in regard to a similar equation for K, while rigorously correct,
yields a result of great uncertainty on account of its sensitiveness
to slight errors in the several determinations of the duration of the
residual sound. The second, (11), is very much better than the
first, but still not satisfactory in this respect. The third, (13), is
wholly satisfactory. It has the same percentage accuracy as t'l.

EXACT SOLUTION 51

and the only elements of difficult determination enter logarithmi-
cally in a small correcting term.

As an illustration of the application of these equations we may
again cite the case of the lobby of the Fogg Art Museum:

by equation (9), a = -^ -^ = 3.3;

, .. ,„, 3.0 X .164 X 96 „ .

by equation (11), a = —— = 3.4;

13.8

by equation (13), a = — - (.164 X 96 + 1.02 X log^ 8.8) = 3.8.
4.59

The first two are approximate only, the last, 3.8, is correct, with

certainty in regard to the last figure.

There is but one other subject demanding consideration in this
way, — the calculation of the absorbing power of objects brought
into the room, as cushions, drapery, chairs, and other furniture.
This may be approached in two ways, either by means of the rate
of decay of the sound and the four organ pipe experiment, or by
open-window calibration and a single organ pipe.

Let A'" be the rate of decay when the object is in the room. A'
being the rate when the room is empty. Then if a' is the absorbing
power of the object :

A'KV

and

Whence

a -\- a' =

13.8

A'" KV

13.8

a' ^ ^A'" - A') -. (,4)

Or from the other point of view, equation (13),

a + a'^^^{KV + ^-flo,J-^y

JJ^, v\J,^'^l - r^^P (15)

whence

KV (t\ -

a =

52 REVERBERATION

where I\ and I"'i are to be calculated as heretofore by a preliminary
and approximate estimate of a and a .

Here also it is easy to show a priori that the first equation, (14),
while perfectly correct and analytically rigorous, is excessively
sensitive to very slight errors of observation, and that on this ac-
count equation (15) is decidedly preferable. For example, felt
being brought iuto the lobby of the Fogg Lecture-room and placed
on the floor, the values of A'" and t"\ were determined to be, re-
spectively, 4.9 and 2.79. Borrowing from the preceding experiment,
and substituting in equations (14) and (15) we have

^ .164 X 96 (4.59 - 8.79) _ /_J_ _ J_ \ ^

4.59 X 2.79 \4.59 "' 2.79 "^ /

a very satisfactory agreement in view of the extreme sensitiveness
of equation (14).

Thus three equations have been deduced, number (12) for the
calculation of the parameter, k, (13) for the absorbing power, a, of
the wall-surface, and (15) for the absorbing power, a', of introduced
material. Each has been verified by other equations analytically
rigorous, and developed along very different lines of attack. In
each case the agreement was satisfactory, especially in view of the
extreme sensitiveness of the equations used as checks.

In the succeeding paper will be deduced, by the method thus
established, the coefficients of absorption of the materials that are
used ordinarily in the construction and furnishing of an auditorium.

THE ABSORBING POWER OF AN AUDIENCE,
AND OTHER DATA

In this paper will be given all the data ordiaarily necessary in
calculating the reverberation in any auditorium from its plans and
specifications. In order to show the degree of confidence to which
these data are entitled a very brief account will be given of the
e^eriments by means of which they were obtained. Such an ac-
count is especially necessary in the case of the determination of the
absorbing power of an audience. This coefficient is, in the nature

ABSORBING POWER OF AN AUDIENCE 53

of things, a factor of every problem, and in a majority of cases it is
one of the most important factors; yet it can be determined only
through the courtesy of a large number of persons, and even then
is attended with diflBculty.

The formulas that will be used for the calculation of absorbing
power are numbers (13) and (15) in the preceding paper, the correct-
ing terms being at times of considerable importance. The applica-
tion of these formulas having been illustrated, the whole discussion
here will be devoted to the conditions of the experiments and the
results obtained.

In every experiment the unavoidable presence of the observer
increases the absorbing power. In small rooms, and in large rooms
if bare of furniture, the relative increase is considerable, and should
always be subtracted from the immediate results of the experiment
in order to determine the absorbing power of the room alone. The
quantity to be subtracted is constant, provided the same clothes
are always worn, and may be determined once for all. For this
determination another observer made a set of experiments in a small
and otherwise empty room before and after the writer had entered
with a duplicate set of apparatus, — air tank, chronograph, and
battery. In fact, two persons made independent observations,
giviQg consistently the result that the writer, in the clothes and
with the apparatus constantly employed, had an absorbing power
of .48 of a unit. For the sake of brevity no further mention will be
made of this, but throughout the work this correction is applied
wherever necessary.

In the second paper of this series a preliminary calculation was
made of the absorbing power of certain wall-surfaces, and the object
in so doing was to get an approximate value for the absorbing power
of glass. It had been decided that the most convenient unit of
absorbing power was a square meter of open window. It is evident,
however, that the process of opening a window during the progress
of an experiment is merely substituting the absorbing power of the
open window for that of the same window closed, — a consideration
of possible moment in the nicer development of the subject. This
preliminary calculation was in anticipation of and preparation for
the more close analysis in the fifth paper. If these coeflficients are

54 REVERBERATION

now calculated, using the corrected formulas of the fifth paper, we
arrive at the following results: Cement, and brick set in cement,
.025, glass, .027 and wood sheathing, .061.

The experiments in the Boston Public Library gave results that
are interesting from several points of view. The total absorbing
power of the large lecture-room was found to be 38.9 units dis-
tributed as follows: A platform of pine sheathing, exposing a total
area of 70 square meters, had an absorbing power of 70 X .061=4.3;
72 square meters of glass windows had an absorbing power of
72 X .027 = 1.9; three large oil paintings, with a total area of 17.4
square meters, had an absorbing power of 17.4 X .28 = 4.9; the
remainder, 27.8 units, was that of the cement floor, tile ceiling, and
plaster on tile walls, in total area 1,095 square meters. This gives
as the coeflBcient of absorption for such construction .0254. A
similar calculation of results obtained in the attendant's room in
the same building — a room in which the construction of the floor,
walls, and ceiling is similar to that in the lecture-room — gives for
the value of the coefficient, .0255. The very close agreement of
these results, and their agreement with the coefficient, .0251, for
cement floor and solid walls of brick set in cement in the constant-
temperature room, is satisfactory. However, a far more interest-
ing consideration is the following:

Heretofore in the argument it has been assumed, tacitly, that
the total absorption of sound in a room is due to the walls, furniture
and audience. There is one other possible absorbent, and only one
— the viscosity of the vibrating air. It is now possible to present
the argument that led to the conclusion that this, the viscosity of
the air throughout the body of the room, is entirely negligible in
comparison with the other sources of absorption. These two rooms
in the Boston Public Library — the lecture-room and the attend-
ant's room — had, in their bare and unfurnished condition, less
absorbing power in the walls than any other rooms of their size yet
found. Therefore, if the viscosity of the air is a practical factor it
ought to have shown in these two rooms if ever. Fortunately, also,
the two rooms differed greatly in size, the volume of one being about
thirty-five times that of the other, while the ratio of the areas of
the wall-surfaces was about twelve. That part of the absorption

ABSORBING POWER OF AN AUDIENCE 55

due to the walls was proportional to the areas of the walls, and the
part due to the viscosity of the air was proportional to the volumes
of the rooms. As a matter of fact the experiments in these two
rooms showed that the whole absorbing power was accurately pro-
portional to the areas of the walls; how accurately is abundantly
evidenced by the agreement of the two coefficients, .0254 and .0255,
deduced on the supposition that the viscosity of the air was negli-
gible. To express it more precisely, had the viscosity of the air
been sufficient to produce one-fiftieth part of the absorption in the
attendant's room, these two coefficients would have differed from
each other by fom* per cent, an easily measurable amount. It is safe
to conclude that in rooms as bare and nonabsorbent as these the
viscosity of the air is inconsiderable, and that in a room filled with
an audience it is certainly wholly negligible. Rooms more suitable
for the demonstration of this point than these two rooms in the
Boston Public Library could hardly be designed, and access to theni
was good fortune in settling so directly and conclusively this funda-
mental question.

The experiments to determine the absorbing power of plastered
walls show it to be variable. If the plaster is applied directly to
tile or brick the absorbing power of the resulting solid wall is uni-
formly .025. But if the plaster is applied to lath held out from the
solid wall by studding, the absorbing power is not nearly so constant,
varying in different rooms. The investigation of this has not been
carried far enough to show with absolute certainty the cause, al-
though it probably arises from the different thickness in which the
plaster is applied. For the examination of this point two modes of
procedure are possible, — experimenting in a large number of
rooms, or experimenting in one room and replastering in many
different ways. The objection to the first method, which appears
the more available, is that it is almost impossible to get accurate
information in regard to the nature of a wall unless one has complete
control of the construction. However, there are probably interest-
ing variations that cannot be found in use, but that, if tried, would
be fruitful in suggestions for future construction. The second
method — experimenting in one room, plastering and replastering
it with systematic variations and careful analysis of the construction

56 REVERBERATION

in each case — would be the most instructive, but the expense of
such procedure is, for the time being at least, prohibitive. Among
the interesting possibilities, of which it can only be said that the
experiments so far point that way, is that with time the plastered
walls improve in absorbing power; how rapidly has not been shown.
This change can be due, of course, only to some real change in the
nature of the wall, and the most probable change would be its grad-
ual drying out. Experiments in four rooms with plaster on wood
lath gave as the average absorbing power per square meter .034 of
a unit. Experiments in eight rooms with plaster on wire lath gave
as the average coeflBcient of absorption .033. In both cases the
variation among the different rooms was such that the figure in the
third decimal place may be greater or less by three, possibly, though
not probably, by more. The fact that a considerable part of the
wall-surface of several of the rooms was of uncertain construction
is partly responsible for this uncertainty in regard to the coefficient.
For the sake of easy reference and comparison these results are
tabulated, the unit being the absorbing power of a square meter of
open-window area.

Absorbing Poweb of Wall-Sukfaces

Open window 1.000

Wood-sheathing (hard pine) 061

Plaster on wood lath 034

Plaster on wire lath 033

Glass, single thickness 027

Plaster on tile 025

Brick set in Portland cement 025

Next in interest to the absorbing power of wall-surfaces is that
of an audience. During the summer of 1897, at the close of a lecture
in the Fogg Art Museum, the duration of the residual sound was
determined before and immediately after the audience left. The
patience of the audience and the silence preserved left nothing to
be desired in- this direction, but a slight rain falling on the roof
seriously interfered with the observations. Nevertheless, the result,
.37 per person, is worthy of record. The experiment was tried again
in the summer of 1899, on a much more elaborate scale and under
the most favorable conditions, in the large lecture-room of the
Jefferson Physical Laboratory. In order to get as much data and

ABSORBING POWER OF AN AUDIENCE

from as independent sources as possible, three chronographs were
electrically connected with each other and with the electro-pneu-
matic valve controlling the air supply of the organ pipe. One
chronograph was on the lecture-table, and the others were on op-
posite sides in the rear of the hall. The one on the table was in
charge of the writer, who also controlled the key turning on and off
the current at the four instruments. The two other chronographs
were in charge of other observers, provision being thus made for
three independent determinations. After a test had been made of
the absorbing power of the whole audience — 157 women and 135
men, sufficient to crowd the lecture-room — one-half, by request,
passed out, 63 women and 79 men remaining, and observations
were again made. On the following night the lecture was repeated
and observations were again taken, there being present 95 women
and 73 men. There were thus six independent determinations on
three different audiences, and by three observers. In the following
table the first column of figures gives the total absorbing power of
the audience present; the second gives the absorbing power per
person; the initials indicate the observer.

Observer

Total Absorbing

Absorbing Power

Power

per Person

First night, whole audience

w. c. s.

123.0

.42

U U K U

G. LeC.

113.0

.39

" half "

W. C. S.

58.3

.41

U U U (I

G. LeC.

58.3

.41

Second " whole "

W. C. S.

66.2

.40

a u u 11

E. D. D.

64.6

.39

.40 (3)

In view of the difficulties of the experiment the consistency of the
determination is gratifying. The average result of the six determi-
nations is probably correct within two per cent.

It is to be noted, however, that this value, .40, is the difference
between the absorbing power of the person and the absorbing power
of the settee and floor which, when the audience left the room, took
its place as an absorbent. It is evident that the experiments de-
termined the difference between the two, while in subsequent cal-

58 REVERBERATION

culations we shall be concerned with the absolute absorbing power
of the audience. To determine this, on a following night all the
settees were carried out of the room, observations being taken be-
fore and after the change. From the data thus obtained the absorb-
ing power of each settee accommodating five persons was found to
be .039, or for a single seat .0077. Of necessity the floor still re-
mained, but from a knowledge of its construction the absorbing
power of as much of the floor as is covered by one person was cal-
culated to be .030. Adding these together we get as the absorbing
power of an audience, seated with moderate compactness, .44 per
person.

In some subsequent work it will be necessary to know the ab-
sorbing power of an audience, not per person, but per square meter,
the audience being regarded broadly as one of the bounding sur-
faces of the room. As each person occupied on an average .46 of a
square meter of floor area, it is evident that the absorbing power
per square meter was .96 of a unit.

Under certain circumstances the audience will not be compactly
seated, but will be scattered about the room and more or less isolated,
for example, in a council-room, or in a private music-room, and it is
evident that under these conditions the individual will expose a
greater surface to the room and his absorbing power wiU be greater.
It is a matter of the greatest ease to distinguish between men and
women coming into a small room, or even between different men.
In fact, early in the investigation, two months' work — over three
thousand observations — had to be discarded because of failure to
record the kind of clothing worn by the observer. The coefficients
given in the following table are averages for three women and for
seven men, and were deduced from experiments in the constant-
temperature room.

Absobbing Power of an Audience

Audience per square meter 96

Audience per person 44

Isolated woman 54

Isolated man 48

When an audience fills the hall one is but little concerned with
the nature of the chairs — acoustically, but otherwise this becomes

ABSORBING POWER OF AN AUDIENCE 59

a matter of considerable importance. The settees in the lecture-
room of the Physical Laboratory, already mentioned, are of plain
ash, and have solid seats, and vertical ribs in the back; they are
without upholstering; and it is interesting, in order to note the
agreement, to compare the absorbing power of such settees per single
seat, .0077, with that of the "bent wood" chairs in the Boston
Public Library, .0082, which are of similar character. In contrast
may be placed the chairs and settees in the faculty-room, which
have cushions of hair covered with leather on seat and back. In
the same table will be entered the absorbing power of Sanders
Theatre cushions, which are of hair covered with canvas and light
damask, and of elastic-felt cushions — cotton covered with corduroy.

Absorbing Power of Settees, Chairs, and Cushions

Plain ash settees 039

" per single seat 0077

" " chairs "bent wood" 0082

Upholstered settees, hair and leather 1.10

" " per single seat 28

" chairs similar in style 30

Hair cushions per seat 21

Elastic-felt cushions per seat 20

A case has arisen even in the present paper where it is necessary
to know the absorbing power of paintings on canvas, and the ques-
tion may not infrequently arise as to how much service is secured
— or injury incurred — acoustically by their use in particular
rooms. The oil paintings in the faculty-room, 19 in number, with
a total area, 19.9 square meters, gave opportunity for the determi-
nation of the desired coefficient; but a question arises in regard to
the method of reckoning the area. Thus, different coeflficients are
obtained according as one measures the canvas only, or includes
the frames. The latter method, on the whole, seems best, although
most of the absorption is probably by the canvas.

The coefficient for house plants, which may be of passing, and
possibly practical, interest, was even harder to express. A green-
house, 140 cubic meters in volume, and in which plants occupied
about one-quarter of the space, showed an absorbing power greater
than that due to the walls and floor by 4 units, or .11 per cubic
meter of plants. It would be of greater value to determine the

60 REVERBERATION

absorbing power of such plants as are used, often very extensively,
in decorating on festival occasions, but no opportunity has yet
presented itself.

Among the cloths used in decorations, cheesecloth and cretonne
may be taken as types. The first is an American gauze, 48 grams
to the square meter. The second is an ordinary cotton-print cloth,
182 grams per square meter. Shelia, an extra quality of chenille,
is a regular curtain material used only in permanent decorations.

Linoleum and cork are commercial products, the first used as
floor covering and the second in walls. Both were tested lying
loosely on the floor; cemented in place, their values would probably
be different.

The carpet rug is a heavy pile carpet about .8 centimeter thick.

In the following table the values are per square meter, except in
the case of plants, where the coefficient is per cubic meter:

Miscellaneous

Oil paintings, inclusive of frames 28

House plants H

Carpet rugs 20

Oriental rugs, extra heavy 29

Cheesecloth 019

Cretonne cloth 15

Shelia curtains 23

Hairfelt, 2.5 cm. thick, 8 cm. from wall 78

Cork, 2.5 cm. thick, loose on floor 16

Linoleum, loose on floor 12

CALCULATION IN ADVANCE OF CONSTRUCTION

In the present paper it is the purpose to show the application of
the preceding analysis and data, taking as an example the design
of the new Boston Music Hall^ now under construction, Messrs.
McKim, Mead & White, architects.

In the introductory paper the general problem of architectural
acoustics was shown to be a fairly complicated one, and to involve
in its solution considerations of loudness, of interference, of reso-
nance, and of reverberation. All these points received considera-
tion while the Hall was being designed, but it is proposed to discuss

' Boston Symphony Hall.

CALCULATION IN CONSTRUCTION 61

here only the case of reverberation. In this respect a music hall is
peculiarly interesting. In a theatre for dramatic performances,
where the music is of entirely subordinate importance, it is desirable
to reduce the reverberation to the lowest possible value in all ways
not inimical to loudness; but in a music hall, concert room, or
opera house, this is decidedly not the case. To reduce the rever-
beration in a hall to a minimum, or to make the conditions such that
it is very great, may, in certain cases, present practical difficulties
to the architect — theoretically it presents none. To adjust, in
original design, the reverberation of a hall to a particular and ap-
proved value requires a study of conditions, of materials, and of
arrangement, for which it has been the object of the preceding
papers to prepare.

It is not at all difficult to show a 'priori that in a hall for orches-
tral music the reverberation should neither be very great, nor, on
the other hand, extremely small. However, in this matter it was
not necessary to rely on theoretical considerations. Mr. Gericke,
the conductor of the Boston Symphony Orchestra, made the state-
ment that an orchestra, meaning by this a symphony orchestra, is
never heard to the best advantage in a theatre, that the sound
seems oppressed, and that a certain amount of reverberation is
necessary. An examination of all the available plans of the halls
cited as more or less satisfactory models, in the preliminary dis-
cussion of the plans for the new hall, showed that they were such
as to give greater reverberation than the ordinary theatre style of
construction. While several plans were thus cursorily examined
the real discussion was based on only two buildings — the present
Boston Music Hall and the Leipzig Gewandhaus; one was familiar
to all and immediately accessible, the other familiar to a number of
those in consultation, and its plans in great detail were to be
found in Das neue Gewandhaus in Leipzig, von Paul Gropius und H.
Schmieden. It should, perhaps, be immediately added that neither
hall served as a model architecturally, but that both were used
rather as definitions and starting points on the acoustical side of
the discussion. The old Music Hall was not a desirable model in
every respect, even acoustically, and the Leipzig Gewandhaus,
having a seating capacity about that of Sanders Theatre, 1500,

62 REVERBERATION

was so small as to be debarred from serving directly, for this if for
no other reason.

The history of the new hall is about as follows: A number of
years ago, when the subject was first agitated, Mr. McKim prepared
plans and a model along classical lines of a most attractive audi-
torium, and afterwards, at Mr. Higginson's instance, visited
Europe for the purpose of consulting with musical and scientific
authorities in France and Germany. But the Greek Theatre as a
music hall was an untried experiment, and because untried was re-
garded as of uncertain merits for the purpose by the conductors
consulted by Mr. Higginson and Mr. McKim. It was, therefore,
abandoned. Ten years later, when the project was again revived,
the conventional rectangular form was adopted, and the intention
of the building committee was to follow the general proportions and
arrangement of the Leipzig Gewandhaus, so enlarged as to increase
its seating capacity about seventy per cent; thus making it a little
more than equal to the old hall. At this stage calculation was first
applied.

The often-repeated statement that a copy of an auditorium
does not necessarily possess the same acoustical qualities is not
justified, and invests the subject with an unwarranted mysticism.
The fact is that exact copies have rarely been made, and can hardly
be expected. The constant changes and improvements in the ma-
terials used for interior construction in the line of better fireproofing
— wire lath or the application of the plaster directly to tUe walls —
have led to the taking of liberties in what were perhaps regarded as
nonessentials; this has resulted, as shown by the tables, in a
changed absorbing power of the walls. Our increasing demands
in regard to heat and ventilation, the restriction on the dimensions
enforced by location, the changes in size imposed by the demands
for seating capacity, have prevented, in different degrees, copies
from being copies, and models from successfully serving as models.
So different have been the results under what was thought to be
safe guidance ^ — but a guidance imperfectly followed^ that the
belief has become current that the whole subject is beyond control.
Had the new Music Hall been enlarged from the Leipzig Gewandhaus
to increase the seating capacity seventy per cent, which, proportions
being preserved, would have doubled the volume, and then built, as

CALCULATION IN CONSTRUCTION 63

it is being built, according to the most modern methods of fireproof
construction, the result, unfoKunately, would have been to con-
firm the belief. No mistake is more easy to make than that of
copying an auditorium — but in different materials or on a differ-
ent scale — in the expectation that the result will be the same.
Every departure must be compensated by some other — a change
in material by a change in the size or distribution of the audience,
or perhaps by a partly compensating change in the material used
in some other part of the hall — a change in size by a change in
the proportions or shape. For moderate departures from the
model such compensation can be made, and the model will serve
well as a guide to a first approximation. When the departure is
great the approved auditorium, unless discriminatingly used, is
liable to be a treacherous guide. In this case the departure was
necessarily great.

The comparison of halls should be based on the duration of the
residual sound after the cessation of a source that has produced
over the hall some standard average intensity of sound, — say one
million times the minimum audible intensity, 1,000,000 i'. The
means for this calculation was furnished in the fifth paper. The
values of V and a for the three halls under comparison are shown
on the next page.

The length given for the Leipzig Gewandhaus, 38 meters, is
measured from the organ front to the architecturally principal wall
in the rear. On the floor and by boxes in the balconies the seats
extend 3 meters farther back, making the whole length of the hall,
exclusive of the organ niche, 41 meters. This increases the volume
of the hall about 200 cubic meters, making the total volume 11,400
cubic meters.

The height given for the new Boston Music Hall, 17.9, is the
average height from the sloping floor. The length is measured on
the floor of the main part of the hall; above the second gallery it
extends back 2.74 meters, giving an additional volume of 580 cubic
meters. The stage, instead of being out in the room, is in a con-
tracted recess having a depth of 7.9 meters, a breadth, front and
back, of 18.3 and 13.6, respectively, and a height, front and back,
of 13.4 and 10.6, respectively, with a volume of 1,500 cubic meters.
The height of the stage recess is determined by the absolute re-

REVERBERATION

Dimensions of the Three Halls in Meters '

Leipzig Gewandhaus

Boston Music Hall,
Old

Boston Music Hallt
New

Length .
Breadth
Height .

Volume .

(38)
19
15.5

(11,200)

39.2
23.5
20.0

18,400

(39.5)
22.8
17.9

(16,200)

quirements of the large organ to be built by Mr. George S. Hutch-
ings. This organ will extend across the whole breadth of the stage.
The total volume of the new Boston Music Hall is, therefore,
18,300 cubic meters.

In the following table of materials in the three halls no distinction
is made between plaster on wire lath and plaster on wood lath, the
experiments recorded in the preceding paper having shown no cer-
tain difference in absorbing power. The areas of wall-surface are
expressed in square meters. The number of persons in the audience
is reckoned from the number of seats, no account being taken of
standing room.

'■ Dimensions of the Three Halls in Feet

Leipzig
Gewandliaus

Boston
Music Hall, Old

Boston
Music Hall, New

Length.
Breadth
Height.

Volume.

(124)
62
52

(400,000)

129

77
66

656,000

(130)
75
59

(575,000)

The length given for the Leipzig Gewandhaus, 124 feet, is measured from the organ front
to the architecturally principal wall in the rear. On the floor and by boxes in the balconies
the seats extend 10 feet farther back, making the total length of the' hall, exclusive of the
organ niche, 134 feet. This increases the volume 7,000 cubic feet, making the total volume
407,000 cubic feet.

The height given for the new hall, 59 feet, is the average height from the sloping floor.
The length is measured on the floor of the main part of the hall; above the second gallery it
extends back 9 feet, giving an additional volume of 20,000 cubic feet. The stage, instead of
being out in the room, is in a contracted recess, having a depth of 26 feet, a breadth, front and
back, of 60 feet and 45 feet, respectively, and a height, front and back, of 44 feet and 35 feet,
respectively, with a volume of 54,000 cubic feet. The total volume of the new Music Hall is,
therefore, 649,000 cubic feet.

CALCULATION IN CONSTRUCTION

Absorbing Material

Leipzig
Gewandhaus

Boston Music Hall,
Old

Boston Music Hall,
New

Plaster on lath . .

Plaster on tile . .

Glass

Wood. .

Drapery

Audience:

on floor

in 1st balcony
in 2d balcony .

Total audience . .

Orchestra

2,206

235

990

494

1,517

3,030

771

1,251
680
460

2,391

1,040
1,830

625

1,466
606
507

2,579

The drapery in the Leipzig Gewandhaus will be rated as shelia,
and in the old Music Hall as cretonne, to which it approximates in
each case. It is an almost needless refinement to rate differently
the orchestra and the audience merely because the members of the
orchestra sit more or less clear of each other, but for the sake of a
certain formal completeness it will be done. For the above materials
the coeflScients, taken from the preceditig paper, are as follows :

Coefficients of Absorption

Plaster on lath 033

Plaster on tile 025

Glass .027

Wood 061

„ f shelia 23

^ ^ \ cretonne 15

Audience per person 44

Orchestra per man 48

In the table (p. 67) is entered the total absorbing power con-
tributed by each of these elements. As this is the first example of
such calculation all the elements will be shown, although it will
then be immediately evident that some are of wholly negligible
magnitude.

Fig. 20. The Leipzig Gewandhaus.

■3 9.2 m.-

Fig. 21. The Old Boston Music HaU.

■S9.B /».-

Fig. 22. The New Boston Music HaU.

CALCULATION IN CONSTRUCTION

Absorbing Power

Leipzig
Gewandhaus

Boston Music Hall,
Old

Boston Music Hall,
New

Plaster on lath

0.4

667

100

1.5
47
0.6
1,052
38

Plaster on tile

Glass

0.6

Wood

Draperv

Audience

1,135

Orchestra

Total =a

810

1,239

1,292

V and a being determined for each of the three halls, the dura-
tion, T, of the residual sound after standard initial intensity can be
calculated.

The results, in seconds, are as follows :

Leipzig Gewandhaus 2.30

Old Boston Music Hall 2.44

New Boston Music Hall 2.31

In other words, the new hall, although having a seating capacity
for over a thousand more than the Gewandhaus and nearly two
hundred more than the old hall, will have a reverberation between
the two, and nearer that of the Gewandhaus than that of the old
hall.

It is interesting to contrast this with the result that would have
been obtained had the plan been followed of reproducing on an en-
larged scale the Gewandhaus. Assuming perfect reproduction of
all proportions with like materials, the volume would have been
25,300 cubic meters, and the absorbing power 1,370, resulting in the
value, T = 3.02. This would have differed from the chosen result
by an amount that would have been very noticeable.

The new Boston Music Hall is, therefore, not a copy of the
Gewandhaus, but the desired results have been attained in a very
different way.

A few general considerations, not directly connected with rever-
beration, may be of interest. The three halls are of nearly the same
length on the floor; but in the old hall and in the Gewandhaus the

68 REVERBERATION

platform for the orchestra is out in the hall, and the galleries extend
along both sides of it; while in the new hall the orchestra is not out
in the main body of the room, and for this reason is slightly farther
from the rear of the hall; but this is more than compensated for in
respect to loudness by the orchestra being in a somewhat contracted
stage recess, from the side walls of which the reflection is better
because they are nearer and not occupied by an audience. Also it
may be noted that the new hall is not so high as the old and is not
so broad.

Thus is opened up the question of loudness, and this has been
solved to a first approximation for the case of sustained tones.
But as the series of papers now concluded is devoted to the question
of reverberation, this new problem must be reserved for a subse-
quent discussion.

ARCHITECTURAL ACOUSTICS^

INTRODUCTION

1 HE problem of architectural acoustics requires for its complete
solution two distinct lines of investigation, one to determine quan-
titatively the physical conditions on which loudness, reverberation,
resonance, and the allied phenomena depend, the other to determine
the intensity which each of these should have, what conditions are
best for the distinct audition of speech, and what effects are best for
music in its various forms. One is a purely physical investigation,
and its conclusions should be based iand should be disputed only on
scientific grounds; the other is a matter of judgment and taste, and
its conclusions are weighty in proportion to the weight and unanimity
of the authority in which they find their source. For this reason,
these papers are in two series. The articles which appeared six
years ago began the first, and the paper immediately following is
the beginning of the second.

Of the first series of papers, which have to do with the purely
physical side of the problem, only one paper has as yet been pub-
lished. This contained a discussion of reverberation, complete as
far as one note is concerned. There is on hand considerable material
for a paper extending this discussion to cover the whole range of the
musical scale, and therefore furnishing a basis for the discussion of
what has sometimes been called the musical quality of an audito-
rium. There has also been collected a certain amount of data in
regard to loudness, resonance, interference, echoes, irregularities of
air currents and temperature, and the transmission of sound through
walls and partitions, — all of which will appear as soon as a com-
plete presentation is possible in each case. Each problem has been
taken up as it has been brought to the writer's attention by an
architect in consultation either over plans or in regard to a com-
pleted building. This method is slow, but it has the advantage of

' Proceedings of the American Academy of Arts and Sciences, vol. xlii, no. 2, June, 1906.

70 ARCHITECTURAL ACOUSTICS

making the work practical, and may be relied on to prevent the
magnification to undue importance of scientifically interesting but
practically subordinate points. On the other hand, there is the
danger that it may lead to a fragmentary presentation. An effort
has been made to guard against this, and the effort for completeness
is the reason for delay in the appearance of some of the papers.
Sufficient progress has been made, however, to justify the assertion
that the physical side of the problem is solvable, and that it should
be possible ultimately to calculate in advance of construction all
the acoustical qualities of an auditorium.

Thus far it is a legitimate problem in physics, and as such a
reasonable one for the writer to undertake.

The second part of the problem, now being started, the question
as to what constitutes good and what constitutes poor acoustics,
what effects are desirable in an auditorium designed for speaking,
and even more especially in one designed for music, is not a question
in physics. It is therefore not one for which the writer is especially
qualified, and would not be undertaken here were it not in the first
place absolutely necessary in order to give effect to the rest of the
work, and in the second place were it not the plan rather to gather
and give expression to the judgment of others acknowledged as
qualified to speak, than to give expression to the taste and judg-
ment of one. It is thus the purpose to seek expert judgment in
regard to acoustical effects, and if possible to present the results in
a form available to architects. This will be slow and difficult work,
and it is not at all certain that it will be possible to arrive, even ulti-
mately, at a finished product. It is worth undertaking, however, if
the job as a whole is worth undertaking, for without it the physical
side of the investigation will lose much of its practical value. Thus
it is of little value to be able to calculate in advance of construction
and express in numerical measure the acoustical quality which any
planned auditorium will have, unless one knows also in numerical
measure the acoustical quality which is desired. On the other hand,
if the owner and the architect can agree on the desired result, and
if this is within the limits of possibility considering all the demands
on the auditorium, of utility, architecture, and engineering, this
result can be secured with certainty, — at least there need be no

ACCURACY OF MUSICAL TASTE 71

uncertainty as to whether it will or will not be attained in the com-
pleted building.

The papers following this introduction will be : The Accuracy of
Musical Taste in regard to Architectural Acoustics, and Variation in
Reverberation with Variation in Pitch.

THE ACCURACY OF MUSICAL TASTE IN REGARD
TO ARCHITECTURAL ACOUSTICS

PIANO MUSIC

L HE experiments described in this paper were undertaken in order
to determine the reverberation best suited to piano music in a music
room of moderate size, but were so conducted as to give a measure of
the accuracy of cultivated musical taste. The latter point is obvi-
ously fundamental to the whole investigation, for unless musical
taste is precise, the problem, at least as far as it concerns the design
of the auditorium for musical purposes, is indeterminate.

The first observations in regard to the precision of musical taste
were obtained during the planning of the Boston Symphony Hall,
Messrs. McKim, Mead, and White, Architects. Mr. Higginson,
Mr. Gericke, the conductor of the orchestra, and others connected
with the Building Committee expressed opinions in regard to a
number of auditoriums. These buildings included the old Boston
Music Hall, at that time the home of the orchestra, and the places
visited by the orchestra in its winter trips, Sanders Theatre in
Cambridge, Carnegie Hall in New York, the Academy of Music in
Philadelphia, and the Music Hall in Baltimore, and in addition to
these the Leipzig Gewandhaus. By invitation of Mr. Higginson,
the writer accompanied the orchestra on one of its trips, made
measurements of all the halls, and calculated their reverberation.
The dimensions and the material of the Gewandhaus had been
published, and from these data its reverberation also was calculated.
The results of these measurements and calculations showed that the
opinions expressed in regard to the several halls were entirely con-
sistent with the physical facts. That is to say, the reverberation in
those halls in which it was declared too great was in point of physi-
cal measurement greater than in halls in which it was pronounced

72 ARCHITECTURAL ACOUSTICS

too small. This consistency gave encouragement in the hope that
the physical problem was real, and the end to be attained definite.

Much more elaborate data on the accuracy of musical taste were
obtained four years later, 1902, in connection with the new building
of the New England Conservatory of Music, Messrs. Wheelwright
and Haven, Architects. The new building consists of a large audi-
torium surrounded on three sides by smaller rooms, which on the
second and third floors are used for purposes of instruction. These
smaller rooms, when first occupied, and used in an unfurnished or
partially furnished condition, were found unsuitable acoustically,
and the writer was consulted by Mr. Haven in regard to their final
adjustment. In order to learn the acoustical condition which would
accurately meet the requirements of those who were to use the
rooms, an experiment was undertaken in which a number of rooms,
chosen as typical, were varied rapidly in respect to reverberation by
means of temporarily introduced absorbing material. Approval or
disapproval of the acoustical quality of each room at each stage was
expressed by a committee chosen by the Director of the Conserva-
tory. At the close of these tests, the reverberation in the rooms was
measured by the writer in an entirely independent manner as
described in the paper on Reverberation (1900). The judges were
Mr. George W. Chadwick, Director of the Conservatory, and Signer
Oresti Bimboni, Mr. WilUam H. Dunham, Mr. George W. Proctor,
and Mr. William L. Whitney, of the Faculty. The writer suggested
and arranged the experiment and subsequently reduced the results
to numerical measure, but expressed no opinion in regard to the
quality of the rooms.

The merits of each room in its varied conditions were judged
solely by listening to piano music by Mr. Proctor. The character
of the musical compositions on which the judgment was based is a
matter of interest in this connection, but this fact was not appre-
ciated at the time and no record of the selections was made. It is
only possible to say that several short fragments, varied in nature,
were tried in each room.

As will be evident from the descriptions given below, the rooms
were so differently furnished that no inference as to the reverbera-
tion could be drawn from appearances, and it is certain that the

ACCURACY OF MUSICAL TASTE 73

opinions were based solely on the quality of the room as heard in
the piano music.

The five rooms chosen as typical were on the second floor of the
building. The rooms were four meters high. Their volumes varied
from 74 to 210 cubic meters. The walls and ceilings were finished in
plaster on wire lath, and were neither papered nor painted. There
was a piano in each room; in room 5 there were two. The amount
of other furniture in the rooms varied greatly :

In room 1 there was a bare floor, and no furniture except the
piano and piano stool.

Room 2 had rugs on the floor, chairs, a sofa with pillows, table,
music racks, and a lamp.

Room 3 had a carpet, chairs, bookcases, and a large number of
books, which, overflowing the bookcases, were stacked along the
walls.

Room 4 had no carpet, but there were chairs and a small table.

Room 5 had a carpet, chairs, and shelia curtains.

Thus the rooms varied from an almost unfurnished to a reasonably
furnished condition. In all cases the reverberation was too great.

The experiment was begun in room 1. There were, at the time,
besides the writer, five gentlemen in the room, the absorbing effect
of whose clothing, though small, nevertheless should be taken into
account in an accurate calculation of the reverberation. Thirteen
cushions from the seats in Sanders Theatre, whose absorbing power
for sound had been determined in an earlier investigation, were
brought into the room. Under these conditions the unanimous
opinion was that the room, as tested by the piano, was lifeless. Two
cushions were then removed from the room with a perceptible change
for the better in the piano music. Three more cushions were re-
moved, and the effect was much better. Two more were then taken
out, leaving six cushions in the room, and the result met unanimous
approval. It was suggested that two more be removed. This being
done the reverberation was found to be too great. The agreement
was then reached that the conditions produced by the presence of
six cushions were the most nearly satisfactory.

The experiment was then continued in Mr. Dunham's room,
number 2. Six gentlemen were present. Seven cushions were

74 ARCHITECTURAL ACOUSTICS

brought into the room. The music showed an insufficient rever-
beration. Two of the cushions were then taken out. The change
was regarded as a distinct improvement, and the room was satis-
factory.

In Mr. Whitney's room, number 3, twelve cushions, with which
it was thought to overload the room, were found insufficient even
with the presence in this case of seven gentlemen. Three more
cushions were brought in and the result declared satisfactory.

In the fom-th room, five, eight, and ten cushions were tried be-
fore the conditions were regarded as satisfactory.

In Mr. Proctor's room, number 5, it was evident that the ten
cushions which had been brought into the room had overloaded it.
Two were removed, and afterwards three more, leaving only five,
before a satisfactory condition was reached.

This completed the direct experiment with the piano.

The bringing into a room of any absorbing material, such as these
cushions, affects its acoustical properties in several respects, but
principally in respect to its reverberation. The prolongation of
sound in a room after the cessation of its source may be regarded
either as a case of stored energy which is gradually suffering loss by
transmission through and absorption by the walls and contained
material, or it may be regarded as a process of rapid reflection from
wall to wall with loss at each reflection. In either case it is called
reverberation. It is sometimes called, mistakenly as has been ex-
plained, resonance. The reverberation may be expressed by the
duration of audibility of the residual sound after the cessation of a
source so adjusted as to produce an average of sound of some stand-
ard intensity over the whole room. The direct determination of
this, under the varied conditions of this experiment, was impracti-
cable, but, by measuring the duration of audibility of the residual
sound after the cessation of a measured organ pipe in each room
without any cushions, and knowing the coefficient of absorption of
the cushions, it was possible to calculate accurately the reverbera-
tion at each stage in the test. It was impossible to make these
measurements immediately after the above experiments, because,
although the day was an especially quiet one, the noises from the
street and railway traffic were seriously disturbing. Late the follow-

ACCURACY OF MUSICAL TASTE

ing night the conditions were more favorable, and a series of fairly
good observations was obtained in each room. The cushions had
been removed, so that the measurements were made on the rooms in
their original condition, furnished as above described. The appara-
tus and method employed are described in full in a series of articles
in the Engineering Record^ and American Architect for 1900.
The results are given in the accompanying table.

1
.Ha

boa
11

t2«

<
1%

•S
a
.2

Remarks

<§

:§-s

z*s

^•3

^£

1=^

5.0

2.43

Reverberation too great.

2.4

7.4

1.64

Reverberation too great.

12.8

20.2

.60

Reverberation too little.

10.1

17.5

.70

Better.

7.3

14.7

.83

Better.

5.5

12.9

.95

Condition approved.

3.6

11.0

1.22

Reverberation too great.

6.3

2.39

Reverberation too great.

2.9

9.2

1.95

Reverberation too great.

6.4

15.6

.95

Reverberation too little.

4.6

13.8

1.10

Condition approved.

210

14.0

2.46

Reverberation too great.

3.4

17.4

2.00

Reverberation too great.

11.0

28.4

1.21

Better.

13.7

31.1

1.10

Condition approved.

133

8.3

2.65

Reverberation too great.

3.4

11.7

1.87

Reverberation too great.

((

5.5

17.2

1.26

Better.

9.1

20.8

1.09

Condition approved.

7.0

2.24

Reverberation too great.

1.9

8.9

1.76

Reverberation too great.

((

9.1

18.0

.87

Reverberation too little.

7.3

16.2

.98

Better.

4.6

13.5

1.16

Condition approved.

1 The article in the Engineering Record is identical with the paper in the American
Architect for 1900, reprinted in this volume as Part 1.

76 ARCHITECTURAL ACOUSTICS

The table is a record of the &st of what, it is hoped, will be a
series of such experiments extending to rooms of much larger dimen-
sions and to other kinds of music. It may well be, in fact it is
highly probable, that very much larger rooms would necessitate a
different amount of reverberation, as also may other types of musical
instruments or the voice. As an example of such investigations, as
well as evidence of their need, it is here given in full. The following
additional explanations may be made. The variation in volume of
the rooms is only threefold, corresponding only to such music rooms
as may be found in private houses. Over this range a perceptible
variation in the required reverberation should not be expected. The
third column in the table includes in the absorbing power of the
room (ceiling, walls, furniture, etc.) the absorbing powers of the
clothes of the writer, who was present not merely at all tests, but in
the measurement of the reverberation the following night. From
the next two columns, therefore, the writer and the effects of his
clothing are omitted. The remarks in the last column are reduced
to the form "reverberation too great," "too little," or "approved."
The remarks at the time were not in this form, however. The room
was pronounced "too resonant," "too much echo," "harsh," or
"dull," "lifeless," "overloaded," expressions to which the forms
adopted are equivalent.

If from the larger table the reverberation in each room, in its
most approved condition, is separately tabulated, the following is
obtained:

Rooms Reverberation

1 95

2 1.10

3 1.10

4 1.09

5 1.16

1.08 mean

The final result obtained, that the reverberation in a music room
in order to secure the best effect with a piano should be 1.08, or in
round numbers 1.1, is in itseK of considerable practical value; but
the five determinations, by their mutual agreement, give a numeri-
cal measure to the accuracy of musical taste which is of great
interest. Thus the maximum departm-e from the mean is .13 seconds.

ACCURACY OF MUSICAL TASTE 77

and the average departure is .05 seconds. Five is rather a small
number of observations on which to apply the theory of probabilities,
but, assuming that it justifies such reasoning, the probable error is
.02 seconds, — surprisingly small.

A close inspection of the large table will bring out an interesting
fact. The room in which the approved condition differed most from
the mean was the first. In this room, and in this room only, was it
suggested by the gentlemen present that the experiment should be
carried further. This was done by removing two more cushions.
The reverberation was then 1.22 seconds, and this was decided to
be too much. The point to be observed is that 1.22 is further above
the mean, 1.08, than .95 is below. Moreover, if one looks over the
list in each room it will be seen that in every case the reverberation
corresponding to the chosen condition came nearer to the mean than
that of any other condition tried.

It is conceivable that had the rooms been alike in all respects and
required the same amount of cushions to accomplish the same re-
sults, the experiment in one room might have prejudiced the ex-
periment in the next. But the rooms being different in size and
furnished so differently, an impression formed in one room as to the
number of cushions necessary could only be misleading if depended
on in the next. Thus the several rooms required 6, 5, 15, 10, and 5
cushions. It is further to be observed that in three of the rooms the
final condition was reached in working from an overloaded con-
dition, and in the other two rooms from the opposite condition, —
in the one case by taking cushions out, and in the other by bringing
them in.

Before beginning the experiment no explanation was made of its
nature, and no discussion was held as to the advantages and disad-
vantages of reverberation. The gentlemen present were asked to
express their approval or disapproval of the room at each stage of
the experiment, and the final decision seemed to be reached with
perfectly free unanimity.

This surprising accuracy of musical taste is perhaps the explana-
tion of the rarity with which it is entirely satisfied, particularly
when the architectural designs are left to chance in this respect.

78 ARCHITECTURAL ACOUSTICS

VARIATION IN REVERBERATION WITH
VARIATION IN PITCH

Six years ago there was published in the Engineering Record and
the American Architect a series of papers on architectural acoustics
intended as a beginning in the general subject. The particular phase
of the subject under consideration was reverberation, — the continua-
tion of sound in a room after the source has ceased. It was there
shown to depend on two things,^the volume of the room, and the
absorbing character of the walls and of the material with which the
room is filled. It was also mentioned that the reverberation depends
in special cases on the shape of the room, but these special cases were
not considered. The present paper also will not take up these special
cases, but postpone their consideration, although a good deal of
material along this line has now been collected. It is the object
here to continue the earlier work rather narrowly along the original
lines. The subject was then investigated solely with reference to
sounds of one pitch, C4 512 vibrations per second. It is the inten-
tion here to extend this over nearly the whole range of the musical
scale, from Ci 64 to C7 4096.

It can be shown readily that the various materials of which the
walls of a room are Constructed and the materials with which it is
filled do not have the same absorbing power for all sounds regard-
less of pitch. Under such circumstances the previously published
work with C4 512 must be regarded as an illustration, as a part of a
much larger problem, — the most interesting part, it is true, be-
cause near the middle of the scale, but after all only a part. Thus a
room may have great reverberation for sounds of low pitch and very
little for sounds of high pitch, or exactly the reverse; or a room may
have comparatively great reverberation for sounds both of high and
of low pitch and very little for sounds near the middle of the scale.
In other words, it is not putting it too strongly to say that a room
may have very different quality in different registers, as different
as does a musical instrument; or, it the room is to be used for
speaking purposes, it may have different degrees of excellence or
defect for a whisper and for the full rounded tones of the voice,
different for a woman's voice and for a man's — facts more or less

VARIATION IN REVERBERATION 79

well recognized. Not to leave this as a vague generalization the
following cases may be cited. Recently, in discussing the acoustics
of the proposed cathedral of southern California in Los Angeles
with Mr. Maginnis, its architect, and the writer, Bishop Conaty
touched on this point very clearly. After discussing the general
subject with more than the usual insight and experience, possibly
in part because Catholic churches and cathedrals have great rever-
beration, he added that he found it diflBcult to avoid pitching his
voice to that note which the auditorium most prolongs notwith-
standing the fact that he found this the worst pitch on which to
speak. This brings out, perhaps more impressively because from
practical experience instead of from theoretical considerations, the
two truths that auditoriums have very different reverberation for
different pitches, and that excessive reverberation is a great hin-
drance to clearness of enunciation. Another incident may also serve,
that of a church near Boston, in regard to which the writer has just
been consulted. The present pastor, in describing the nature of its
acoustical defects, stated that different speakers had different de-
grees of difficulty in making themselves heard; that he had no diffi-
culty, having a rather high pitched voice; but that the candidate
before him, with a louder but much lower voice, failed of the ap-
pointment because unable to make himself heard. Practical ex-
perience of the difference in reverberation with variation of pitch
is not unusual, but the above cases are rather striking examples.
Corresponding effects are not infrequently observed in halls devoted
to music. Its observation here, however, is marked in the rather
complicated general effect. The full discussion of this belongs to
another series of papers, in which will be taken up the subject of the
acoustical effects or conditions that are desirable for music and for
speech. While this phase of the subject will not be discussed here
at length, a little consideration of the data to be presented will show
how pronounced these effects may be and how important in the
general subject of architectural acoustics.

In order to show the full significance of this extension of the in-
vestigation in regard to reverberation, it is necessary to point out
some features which in earlier papers were not especially empha-
sized. Primarily the investigation is concerned with the subject of

80 ARCHITECTURAL ACOUSTICS

reverberation, that is to say, with the subject of the continuation of
a sound in a room after the source has ceased. The immediate effect
of reverberation is that each note, if it be music, each syllable or
part of a syllable, if it be speech, continues its sound for some time,
and by its prolongation overlaps the succeeding notes or syllables,
harmoniously or inharmoniously in music, and in speech always
towards confusion. In the case of speech it is inconceivable that
this prolongation of the sound, this reverberation, should have any
other effect than that of confusion and injury to the clearness of the
enunciation. In music, on the other hand, reverberation, unless in
excess, has a distinct and positive advantage.

Perhaps this will be made more clear, or at least more easily
realized and appreciated, if we take a concrete example. Given a
room comparatively empty, with hard wall-surfaces, for example
plaster or tile, and having in it comparatively little furniture, the
amount of reverberation for the sounds of about the middle register
of the double-bass viol and for the sounds of the middle register of
the violin will be very nearly though not exactly equal. If, how-
ever, we bring into the room a quantity of elastic felt cushions,
suflBcient, let us say, to accommodate a normal audience, the effect
of these cushions, the audience being supposed absent, will be to
diminish very much the reverberation both for the double-bass viol
and for the violin, but will diminish them in very unequal amounts.
The reverberation will now be twice as great for the double-bass as
for the violin. If an audience comes into the room, filling up the
seats, the reverberation will be reduced still further and in a still
greater disproportion, so that with an audience entirely filling the
room the reverberation for the violin will be less than one-third that
for the double-bass. When one considers that a difference of five
per cent in reverberation is a matter for approval or disapproval on
the part of musicians of critical taste, the importance of considering
these facts is obvious.

This investigation, nominally in regard to reverberation, is in
reality laying the foundation for other phases of the problem. It
has as one of its necessary and immediate results a determination of
the coeflacient of absorption of sound of various materials. These
coefficients of absorption, when once known, enable one not merely

VARIATION IN REVERBERATION 81

to calculate the prolongation of the sound, but also to calculate the
average loudness of sustained tones. Thus it was shown in one of
the earlier papers, though at that time no very great stress was laid
on it, that the average loudness of a sound in a room is proportional
inversely to the absorbing power of the material in the room. There-
fore the data which are being presented, covering the whole range
of the musical scale, enable one to calculate the loudness of different
notes over that range, and make it possible to show what effect the
room has on the piano or the orchestra in different parts of the
register.

To illustrate this by the example above cited, if the double-bass
and the violin produce the same loudness in the open air, in the bare
room with hard walls both would be reenforced about equally. The
elastic felt brought into the room would decidedly diminish this re-
enforcement for both instruments. It would, however, exert a much
more pronounced effect in the way of diminishing the reenforcement
for the violin than for the double-bass. In fact, the balance will be
so affected that it will require two violins to produce the same vol-
ume of sound as does one double-bass. The audience coming into
the room will make it necessary to use three violins to a double-
bass to secure the same balance as before.

Both cases cited above are only broadly illustrative. As a matter
of fact the effect of the room and the effect of the audience in the
room is perceptibly different at the two ends of the register of the
viohn and of the double-bass viol.

There is stUl a third effect, which must be considered to appre-
ciate fully the practical significance of the results that are being
presented. This is the effect on the quality of a sustained tone.
Every musical tone is composed of a great number of partial tones,
the predominating one being taken as the fundamental, and its
pitch as the pitch of the sound. The other partial tones are re-
garded as giving quality or color to the fundamental. The musical
quality of a tone depends on the relative intensities of the overtones.
It has been customary, at least on the part of physicists, to regard
the relative intensities of the overtones, which define the quality of
the sound, as depending simply on the source from which the sound
originates. Of course, primarily, this is true. Nevertheless, while

82 ARCHITECTURAL ACOUSTICS

the source defines the relative intensities of the issuing sounds, their
actual intensities in the room depend not merely on that, but also,
and to a surprising degree, on the room itseK. Thus, for example,
given an eight-foot organ pipe, if blown in an empty room, such as
that described above, the overtones would be pronounced. If ex-
actly the same pipe be blown with the same wind pressure in a room
in which the seats have been covered with the elastic felt, the first
upper partial will bear to the fundamental a ratio of intensity
diminished over 40 per cent, the second upper partial a ratio to the
fundamental diminished in the same per cent, the third upper
partial a ratio diminished over 50 per cent, while the fourth upper
partial will bear a ratio of intensity to the fundamental diminished
about 60 per cent. Quality expressed numerically in this way
probably does not convey a very vivid impression as to its real
eflPect. It may signify more to say merely that the change in quality
is very pronounced and noticeable, even to comparatively untrained
ears. On the other hand, if one were to try the experiment with a
six-inch instead of with an eight-foot organ pipe, the effect of
bringing the elastic felt cushions into the room would be to increase
the relative intensities of the overtones, and thus to diminish the
purity of the tone.

All tones below that of a six-inch organ pipe will be purified by
bringing into the room elastic felt. All tones above and including
that pitch will be rendered less pure. The effect of an audience
coming into a room is still different. Assuming that the audience
has filled the room and so covered all the elastic felt cushions, the
effect of the audience is to purify all tones up to violin C4 512, and
to have very little effect on all tones from that pitch upward. On
very low tones the effect of the audience in the room is more pro-
nounced. For example, again take Ci 64, the effect of the audience
will be to diminish its first overtone about 60 per cent relative to
the fundamental and its second overtone over 75 per cent.

The effect of the material used in the construction of a room, and
the contained furniture, in altering the relative intensities of the
fundamental and the overtones, is to improve or injure its quality
according to circxmistances. It may be, of course, that the tone
desired is a very pure one, or it may be that what is wanted is a

VARIATION IN REVERBERATION 83

tone with pronounced upper partials. Take, for example, the
"night horn" stop in a pipe organ. This is intended to have a very
pure tone. The room in contributing to its purity would improve
its quality. On the other hand, the mixture stop in a pipe organ is
intended to have very pronounced overtones. In fact to this end
not one but several pipes are sounded at once. The effect of the
above room to emphasize the fundamental and to wipe out the
overtones would be in opposition to the original design of the stop.
To determine what balance is desirable must lie of course with the
musicians. The only object of the present series of papers is to
poiut out the fundamental facts, and that our conditions may be
varied in order to attain any desired end. One great thing needed
is that the judgment of the musical authorities should be gathered
in an available form; but that is another problem, and the above
bare outline is intended only to indicate the importance of extend-
ing the work to the whole range of the musical scale, — the work
undertaken in the present paper.

The method pursued in these experiments is not very unlike that
followed in the previous experiments with C4 512. It differs in minor
detail, but to explain these details would involve a great deal of
repetition which the modifications in the method are not of sufficient
importance to justify.

Broadly, the procedure consists first in the determination of the
rate of emission of the sound of an organ pipe for each note to be
investigated. This consists in determining the durations of audibil-
ity after the cessation of two sounds, one having four or more, but
a known multiple, times the intensity of the other. From these
results it is possible to determine the rate of emission by the pipes,
each in terms of the minimum audibility for that particular tone.
The apparatus used in this part of the experiment is shown in Fig. 1.
Four small organs were fixed at a minimum distance of five meters
apart. It was necessary to place them at this great distance apart
because, as already pointed out, if placed near each other the four
sounded together do not emit four times the sound emitted by one.
This wide separation was particularly necessary for the large pipes
and the low tones; a very much less separation would have served
the purpose in the case of the high tones.

ARCHITECTURAL ACOUSTICS

From the point where the four tubes leading to the small organs
meet, a supply pipe ran, as shown on the drawing, to an air reservoir
in the room below. This was fed from an electrically driven blower
at the far end of the building. The chronograph was in another
room. The experiments with this apparatus, like the experiments

Fig. 1

heretofore recorded, were carried out at night between twelve and
five o'clock.

The rate of emission of sound by the several pipes having been
determined, the next work was the determination of the coefficients
of absorption. The methods employed having already been suflB-
ciently described, only results will be given.

In the very nature of the problem the most important data is the
absorption coefficient of an audience, and the determination of this
was the fiirst task undertaken. By means of a lecture on one of
the recent developments of physics, an audience was enveigled into
attending, and at the end of the lecture requested to remain for the
experiment. In this attempt the effort was made to determine the
coefficients for the five octaves from C2 128 to Cs 2048, including

VARIATION IN REVERBERATION 85

notes E and G in each octave. For several reasons the experiment
was not a success. A threatening thunder storm made the audience
a small one, and the sultriness of the atmosphere made open win-
dows necessary, while the attempt to cover so many notes, thirteen
in all, prolonged the experiment beyond the endurance of the audi-
ence. While this experiment failed, another the following summer
was more successful. In the year that had elapsed the necessity of
carrying the investigation further than the limits intended became
evident, and now the experiment was carried from Ci 64 to C7 4096,
but including only the C notes, seven notes in all. Moreover,
bearing in mind the experiences of the previous summer, it was
recognized that even seven notes would come dangerously near over-
taxing the patience of the audience. Inasmuch as the coefficient
of absorption for C4 512 had already been determined six years be-
fore in the investigations mentioned, the coeflficient for this note
was not redetermined. The experiment was therefore carried out
for the lower three and the upper three notes of the seven. The
audience, on the night of this experiment, was much larger than
that which came the previous summer, the night was a more com-
fortable one, and it was possible to close the windows during the
experiment. The conditions were thus fairly satisfactory. In order
to get as much data as possible and in as short a time, there were
nine observers stationed at different points in the room. These ob-
servers, whose kindness and skill it is a pleasure to acknowledge,
had prepared themselves by previous practice for this one experi-
ment. As in the work of six years ago, the writer's key controlled
the organ pipes and started the chronograph, the writer and the
other observers each had a key which was connected with the
chronograph to record the cessation of audibility of the sound. The
results of the experiment are shown on the lower curve in Fig. 2.
This curve gives the coeflficient of absorption per person. It is to
be observed that one of the points falls clearly off the smooth curve
drawn through the other points. The observations on which this
point is based were, however, much disturbed by a street car pass-
ing not far from the building, and the departure of this observation
from the curve does not indicate a real departure in the coeflficient
nor should it cast much doubt on the rest of the work, in view of the

ARCHITECTURAL ACOUSTICS

circumstances under which it was secured. Counteracting the per-
haps bad impression which this point may give, it is a considerable
satisfaction to note how accurately the point for C4 512, deter-

1.0

.!J

c. c.

Fig. 2. The absorbing power of an audience for different
notes. The lower curve represents the absorbing power
of an audience per person. The upper curve represents
the absorbing power of an audience per square meter
as ordinarily seated. The vertical ordinates are ex-
pressed in terms of total absorption by a square meter
of surface. For the upper curve the ordinates are thus
the ordinary coefficients of absorption. The several
notes are at octave intervals, as follows: Ci64, C2I28,
C3 (middle C) 256, Ci512, CslOSi, C62048, C74096.

mined six years before by a different set of observers, falls on the
smooth curve through the remaining points. In the audience on
which these observations were taken there were 77 women and

VARIATION IN REVERBERATION 87

105 men. The courtesy of the audience in remaining for the ex-
periment and the really remarkable silence which they maintained
is gratefully acknowledged.

The curve above discussed is that for the average person in an
audience. An interesting form in which to throw the results is to
regard the audience as one side of a room. We may then look at it
as an extended absorbing surface, and determine the coefficient per
square meter. Worked out on this basis the absorption coefficient
is indicated in the higher curve. It is merely the lower curve multi-
plied by a number which expresses the average number of people
per square meter. It is interesting to note that the coefficient of
absorption is about the same from C4 512 up, indicating over that
range nearly complete absorption. Below that point there is a very
great falling off, down to Ci 64. The curve is such as to permit of
an extrapolation indicative of even less absorption and consequently
greater reverberation for the still lower notes. Without entering
into an elaborate discussion of this curve, two points may be noted
as particularly interesting. The first is the nearly complete absorp-
tion for the higher notes, a result which at first sight seems a little
inconsistent with the results which will be shown later on in con-
nection with the absorption by felt. The inconsistency, however,
is oidy apparent. The greater absorption shown by an audience
than that shown by thick felt arises from the fact that the surface
of the audience is irregular and does not result in a single reflection,
but probably, for a very large portion of the sound, of multiple re-
flection before it finally emerges. The physical conditions are such
that they obviously do not admit of analytic expression, but the
explanation of the great absoqjtion by an extended audience sur-
face is not difficult to understand. In addition to the above there
is another partial explanation which contributes to the results.
The felt forms a perfectly continuous medium, and therefore offers
a comparatively rigid reflecting surface. The comparatively light,
thin, and porous nature of the clothing of women, perhaps more
than of men, contributes to the great absorption of the high notes.

The next experiment, taking them up chronologically, and per-
haps next even from the standpoint of interest, was in regard to a
brick wall-surface. This experiment was carried out in the constant-

ARCHITECTURAL ACOUSTICS

temperature room mentioned in the previous papers. The arrange-
ment of apparatus is shown in Fig. 3, where the air reservoir in the
room above is shown in dotted lines. In many respects the constant-
temperature room offered admirable conditions for the experiment.

Fig. 3

Its position in the center of the building and its depth underground
made it comparatively free from outside disturbing noises, — so
much so that it was possible to experiment in this room in the earlier
parts of the evening, although not, of coiu-se, when any one else was
at work in the building. While it possesses these advantages, its

VARIATION IN REVERBERATION

arched ceiling, by placing it in the category of special cases, makes
extra precaution necessary. Fortunately, at the beginning of the
experiment the walls were unpainted. Under these conditions its

.lU

.09

.08

.07

.06

.04

.08

■^

.02

.01

Fig. 4. The absorbing power of a 45 cm. thick brick wall.
The upper curve represents the absorbing power of an
unpainted brick surface. The bricks were hard but not
glazed, and were set in cement. The lower curve repre-
sents the absorbing power of the same surface painted
with two coats of oil paint. The difference between
the two curves represents the absorption due to the
porosity of the bricks. In small part, but probably only
in small part, the difference is due to difference in super-
ficial smoothness. Ca (middle C) 256.

coefficient of absorption for different notes was determined. It was
then painted with an oil paint, two coats, and its coefficient of ab-
sorption redetermined. The two curves are shown in Fig. 4. The

90 ARCHITECTURAL ACOUSTICS

upper curve is for the unpainted brick; the lower curve is that ob-
tained after the walls were painted. The difference between the
two ciu"ves would, if plotted alone, be the curve of absorption due
to the porosity of the brick. It may seem, perhaps, that the paint
in covering the bare brick wall made a smoother surface, and the
difference between the two results might be due in part to less sur-
face friction. Of course this is a factor, but that it is an exceedingly
small factor will be shown later in the discussion of the results on
the absorption of sound by other bodies. The absorption of the
sound after the walls are painted is, of course, due to the yielding of
the walls under the vibration, to the sound actually transmitted
bodily by the walls, and to the absorption in the process of trans-
mission. It is necessary to call attention to the fact that the vertical
ordinates are here magnified tenfold over the ordinates shown in the
last curve.

The next experiment was on the determination of the absorption
of sound by wood sheathing. It is not an easy matter to find con-
ditions suitable for this experiment. The room in which the absorp-
tion by wood sheathing was determined in the earlier experiments
was not available for these. It was available then only because the
building was new and empty. When these more elaborate experi-
ments were under way the room had become occupied, and in a
manner that did not admit of its being cleared. Quite a little search-
ing in the neighborhood of Boston failed to discover an entirely suit-
able room. The best one available adjoined a night lunch room.
The night lunch was bought out for a couple of nights, and the ex-
periment was tried. The work of both nights was much disturbed.
The traffic past the building did not stop until nearly two o'clock,
and began again about four. The interest of those passing by on
foot throughout the night, and the necessity of repeated explana-
tions to the pohce, greatly interfered with the work. This detailed
statement of the conditions under which the experiment was tried
is made by way of explanation of the irregularity of the observa-
tions recorded on the curve, and of the f ailxu-e to carry this particular
line of work further. The first night seven points were obtained for
the seven notes Ci 64 to C7 4096. This work was done by means
of a portable apparatus shown in Fig. 5. The reduction of these

VARIATION IN REVERBERATION

results on the following day showed variations indicative of maxima
and minima, which to be accurately located would require the de-

Fig. 5

termination of intermediate points. The experiment the following
night was by means of the organ shown in Fig. 6, and points were

ARCHITECTURAL ACOUSTICS

determined for the E and G notes in each octave between C2 128 and
Ce 2048. Other points would have been determined, but time did
not permit. It is obvious that the intermediate points in the lower and

Fig. 6

in the higher octave were desirable, but no pipes were to be had on
such short notice for this part of the range, and in their absence the
data could not be obtained. In the diagram, Fig. 7, the points lying
on the vertical lines were determined the first night. The points

VARIATION IN REVERBERATION

lying between the vertical lines were determined the second night.
The accuracy with which these points fall on a smooth curve is

.12
.U
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01

Fig. 7. The absorbing power of wood sheathing, two centi-
meters thick, North Carolina pine. The observations
were made under very unsuitable conditions. The
absorption is here due almost wholly to yielding of the
sheathing as a whole, the surface being shellacked,
smooth, and non-porous. The curve shows one point
of resonance within the range tested, and the prob-
ability of another point of resonance above. It is not
possible now to learn as much in regard to the framing
and arrangement of the studding in the particular room
tested as is desirable. Ca (middle C) 256.

94 ARCHITECTURAL ACOUSTICS

perhaps all that could be expected in view of the difficulty under
which the observations were conducted and the limited time avail-
able. One point in particular falls far off from this curve, the point
for C3 256, by an amount which is, to say the least, serious, and
which can be justified only by the conditions under which the work
was done. The general trend of the curve seems, however, estab-
lished beyond reasonable doubt. It is interesting to note that there
is one point of maximum absorption, which is due to resonance be-
tween the walls and the sound, and that this point of maximum
absorption lies in the lower part, though not in the lowest part, of
the range of pitch tested. It would have been interesting to deter-
mine, had the time and facilities permitted, the shape of the curve
beyond C7 4096, and to see if it rises indefinitely, or shows, as is far
more likely, a succession of maxima. The scale employed in this
ciu-ve is the same as that employed in the diagram of the unpainted
and painted ^all-surfaces. It may perhaps be noted in this con-
nection that at the very least the absorption is four times that of
painted brick walls.

The experiment was then directed to the determination of the ab-
sorption of sound by cushions, and for this purpose return was made
to the constant-temperature room. Working in the manner indicated
in the earlier papers for substances which could be carried in and
out of a room, the curves represented in Fig. 8 were obtained.
Curve 1 shows the absorption coefficient for the Sanders Theatre
cushions, with which the whole investigation was begun ten years
ago. These cushions were of a particularly open grade of packing,
a sort of wiry grass or vegetable fiber. They were covered with
canvas ticking, and that in turn with a very thin cloth covering.
Curve 2 is for cushions borrowed from the Phillips Brooks House.
They were of a high grade, filled with long curly hair, and covered
with canvas ticking, which was in turn covered by a long nap plush.
Curve 3 is for the cushions of Appleton Chapel, hair covered with a
leatherette, and showing a sharper maximum and a more rapid
diminution in absorption for the higher frequencies, as would be
expected under such conditions. Curve 4 is probably the most
interesting, because for more standard commercial conditions. It
is the curve for elastic felt cushions as made by Sperry and Beale.

VARIATION IN REVERBERATION

It is to be observed that all four curves fall off for the higher fre-
quencies, all show a maximum located within an octave, and three

1.0

/■

-^ -

"sVv

•v

c, c.

Fig. 8. The absorbing power of cushions. Curve 1 is
for "Sanders Theatre" cushions of wiry vegetable
fiber, covered with canvas ticking and a thin cloth.
Curve 2 is for "Brooks House" cushions of long hair,
covered with the same kind of ticking and plush.
Curve 3 is for "Appleton Chapel" cushions of hair,
covered with ticking and a thin leatherette. Curve 4
is for the elastic felt cushions of commerce, of elastic
cotton, covered with ticking and short nap plush. The
absorbing power is per square meter of surface.
Cs (middle C) 266.

of the curves show a curious hump in the second octave. This
break in the curve is a genuine phenomenon, as it was tested time
after time. It is perhaps due to a secondary resonance, and it is to

ARCHITECTURAL ACOUSTICS

be observed that it is the more pronounced in those curves that have
the sharper resonance in their principal maxima.

Observations were then obtained on unupholstered chairs and
settees. The result for chairs is shown in Fig. 10. This curve gives
the absorption coefficient per single chair. The effect was surpris-
ingly small; in fact, when the floor of the constant-temperature
room was entirely covered with the chairs spaced at usual seating
distances, the effect on the reverberation in the room was exceed-

FiG. 9

ingly slight. The fact that it was so slight and the consequent dif-
ficulty in measuring the coefficient is a partial explanation of the
variation of the results as indicated in the figure. Nevertheless it
is probable that the variations there indicated have some real basis,
for a repetition of the work showed the points again falling above
and below the line as in the first experiment. The amount that
these fell above and below the line was difficult to determine, and
the number of points along the curve were too few to justify at-
tempting to follow their values by the line. In fact the line is drawn
on the diagram merely to indicate in a general way the fact that the
coefficient of absorption is nearly the same over the whole range. A
varying resonance phenomenon was unquestionably present, but so
small as to be negligible; and in fact the whole absorption by the
chairs is an exceedingly small factor. The chair was of ash, and its
type is shown in the accompanying sketch. Fig. 9.

The results of the observations on settees is shown in Fig. 11.
Those plotted are the coefficients per single seat, there being five
seats to the settee. The settees were placed at the customary dis-

VARIATION IN REVERBERATION

tance. Here again the principal interest attaches to the fact that
the coeflBcient of absorption is so exceedingly small that the total
effect on the reverberation is hardly noticeable. Here also the
plotted results do not fall on the Hne drawn, and the departure is
.03

.OS

.01

' U I

C' c. c. c, c, c. c,

Fig. 10. The absorbing power of ash chairs shown in Fig. 9.

due probably to some slight resonance. The magnitude of the de-
parture, however, could not be determined with accuracy because of
the small magnitude of the total absorption coefficient. For these
reasons and because the number of points was insufficient, no at-

.03

.02

.01

— ^HM^^— ~'^^^^™ "^^^~'~~ I "^ ^^^^^"'

'< '

Fig. 11. The absorbing power of ash settees shown in
Fig. 9. The absorption is per single seat, the settee
as shown seating five.

tempt was made to draw the curve through the plotted points, but
merely to indicate a plotted tendency. The settees were of ash,
and their general style is shown in the sketch.

An investigation was then begun in regard to the nature of the
process of absorption of sound. The material chosen for this work
was a very durable grade of felt, which, as the manufacturers
claimed, was all wool. Even a casual examination of its texture
makes it difficult to believe that it is all wool. It has, however, the

98 ARCHITECTURAL ACOUSTICS

advantage of being porous, flexible, and very durable. Almost con-
stant handling for several years has apparently not greatly changed
its consistency. It is to be noted that this felt is not that mentioned
in the papers of six years ago. That felt was of lime-treated cow's
hair, the kind used in packing steam pipes. It was very much cheaper
in price, but stood little handling before disintegrating. The felt
employed in these experiments comes in sheets of various thick-
nesses, the thickness here employed being about 1.1 cm.

The coefficient of absorption of a single layer of felt was measured
for the notes from Ci 64 to C7 4096 at octave intervals. The experi-
ment was repeated for two layers, one on top of the other, then for
three, and so on up to six thicknesses of felt. Because the greater
thicknesses presented an area on the edge not inconsiderable in
comparison with the surface, the felt was surrounded by a narrow
wood frame. Under such circumstances it was safe to assume that
the absorption was entirely by the upper surface of the felt. The
experiment was repeated a great many times, first measuring the
coefficient of absorption for one thickness for all frequencies, and
then checking the work by conducting experiments in the other
order; that is, measuring the absorption by one, two, three, etc.,
thicknesses, for each frequency. The mean of all observations is
shown in Fig. 12 and Fig. 13. In Fig. 12 the variations in pitch are
plotted as abscissas, as in previous diagrams, whereas in Fig. 13 the
thicknesses are taken as abscissas. The special object of the second
method will appear later, but a general object of adopting this
method of plotting is as follows :

If we consider Fig. 12, for example, the drawing of the line through
any one set of points should be made not merely to best fit those
points, but should be drawn having in mind the fact that it, as a
curve, is one of a family of curves, and that it should be drawn not
merely as a best curve through its own points, but as best fits the
whole set. For example, in Fig. 12 the curve for four thicknesses
would not have been drawn as there shown if drawn simply with
reference to its own points. It would have been drawn directly
through the points for Ci 64 and C2 128. Similarly the curve for
five thicknesses would have been drawn a little nearer the point for
C2 128, and above instead of below the point for Ci 64. Considering,

VARIATION IN REVERBERATION

however, the whole family of curves and recognizing that each point
is not without some error, the curves as drawn are more nearly
correct. The best method of reconciling the several curves to each

•w

/Y>

^/v

•^'^ —

—

c. c.

Fig. 12. The absorbing power of felt of different thick-
nesses. Each piece of felt was 1.1 cm. in thickness.
Curve 1 is for a single thickness, curve 2 for two thick-
nesses placed one on top of the other, etc. As shown
by these curves, the absorption is in part by penetra-
tion into the pores of the felt, in part by a yielding of
the mass as a whole. Resonance in the latter process
is clearly shown by a maximum shifting to lower
and lower pitch with increase in thickness of the felt.
Ca (middle C) 256.

other is to plot two diagrams, one in which the variations in pitch
are taken as abscissa and one in which the variations in thickness
of felt are taken as abscissas; then draw through the points the best

100 ARCHITECTURAL ACOUSTICS

fitting curves and average the corresponding ordinates taken from
the curves thus drawn; and with these average ordinates redraw
both famihes of curves. The points shown on the diagram are of
course the original results obtained experimentally. In general
they fall pretty close to the curves, although at times, as in the
points noted, they fall rather far to one side.

The following will serve to present the points of particular in-
terest revealed by the family of curves in Fig. 12, where the absorp-
tion by the seVeral thicknesses is plotted against pitch for abscissas.
It is to be observed that a single thickness scarcely absorbs the sound
from the eight, four, and two-foot organ pipes, Ci 64, C2 128, and
C3 256, and that its absorption increases rapidly for the next two
octaves, after which it remains a constant. Two thicknesses absorb
more — about twice as much — for the lower notes, the curve rising
more rapidly, passing through a maximum between C4 512 and
Cs 1024, and then falling off for the higher notes. The same is true
for greater thicknesses. All curves show a maximum, each succeed-
ing one corresponding to a little lower note. The maximum for six
thicknesses coincides pretty closely to C4 512. The absorption of
the sound by felt may be ascribed to three causes, — porosity of
structure, compression of the felt as a whole, and friction on the
surface. The presence of the maximum must be ascribed to the
second of these causes, the compression of the felt as a whole. As
to the third of these three causes, it is best to consult the curves of
the next figure.

The following facts are rendered particularly evident by the
curves of Fig. 13. For the tones emitted by the eight-foot organ
pipe, Ci 64, the absorption of the sound is very nearly proportional
to the thickness of the felt over the range tested, six thicknesses,
6.6 cm. The curves for notes of increasing pitch show increasing
value for the coefficients of absorption. They all show that were
the thickness of the felt sufficiently great, a limit would be ap-
proached — a fact, of course, self-evident — but for C5 1024 this
thickness was reached within the range experimented on; and of
course the same is true for all higher notes, Ce 2048 and C7 4096.
The higher the note, the less the thickness of felt necessary to pro-
duce a maximum effect. The curves of Ci 64, C2 128, C3 256, and

VARIATION IN REVERBERATION

101

C4 512, if extended backward, would pass nearly through the origin.
This indicates that for at least notes of so low a pitch the absorption

P6.

.5
4

f uy

.3
.2
.1

■

■^

/ <

Fig. 13. The absorbing power of felt of different thick-
nesses. The data. Fig. 12, is here plotted in a slightly
different manner — horizontally on plotted increasing
thickness — and the curves are for notes of different
frequency at octave intervals in pitch. Thus plotted
the curves show the necessary thickness of felt for
practically maximum efficiency in absorbing sound of
different pitch. These curves also show that for the
lowest three notes surface friction is negligible, at least
in comparison with the other factors. For the high
notes one thickness of felt was too great for the curves
to be conclusive in regard to this point. C3 (middle
C) 256.

of sound would be zero, or nearly zero, for zero thickness. Since
zero thickness would leave surface effects, the argument leads to

102 ARCHITECTURAL ACOUSTICS

the conclusion that surface friction as an agent in the absorption of
sound is of small importance. The curves plotted do not give any
evidence in this respect in regard to the higher notes, C5 1024,
Ce 2048, and C7 4096.

It is of course evident that the above data do not by any means
cover all the ground that should be covered. It is highly desirable
that data should be accessible for glass surfaces, for glazed tile sur-
faces, for plastered and unplastered porous tile, for plaster on wood
lath and plaster on wire lath, for rugs and carpets; but even with
these data collected the job would be by no means completed.
What is wanted is not merely the measurement of existing material
and wall-surfaces, but an investigation of all the possibilities. A
concrete case will perhaps illustrate this. If the wall-surface is to
be of wood, there enter the questions as to what would be the effect
of varying the material, — how ash differs from oak, and oak from
walnut or pine or whitewood; what is the effect of variations in
thickness; what the effect of paneling; what is the effect of the
spacing of the furring on which the wood sheathing is fastened. If
the wall is to be plaster on lath, there arises the question as to the
difference between wood lath and wire lath, between the mortar
that was formerly used and the wall of today, which is made of hard
and impervious plaster. What is the effect of variations in thick-
ness of the plaster ? What is the effect of painting the plaster in
oil or in water colors ? What is the effect of the depth of the air
space behind the plaster ? The recent efforts at fireproof construc-
tion have resulted in the use of harder and harder wall-surfaces,
and great reverberation in the room, and in many cases in poorer
acoustics. Is it possible to devise a material which shall satisfy the
conditions as to fireproof qualities and yet retain the excellence of
some of the older but not fireproof rooms ? Or, if one turns to the
interior furnishings, what type of chair is best, what form of cushions,
or what form of upholstery ? There are many forms of auditorium
chairs and settees, and all these should be investigated if one pro-
poses to apply exact calculation to the problem. These are some of
the questions that have arisen. A few data have been obtained
looking toward the answer to some of them. The difficulty in the
way of the prosecution of such work is greater, however, than ap-

VARIATION IN REVERBERATION 103

pears at first sight, the particular diflScuIties being of opportunity
and of expense. It is difficult, for example, to find rooms whose
walls are in large measure of glass, especially when one bears in
mind that the room must be empty, that its other wall-surfaces
must be of a substance fully investigated, and that it must be in a
location admitting of quiet work. Or, to investigate the effect of
the different kinds of plaster and of the different methods of plaster-
ing, it is necessary to have a room, preferably an underground room,
which can be lined and relined. The constant-temperature room
which is now available for the experiments is not a room suitable
to that particular investigation, and for best results a special room
should be constructed. Moreover, the expense of plastering and
replastering a room — and this process, to arrive at anything like
a general solution of the problem, would have to be done a great
many times — would be very great, and is at the present moment
prohibitive. A little data along some of these lines have been se-
cured, but not at all in final form. The work in the past has been
largely of an analytical nature. Could the investigation take the
form of constructive research, and lead to new methods and greater
possibilities, it would be taking its more interesting form.

The above discussion has been solely with reference to the deter-
mination of the coefficient of absorption of sound. It is now pro-
posed to discuss the question of the application of these coefficients
to the calculation of reverberation. In the first series of papers,
reverberation was defined with reference to C4 512 as the continua-
tion of the sound in a room after the soiu-ce had ceased, the initial
intensity of the sound being one million times minimum audible
intensity. It is debatable whether or not this definition should be
extended without alteration to reverberation for other notes than
C4 512. There is a good deal to be said both for and against its
retention. The whole, however, hinges on the outcome of a physi-
ological or psychological inquiry not yet in such shape as to lead to
a final decision. The question is therefore held in abeyance, and
for the time the definition is retained.

Retaining the definition, the reverberation for any pitch can be
calculated by the formula

104

ARCHITECTURAL ACOUSTICS

where V is the volume of the room, jK is a constant depending on

the initial intensity, and a is the total absorbing power of the walls

and the contained material. K and V are the same for all pitch

C, C, Cs c.

Fig. 14. Curves expressing the reverberation in the large
lecture-room of the Jefferson Physical Laboratory with
(lower curve) and without (upper curve) an audience.
These curves express in seconds the duration of the
residual sound in the room after the cessation of
sources producing intensities 10* times minimum
audible intensity for each note. The upper curve de-
scribes acoustical conditions which are very unsatis-
factory, as the hall is to be used for speaking purposes.
The lower curve describes acoustically satisfactory
conditions. Cs (middle C) 256.

frequencies. K is .164 for an initial iatensity 10® times minimum
audible intensity. The only factor that varies with the pitch is a,
which can be determined from the data given above.

VARIATION IN REVERBERATION 105

In illustration, the curves in the accompanying Fig. 14 give the
reverberation in the large lecture-room of the Jefferson Physical
Laboratory. The upper curve defines the reverberation in the room
when entirely empty; the lower curve deficnes this reverberation in
the same room with an audience two-thirds filling the room. The
upper curve represents a condition which would be entirely impracti-
cal for speaking piurposes; the lower curve represents a fairly satis-
factory condition.

MELODY AND THE ORIGIN OF THE MUSICAL

SCALE ^

In the vice-presidential addresses of the American Association
great latitude in the choice of subjects is allowed and taken, but
there is, I believe, no precedent for choosing the review of a book
printed fifty-five years before. Helmholtz' Tonenemfindungen, pro-
duced by a masterful knowledge of physiology, physics, and mathe-
matics, and a scholar's knowledge of the literature of music, has
warded dS all essential criticism by its breadth, completeness, and
wealth of detail. Since it was first published it has been added to
by the author from time to time in successive editions, and greatly
bulwarked by the scholarly notes and appendices of its translator.
Dr. Alexander J. EUis. The original text remains unchanged, and
unchallenged, as far as physicists are concerned, in all important
respects. In taking exception at this late day to the fundamental
thesis of Part III, I derive the necessary courage from the fact that
should such exception be sustained, it will serve to restore to its
fuU apphcation that greater and more original contribution of Helm-
holtz which he included in Part II. Having given a physical and
physiological explanation of the harmony and discord of simul-
taneous sounds, and, therefore, an explanation of the musical scale
as used in modern composition, Helmholtz was met by an apparent
anachronism. The musical scale, identical with the modern musi-
cal scale in all essentials, antedated by its use in single-part melody
the invention of chordal composition, or, as Helmholtz expressed
it, preceded all experience of musical harmony. In seeking an ex-
planation of this early invention of the musical scale, Helmholtz
abandoned his most notable contribution, and relegated his expla-
nation of harmony and discord to the minor service of explaining
a fortunate, though of course an important use of an already in-
vented system of musical notes. The explanation of the original

' Vice-Presidential Address, Section B, American Association for the Advancement of
Science, Chicago, 1907.

107

108 MELODY

invention of the musical scale and its use in single-part music
through the classical and the early Christian eras, he sought for
in piu-ely aesthetic considerations, — in exactly those devices from
which he had just succeeded in rescuing the explanation of harmony
and discord.

The hmnan ear consists of three parts, — in the nomenclature
of anatomy, of the outer, middle, and inner ear. The outer and
the inner ears are connected by a series of three small bones trav-
ersing the middle ear and transmitting the vibrations of sound.
The inner ear is a peculiarly shaped cavity in one of the hard bones
of the skull. That part of the cavity with which we are here con-
cerned is a long passage called from its resemblance to the interior
of a snail shell the cochlea. The cavity has two windows which are
closed by membranes. It is to the uppermost of these membranes
that the train of three small bones, reaching from the drum of the
outer ear, is attached at its inner end. It is to this upper membrane,
therefore, that the vibration is communicated, and through it the
vibration reaches the fluid which fills the inner cavity. As the
membrane covering the upper window vibrates, the membrane
covering the lower window yielding, also vibrates, and the motion
of the fluid is in the nature of a slight displacement from one to
the other window, to and fro. From between these windows a dia-
phragm, dividing the passageway, eixtends almost the whole length
of the cochlea. This diaphragm is composed in part of a great
number of very fine fibers stretched side by side, transverse to the
cochlea, and called after their discoverer, fibers of Corti. On this
diaphragm terminate the auditory nerves. When the liquid vibrates,
the fibers vibrate in unison, the nerve terminals are stimulated, and
thus the sensation of sound is produced. These fibers of Corti are
of different lengths and presumably are stretched with different
tensions. They therefore have different natural rates of vibration
and a sympathetic resonance for different notes. The whole has
been called a harp of several thousand strings.

Were these fibers of Corti very free in their vibration, each
would respond to and would respond strongly only to that partic-
ular note with whose frequency it is in imison. Because of the fact
that they are in a liquid, and possibly also because of the manner

ORIGIN OF THE MUSICAL SCALE 109

of their terminal connections, they are considerably damped. Be-
cause of this their response is both less in amount and less selective
in character. In fact, under these conditions, not one, but many
fibers vibrate in response to a single pure note. A considerable
length or area of the diaphragm is excited. So long as the exciting
sound remains pure in quality, constant in pitch, and constant in
intensity, the area of the diaphragm affected and the amplitude of
its vibration remain unchanged. If, however, two notes are sounded
of nearly the same pitch, the areas of the diaphragm affected by the
two notes overlap. In the overlapping region the vibration is violent
when the two notes are in the same phase, weak when they are in
opposite phase. The result is the familiar phenomena of beats.
Such beats when slow are not disagreeable and not without musical
value. If the difference between the two notes is increased, the
beats become more rapid and more disagreeable. To this violent
disturbance, to the starting and stopping of the vibration of the
fibers of Corti, Helmholtz ascribed the sense of roughness which we
call discord. As the notes are more widely separated in pitch, the
overlapping of the affected areas diminishes. Between pure notes
the sense of discord disappears with sufficient separation in pitch.
When the two vibrating areas exactly match, because the two notes
are of exactly the same pitch, and when the two areas do not in the
least overlap, because of a sufficiently wide separation in pitch, the
result according to Helmholtz is harmony. Partial overlapping of
the affected areas produces beats, and the roughness of beats is
discord. Such, reduced to its fewest elements, is Helmholtz' expla-
nation of the harmony and discord of tones which are pure.

But no musical tone is simple. It always consists of a combina-
tion of so-called partial tones which bear to each other a more or
less simple relationship. Of these partial tones, one is called the
fundamental, — so-called because it is the loudest or lowest or,
better still, because it is that to which the other partial tones bear
the simplest relation. A musical tone, therefore, affects not one,
but, through its fundamental and upper partial tone^, several areas
of the diaphragm in the cochlea. Two musical tones, each with its
fundamental and upper partials, therefore, affect areas of the dia-
phragm which overlap each other in a more or less complicated

110 MELODY

manner, depending on the relative frequencies of the fundamental
tones and the relationships of their upper partials. The exact
matching of the areas affected by these two systems of partial tones,
or the entire separation of the affected areas, give harmony. The
overlapping of these affected areas, if great, produces discord, or, if
slight in amount, modifications and color of harmony.

In the great majority of musical tones the upper partials bear
simple relationships to the fundamentals, being integral multiples
in vibration frequency. Helmholtz showed that if of two such
tones one continued to sound unchanged in pitch, and the other
starting in unison was gradually raised in pitch, the resulting dis-
cord would pass through maxima and minima, and that the minima
would locate the notes of the pentatonic scale. The intermediate
notes of the complete modern musical scale are determined by
a repetition of this process starting from the notes thus deter-
mined.

If to this is added a similar consideration of the mutual inter-
ference of the combinational tones which are themselves due to
the interaction of the partial tones, we have the whole, though of
course in the briefest outline, of Helmholtz' theory of the harmony
and discord of simultaneously sounding musical tones.

Having thus in Parts I and II developed a theory for the har-
mony and discord of simultaneous sounds, and having developed
a theory which explains the modern use of the musical scale in
chords and harmonic music, Helmholtz pointed out, in Part III,
that the musical scale in its present form existed before the inven-
tion of harmonic music and before the use of chords.

Music may be divided into three principal periods : —

1. "Homophonic or Unison Music of the ancients," including the music

of the Christian era up to the eleventh century, "to which also
belongs the existing music of Oriental and Asiatic nations."

2. "Polyphonic music of the middle ages, with several parts, but with-

out regard to any independent musical significance of the har-
monies, extending from the tenth to the seventeenth century."

3. "Harmonic or modem music characterized by the independent

significance attributed to the harmonies as such."

ORIGIN OF THE MUSICAL SCALE 111

Polyphonic music was the first to call for the production of
simultaneous sounds, and, therefore, for the hearing or the experi-
ence of musical harmony. Homophonic music, that which alone
existed up to the tenth or eleventh century, consisted in the pro-
gression of single-part melody. Struck by this fact, Helmholtz
recognized the necessity of seeking another explanation for the
invention and the use of a scale of fixed notes in the music of this
period. To borrow his own words, "scales existed long before
there was any knowledge or experience of harmony." Again, else-
where, he says in emphasizing the point: "The individual parts of
melody reach the ear in succession. We cannot perceive them all
at once; we cannot observe backwards and forwards at pleasure."
Between sounds produced and heard in discrete succession, there
can be neither harmony nor discord, there cannot be beats, or
roughness or interruption of continuous vibrations. Regarding the
sounds of a melody as not merely written in strict and non-over-
lapping succession, but also as produced and heard in discrete suc-
cession, Helmholtz sought another basis for the choice of the notes
to constitute a scale for homophonic music. His explanation of
this invention can be best presented by a few quotations : —

Melody has to express a motion in such a manner that the hearer may
easily, clearly, and certainly appreciate the character of that motion by
immediate perception. This is only possible when the steps of this motion,
their rapidity, and their amount, are also exactly measurable by immediate
sensible perception. Melodic motion is change of pitch in time. To meas-
ure it perfectly, the length of time elapsed and the distance between the
pitches must be measurable. This is possible for immediate audition only
on condition that the alterations both in time and pitch should proceed by
regular and determinate degrees.

Again Helmholtz says : — ■

For a clear and sure measurement of the change of pitch, no means was
left but progression by determinate degrees. This series of degrees is laid
down in the musical scale. When the wind howls and its pitch rises or falls
in insensible gradations without any break, we have nothing to measure
the variations of pitch, nothing by which we can compare the later with the
earlier sounds, and comprehend the extent of the change. The whole phe-
nomenon produces a confused, unpleasant impression. The musical scale
is as it were the divided rod, by which we measure progression in pitch, as
rhythm measures progression in time.

112 MELODY

Later he says : —

Let us begin with the Octave, in which the relationship to the funda-
mental tone is most remarkable. Let any melody be executed on any in-
strument which has a good musical quaUty of tone, such as a human voice;
the hearer mufet have heard not only the primes of the compound tones, but
also their upper octaves, and, less strongly, the remaining upper partials.
When, then, a higher voice afterwards executes the same melody an Octave
higher, we hear again a part of what we heard before, namely the evenly
numbered partial tones of the former compound tones, and at the same
time we hear nothing that we had not previously heard.

What is true of the Octave is true in a less degree for the Twelfth.
If a melody is repeated in the Twelfth we again hear only what we had
aheady heard, but the repeated part of what we heard is much weaker,
because only the third, sixth, ninth, etc., partial tone is repeated, whereas
for repetition in the Octave, instead of the third partial, the much stronger
second and weaker fourth partial is heard, and in place of the ninth, the
eighth and tenth occur, etc.

For the repetition on the Fifth, only a part of the new sound is iden-
tical with a part of what had been heard, but it is, nevertheless, the most
perfect repetition which can be executed at a smaller interval than an
Octave.

Without carrying these quotations further they will suflBce to
illustrate the basis which Helmholtz would ascribe to homophonic
music and early melodic composition. On this explanation the
basis of melody is purely that of rhythm and rhythm based on a
scale of intervals. The scale of intervals in turn is based on a
recognition, conscious or subconscious, of the compound character
of musical tones, and of the existence in tones of different pitch of
partials of the same pitch. This calls for a degree of musical in-
sight and discrimination which it is difficult to credit to a primitive
art. It is in reality the skill of the highly trained musician, of a
musician trained by long experience with sounds which are rich
and accurate in quality. This power of analysis goes rather with
supreme skill than with the early gropings of an art.

After having developed a theory of harmony and discord based
on elaborate experimental and mathematical investigations, which
was remarkable in bringing together three such diverse fields as
physics, physiology, and aesthetics, he relegated it to the minor
application of explaining the use in modern music of an already

ORIGIN OF THE MUSICAL SCALE 113

existing and highly developed musical scale, and sought an expla-
nation of the earlier use of the scale in melody and its original in-
vention in the principle which is very far from possessing either
the beauty or the convincing quality of his earlier hypothesis. He
was forced to this by a priority of melodic or homophonic compo-
sition. He saw in melody only a succession of notes, no two exist-
ing at the same time, and therefore incapable of producing harmony
or discord in a manner such as he had been considering.

It is true that melody is written as a pure succession of discrete
notes, one beguming only when the other has ceased. It is true also
that melody is so sung and so produced on a homophonic instru-
ment, such as the voice, flute, reeds, or one-stringed instruments.
This is peculiarly true of the voice, and it is with the voice that
one naturally associates the earliest invention of the scale. But
while it is true that the earliest song must have consisted of tones
produced only in succession, it is not necessarily true that such
sounds were heard as isolated notes. A sound produced in a space
which is in any way confined continues until it is dimiuished by
transmission through openings or is absorbed by the retaining walls,
or contained material to such a point that it is past the threshold
of audibility, and this prolongation of audibility of sound is under
many conditions a factor of no inconsiderable importance. In many
rooms of ordinary construction the prolongation of audibility
amounts to two or three seconds, and it is not exceedingly rare that
a soimd of moderate initial intensity should continue audible for
eight, nine, or even ten seconds after the source has ceased. As a
result of this, single-part music produced as successive separate
sounds is, nevertheless, heard as overlapping, and at times as greatly
overlapping tones. Each note may well be audible with appreciable
intensity not merely through the next, but through several suc-
ceeding notes. Under such conditions we have every opportunity,
even with single-part music, for the production of all the phenomena
of harmony and discord which has been discussed by Helmholtz in
explanation of the chordal use of the musical scale. In any ordi-
narily bare and uncarpeted room, one may sing in succession a
series of notes and then hear for some time afterward their full
chordal effect.

114 MELODY

All the arguments that Helmholtz advanced in support of his
hypothesis, that the musical scale was devised solely from con-
siderations of rhythm and founded on a repetition of faint upper
partials, hold with equal force in the explanation here proposed.
The identity of partial tones in compound tones with different
fundamentals is one of the conditions of harmony, and the scale
devised by considerations of the mutual harmony of the notes
soimded simultaneously, would, in every respect, be the same as
that of a scale based on repeated upper partials. In the one case
the identity of upper partials is an act of memory, in the other it
is determined by the harmony of sustained tones. All the argu-
ments by Helmholtz based on historical considerations and on
racial and national differences are equally applicable to the hy-
pothesis of sustained tones. In fact, they take on an additional
significance, for we may now view all these differences not merely
in the light of differences in racial development and temperament,
but in the light of physical environment. Housed or unhoused,
dwelling in reed huts or in tents, in houses of wood or of stone, in
houses and temples high vaulted or low roofed, of heavy furnish-
ing or hght, in these conditions we may look for the factors which
determine the development of a musical scale in any race, which
determine the rapidity of the growth of the scale, its richness, and
its considerable use in single-part melody.

The duration of audibility of a sound depends on its initial in-
tensity and on its pitch, to a small degree on the shape of the con-
fined space, and to a very large degree on the volume of the space
and on the material of which the walls are composed. The duration
of audibility is a logarithmic function of the initial intensity, and
as the latter is practically always a large multiple of the minimum
audible intensity, this feature of the problem may be neglected
when considering it broadly. For this discussion we may also leave
out of consideration the effect of shape as being both minor and too
intricately variable. The pitch here considered will be the middle
of the musical scale; for the extremes of the scale the fiigures would
be very different. The problem then may be reduced to two factors,
volume and material. It is easy to dispose of the problem reduced
to these two elements.

ORIGIN OF THE MUSICAL SCALE 115

The duration of audibility of a sound is directly proportional to
the volume of a room and inversely proportional to the total ab-
sorbing power of the walls and the contained material. The volume
of the room, the shape remaining the same, is proportional to the
cube, while the area of the walls is proportional to the square of
the linear dimensions. The duration of audibility, proportional to
the ratio of these two, is proportional to the first power of the linear
dimension. Other things being equal, the duration of audibility,
the overlapping of successive sounds, and, therefore, the experience
of harmony in single-part music is proportional to the linear di-
mensions of the room, be it dwelling house or temple.

Turning to the question of material the following figures are
suggestive: Any opening into the outside space, provided that
outside space is itself unconfined, may be regarded as being totally
absorbing. The absorbing power of hard pine wood sheathing
of one-half inch thickness is 6.1 per cent; of plaster on wood lath,
3.4 per cent; of single-thickness glass, 2.7 per cent; of brick in
Portland cement, 2.5 per cent; of the same brick painted with oil
paint, 1.4 per cent. Wood sheathing is nearly double any of the
rest. On the other hand, a man in the ordinary clothing of today
is equal in his absorbing power to nearly 48 per cent of that of a
square meter of unobstructed opening, a woman is 54 per cent, and
a square meter of audience at ordinary seating distance is nearly
96 per cent. Of significance also in this connection is the fact that
Oriental rugs have an absorbing power of nearly 29 per cent, and
house plants of 11 per cent.

Of course, the direct application of these figures in any accurate
calculation of the conditions of life among different races or at dif-
ferent periods of time is impossible, but they indicate in no uncer-
taia manner the great differences acoustically in the environment
of Asiatic races, of aboriginal races in central and southern Africa,
of the Mediterranean countries, of northern Europe at different
periods of time. We have explained for us by these figures why the
musical scale has but slowly developed in the greater part of Asia
and of Africa. Almost no traveler has reported a musical scale,
even of the most primitive sort, among any of the previously un-
visited tribes of Africa. This fact could not be ascribed to racial

116 MELODY

inaptitude. If melody was, as Helmholtz suggested, but rhythm in
time and in pitch, the musical scale should have been developed in
Africa if anywhere. These races were given to the most rhythmical
dancing, and the rhythmical beating of drums and tomtoms.
Rhythm in time they certainly had. Moreover, failure to develop
a musical scale could not be ascribed to racial inaptitude to feeling
for pitch. Transported to America and brought in contact with
the musical scale, the negro became immediately the most musical
part of our population. The absence of a highly developed scale in
Africa must then be ascribed to environment.

Turning to Europe we find the musical scale most rapidly de-
veloping among the stone-dweUing people along the shores of the
Mediterranean. The development of the scale and its increased
use kept pace with the increased size of the dwellings and temples.
It showed above all in their religious worship, as their temples and
churches reached cathedral size. The reverberation which accom-
panied the lofty and magnificent architecture increased until even
the spoken service became intoned in the Gregorian chant. It is
not going beyond the bounds of reason to say that in those churches
in Europe which are housed in magnificent cathedrals, the Catholic,
the Lutheran, and Protestant Episcopal, the form of worship is in
part determined by their acoustical conditions.

This presents a tempting opportunity to enlarge on the fact
that the alleged earhest evidence of a musical scale, a supposed
fiute, belonged to the cave dwellers of Europe. This and the im-
pulse to sing in an empty room, and the ease with which even the
unmusical can keep the key in simple airs under such conditions,
are significant facts, but gain nothing by amplification. The same
may be said of the fact that since music has been written for more
crowded auditoriums and with harmonic accompaniment melody
has become of less harmonious sequence. These and many other
instances of the effect of reverberation come to mind.

In conclusion, it may not be out of place to repeat the thesis
that melody may be regarded not only as rhythm in time and
rhythm in pitch, but also as harmony in sustained tones, and that
we may see in the history of music, certainly in its early beginnings,
but possibly also in its subsequent development, not only genius
and invention, but aJso the effect of physical environment.

ARCHITECTURAL ACOUSTICS^

EFFECTS OF AIR CURRENTS AND OF TEMPERATURE

VJrdinakily there is not a close connection between the flow of
air in a room and its acoustical properties, although it has been fre-
quently suggested that thus the sound may be carried effectively
to different parts. On the other hand, while the motion of the air
is of minor importance, the distribution of temperature is of more
importance, and it is on reliable record that serious acoustical diffi-
culty has arisen from abrupt differences of temperature in an audi-
torium. Finally, transmission of disturbing noises through the
ventilation ducts, perhaps theoretically a side issue, is practically
a legitimate and necessary part of the subject. The discussion will
be under these three heads.

The first of the above three topics, the possible effect of the mo-
tion of the air on the acoustical property of a room, is the immediate
subject.

Ventilation

It was suggested during the planning of the Boston Symphony
Hall that its acoustical properties would be greatly benefited by
introducing the air for ventilation at the front and exhausting at
the back, thus carrying the sound by the motion of the air the length
of the room. The same suggestion has been made to the writer by
others in regard to other buildings, but this case will serve as suffi-
cient example. The suggestion was unofficial and the gentleman
proposing it accompanied it by a section of a very different hall from
the hall designed by Mr. McKim, but as this section was only a
sketch and without dimensions the following calculation will be
made as if the idea were to be applied to the present hall. It will
be shown that the result thus to be secured, while in the right

* Engineering Record, June, 1910.
lir

118 ARCHITECTURAL ACOUSTICS

direction, is of a magnitude too small to be appreciable. To make
this the more decisive we shall assmne throughout the argument
the most favorable conditions possible.

If a sound is produced in still air in open space it spreads in a
spherical wave diminishing in intensity as it covers a greater area.
The area of a sphere being proportioned to the square of the radius,
we arrive at the common law that the intensity of sound in still air
is inversely proportional to the square of the distance from the
source. If in a steady wind the air is moving uniformly at all alti-
tudes, the sound still spreads spherically, but with a moving center,

Fig. 1

the whole sphere being carried along. If the air is moving toward
the observer, the sound reaches him in less time than it otherwise
would, therefore spread over a less spherical surface and louder.
If, on the other hand, the observer is to windward, the sound has
had to come against the wind, has taken a longer time to reach him,
is distributed over a greater surface, and is less loud.

The three cases are represented in the accompanying diagram.
The stationary source of sound being at S, a is the wave in still air
arriving at both observers at the same time and with the same in-
tensity. If the air is moving to the left, the center of the wave will
be shifted by an amount d to the left while the wave has spread to
Oi. On arrival it will have the size b, less than a, and will be louder.
On the other hand, while the wave is reaching 02, the observer to
windward, the center will have been shifted to the left by an even
greater amount da. In this case the size of the wave will be c, larger
than a, and the sound will be less. The loudness of the sound in the
three cases is inversely as the three surfaces a, b, and c. If the dis-

EFFECTS OF AIR CURRENTS 119

tance of the observer from S is denoted by r, the loudness of the
sound in the three cases will be as

and-

The above result may be expressed m the following more simple
and practical form. If, in the diagram, a is the wave in still air, its
corresponding position when of the same size and, therefore, of the
same intensity in moving air will be a', the movement of the air
having been sufficient to carry the wave a distance d while it has
expanded with the velocity of sound to a sphere of radius r. The
distance d and the radius r are to each other as the velocity of wind
and the velocity of sound. If the observers Oi and 02 move, the one
away from the source and the other toward it, by a distance d, the
sound will be of the same intensity to both as in their first positions
in stiU air.

In order to make application of this to the particular problem
in hand, we shall assume a normal air supply to the room for ven-
tilation purposes of one-seventieth of a cubic meter per person per
second. This, i£ introduced all at one end and exhausted all at the
other, in a room 17.9 meters high, 22.8 meters broad, and seating
about 2600 persons, would produce a velocity of the air of 0.09
meters per second, assuming the velocity to be the same at every
point of a transverse section. Leaving out of account the ques-
tionable merits of this arrangement from the ventilation standpoint,
its acoustical value can be calculated readily.

The velocity of sound under normal conditions being about
340 meters per second, the time required to traverse a hall 40 meters
long is only about one-ninth of a second. In this short interval of
time the motion of the air in the room, due to the ventilation, would
be sufficient to advance the sound-wave only 0.01 meters, or one cen-
timeter. It would thus arrive at the back of the room as a sphere
with its center one centimeter nearer than the source. That is to say,
the beneficial effect of this proposed system of ventilation, greatest
for the auditor on the rear seat, would to him be equivalent at the
very maximum to bringing the stage into the room one centimeter
further, or it would be equivalent to bringing the auditor on the

120 ARCHITECTURAL ACOUSTICS

rear seat forward one centimeter. This distance is so slight that
without moving in his seat, in fact, without moving his shoulders,
a slight inclination of the head would accomplish an equivalent
gain. Thus, while the effect is in the right direction, it is of entirely
imperceptible magnitude. If we take into account the sound re-
flected from walls and ceiling, the gain is even less.

But the suggestion which is the text of the present paper was
not made by one, but by several gentlemen, and is based on the
well-recognized fact that one can hear better, often very much
better, with the wind than against it, and better than in still air.
Therefore, the suggestion is not groundless and cannot be disposed
of thus summarily, certainly not without submitting to the same
calculation the out-of-door experience that gave rise to the thought.

In the nomenclature of the United States Weather Bureau a
wind of from "1 to 5 miles an hour is called light, 6 to 14 miles
fresh, 15 to 24 miles brisk, 25 to 37 miles high, and a wind of from
40 to 59 miles is called a gale." Taking the case of a "high wind"
as a liberal example, its average velocity is about 14 meters per
second, or about one twenty-fifth the velocity of sound. In such
a wind the sound 1000 meters to leeward would be louder than in
still air only by an amount which would be equivalent to an ap-
proach of 40 meters, or 8 per cent. Similarly, to windward the sound
would be less loud by an amount equivalent to increasing the dis-
tance from 1000 to 1040 meters. This is not at all commensurate
with general experience. The difference in audibility, everyone will
agree, is generally greater and very much greater than this. The
discrepancy, however, can be explained. The discrepancy is not
between observation and theory, but between observation and a
very incomplete analysis of the conditions in the out-of-door ex-
perience. Thus, the ordinary view is that one is merely hearing
with or against the wind and this wind is thought of as steady and
uniform. As a matter of fact, the wind is rarely steady, and partic-
ularly is it of different intensity at different altitudes. Fortunately,
the out-of-door phenomenon, which in reality is very complex, has
been carefully studied in connection with fog signals.

The first adequate explanation of the variation in loudness of a
sound with and against the wind was by the late Sir George G.

EFFECTS OF AIR CURRENTS 121

Stokes in an article "On the Effect of Wind on the Intensity of
Sound," in the Report of the British Association for the Advancement
of Science for 1857. The complete paper is as follows :

The remarkable diminution in the intensity of sound, which is produced
when a strong wind blows in a direction from the observer toward the
source of sound, is familiar to everybody, but has not hitherto been ex-
plained, so far as the author is aware. At first sight we might be disposed
to attribute it merely to the increase in the radius of the sound-wave which
reaches the observer. The whole mass of air being supposed to be carried
uniformly along, the time which the sound would take to reach the ob-
server, and consequently the radius of the sound-wave would be increased
by the wind in the ratio of the velocity of sound to the sum of the velocities
of soimd and of the wind, and the intensity would be diminished in the
inverse duphcate ratio. But the effect is much too great to be attributable
to this cause. It would be a strong wind whose velocity was a twenty-
fourth part of that of sound; yet even in this case the intensity would be
diminished by only about a twelfth part.

The first volume of the Annales de Chimie (1816) contains a paper
by M. Delaroche, giving the results of some experiments made on this
subject. It appeared from the experiments, first, that at small distances
the wind has hardly any perceptible effect, the sound being propagated
almost equally well in a direction contrary to the wind and in the direction
of the wind; second, that the disparity between the intensity propagated
in these two directions becomes proportionally greater and greater as the
distance increases; third, that sound is propagated rather better in a direc-
tion perpendicular to the wind than even in the direction of the wind. The
explanation offered by the author of the present communication is as
follows :

If we imagine the whole mass of air in the neighborhood of the source of
disturbance divided into horizontal strata, these strata do not move with
the same velocity. The lower strata are retarded by friction against the
earth and by the various obstacles they meet with; the upper by friction
against the lower, and so on. Hence, the velocity increases from the
ground upward, conformably with observation. This increase of velocity
disturbs the spherical form of the sound-wave, tending to make it some-
what of the form of an ellipsoid, the section of which by a vertical diametral
plane parallel to the direction of the wind is an ellipse meeting the ground
at an obtuse angle on the side towards which the wind is blowing, and an
acute angle on the opposite side.

Now, sound tends to propagate itself in a direction perpendicular to the
sound-wave; and if a portion of the wave is intercepted by an obstacle of
larger size the space behind is left in a sort of sound-shadow, and the only

122 ARCHITECTURAL ACOUSTICS

sound there heard is what diverges from the general wave after passing
the obstacle. Hence, near the earth, in a direction contrary to the wind,
the sound continually tends to be propagated upwards, and consequently
there is a continual tendency for an observer in that direction to be left in
a sort of sound-shadow. Hence, at a suflScient distance, the sound ought
to be very much enfeebled; but near the source of disturbance this cause
has not yet had time to operate, and, therefore, the wind produces no
sensible effect, except what arises from the augmentation in the radius of
the sound-wave, and this is too small to be perceptible.

In the contrary direction, that is, in the direction towards which the
wind is blowing, the sound tends to propagate itself downwards, and to be
reflected from the surface of the earth; and both the direct and reflected
waves contribute to the effect perceived. The two waves assist each other
so much the better, as the angle between them is less, and this angle van-
ishes in a direction perpendicular to the wind. Hence, in the latter direction
the sound ought to be propagated a little better than even in the direction
of the wind, which agrees with the experiments of M. Delaroche. Thus,
the effect is referred to two known causes, — the increased velocity of the
air in ascending, and the diffraction of sound.

As a matter of fact, the phenomenon is much more complicated
when one takes into consideration the fact that a wind is almost
always of very irregular intensities at different altitudes. The
phenomenon, in its most complicated form, has been investigated
in connection with the subject of fog signals by Professor Osborn
Reynolds and Professor Joseph Henry, but with this we are not at
present concerned, for the above discussion by Professor Stokes is
entirely sufficient for the problem in hand.

The essence of the above explanation is, therefore, this, that the
great difference in loudness of sound with and against the wind is
not due to the fact that the sound has been simply carried forward
or opposed by the wind, but rather to the fact that its direction has
been changed and its wave front distorted. The application of this
consideration in the present architectural problem leads to the con-
clusion that the greatest benefit will come not from an attempt to
carry the sound by the ventilating movement of the air, but by
using the motion of the air to incline the wave front forward and
thus direct the sound down upon the audience.

This can be done in either one of two ways, by causing the air
to flow through the room from front to back, more strongly at the

EFFECTS OF AIR CURRENTS 123

ceiling than at the floor, or by causing the air to flow from the back
to the front, more strongly at the floor than at the ceiling. The one
process carrying the upper part of the wave forward, the other re-
tarding the lower part of the wave, will tip the wave in the same
way and by an equal amount.

Again, taking an extreme case, the assumption will be made that
the motion of the air is such that it is not moving at or near the floor,
that it is moving with its maximum velocity at the ceiling, and that
the increase in velocity is gradual from floor to ceiling. Keeping
the same amount of air moving as in the preceding calculation, the
velocity of the air under this arrangement would be twice as great
as the average velocity at the ceiling; in the preceding case the
wave was advanced one centimeter by the motion of the air while
traveling the whole length of the hall. In this case, obviously, the
upper part of the wave would be carried twice as far, two centime-
ters, and the lower part not advanced at all. This would, therefore,
measure the total forward tip of the wave.

Fortunately, the acoustical value of this can be expressed in a
very simple and practical manner. An inclination of the sound-
wave is equivalent acoustically to an equal angular inclination of
the floor in the opposite direction. The height of the hall being
17.9 meters, the inclination forward of the sound-wave would be
2 in 1790. The length of the hall being 40 meters, an equal incli-
nation, and thus an equal acoustical effect would be produced by
raising the rear of the floor about 5 centimeters. This considers
only the sound which has come directly from the stage. It is ob-
vious that if the reflection of the .sound from the ceiling and the side
walls is taken into account, the gain is even less.

It, therefore, appears that, using the motion of the air in the
most advantageous way possible, the resulting improvement in the
acoustical property of the hall is of an amount absolutely negligible.
A negative result of this sort is perhaps not so interesting as if a
positive advantage has been shown; but the problem of properly
heating and ventilating a room is sufficiently difiBcult in itself, and
the above considerations are worth while if only to free it from this
additional complication.

124 ARCHITECTURAL ACOUSTICS

Temperature

The effect of raising the temperature of a room, involving as it
does the contained air and all the reflecting walls and objects, is
twofold. It is not diflficult to show that, whether we consider the
rise in temperature of the air or the rise in temperature of the walls
and other reflecting surfaces, the effect of a change of temperature
between the limits which an audience can tolerate is negligible,
provided the rise in temperature is uniform throughout the room.

The effect of uniformly raising the temperature of the air is to
increase the velocity of propagation of sound in all directions. It
is, therefore, essentially unlike the effect produced by motion of
the air. In the case of a uniform motion of the air, the sound spreads
spherically but with unchanged velocity, moving its center in the
direction and with the velocity of the wind. Thus, when blown
toward the observer, it reaches him as if coming from a nearer
source. Blown away from the observer, it arrives as from a more
distant source. An increasing temperature of the air increases the
velocity, but does not shift the center. The sound reaches the ob-
server coming from a source at an unchanged distance. A rise in
temperature, therefore, provided it be uniform, neither increases
nor decreases the apparent intensity of the sound. The intensity
at all points remains wholly unaltered.

The above is on the assumption that the temperature of the air
at all points is the same. If the temperature of the air is irregular,
the effect of such irregularity may be pronounced; for example, let
us assume a room in which the temperature of the air at the upper
levels is greater than at lower levels. In order to make the case as
simple as possible, let us assume that the temperature increases
uniformly from the floor to the ceiling. To make the case concrete,
let us assume that the hall is the same as that described above,
practically rectangular, 40 X 22.8 X 17.9 meters. The velocity of
the sound at the ceiling, the air being uniform, is greater than it is
at the floor. In traversing the room the sound-wave will thus be
tipped forward. The effect is practically equivalent as before to an
increased pitch of the floor or to an increased elevation of the plat-
form. Without going irito the details of this very obvious calcula-

EFFECTS OF AIR CURRENTS 125

tion, it is sufficient to say that in the case of the hall here taken as
an example, a difference of temperature top and bottom of 10° C.
would be equivalent to an increase in pitch of the floor sufficient to
produce an increased elevation of the very back of 10 centimeters.
A difference in temperature of 10° C. is not excessive, and it is obvi-
ous that this has a greater effect than has that of the motion of the
air.

In the above discussion of the effects of motion and of tempera-
ture on the acoustical quality of a room, it has been assumed that
we are dealing solely with the sound which has come directly from
the platform. The argument holds to a less degree for the sound
reflected from the ceiling and from the walls. The above estimates,
therefore, are outside estimates. The effect is on the whole cer-
tainly less. It is safe to say that the total attainable result is not
worth the effort that would be involved in altering the architectural
features or in compromising the engineering plans.

But, while uniform variation in the motion or in the temperature
of the air in the room are on the whole negligible factors in its acous-
tical character, this is by no means true of irregularities in the
temperature of the air, such as would be produced by a column of
warm air rising from a floor inlet. That this is a practical point is
shown by the testimony of Dr. David B. Reid before the Committee
of the Houses of Parliament published in its Report of 1835. This
committee was appointed to look into the matter of the heating,
ventilation and acoustics of the houses which were being designed
to replace those burned in 1832. Of the gentlemen called before
the committee. Dr. Reid gave by far the best testimony, part of
which was as follows.

Speaking of the hall temporarily occupied by the House of
Commons, he said: "Another source of interruption which might
be guarded against is the great body of air which I presume arises
whenever the heating apparatus is in action below. In different
buildings I have had occasion to remark that whenever the atmos-
phere was preserved in a state of unity as much as possible, equal
in every respect, the sound was most distinctly audible; it occurred
to me that when the current of hot air rises from the large ap-
paratus in the middle of the House of Commons it would very likely

126 ARCHITECTURAL ACOUSTICS

interfere with the communication of sound. On inquiry, one of the
gentlemen now present told me he had frequently observed it was
impossible to hear individuals who were on the opposite side of this
current, although those at a distance were heard distinctly where
the current did not intervene." Elsewhere Dr. Reid said: "A cur-
rent of hot air, rising in a broad sheet along the center of the House,
reflected the sound passing from side to side and rendered the in-
tonation indistinct. One of the members of the committee, when I
explained this circumstance, stated that he had often noticed that
he could not hear a member opposite him distinctly at particular
times unless he shifted his seat along the bench, and on examining
the place referred to, it was found that he had moved to a position
where the hot air current no longer passed between him and the
member speaking."

A more recent instance of this sort of diflBculty was mentioned
to the writer by Mr. W. L. B. Jenney, of Chicago, as occurring in
his practice, and later was described in detail in a letter from which
the following is quoted:

The building I referred to in my conversation was a court house at
Lockport. No plans exist as far as I am aware. Note the sketch I made
from remembrance.

Note the passage across the room with stove in center. As the courts
were held only during winter there was invariably a fire in that stove.
When I examined the room the attendant that was with me informed me
that the remarks made by the judge, lawyers and witness could not be
heard by the audience on the opposite side of the passageway containing
the stove.

At that time, the court room not being occupied, there was no fire in
the stove and the doors were closed. I experimented; put the attendant
in the judge's stand and took position at "A." I could hear perfectly well.
I spoke to him and he replied, "Why, I can hear you perfectly well." I
reached this conclusion. That the heated air from the stove and the air
supplied by the doors that were constantly fanning at each end of the
passageway produced a stratum of air of different density from that of
the other parts of the room, which acted like a curtain hanging between
the speakers and the hearers. I made my report verbally to the committee
that I left below and brought them with me to the room. The experiments
were renewed and they accepted my theory. I recommended that the
stove be moved and that the warm air should be let into the room from
steam coils below at the the end "A" and taken out by exhaust ventilators

EFFECTS OF AIR CURRENTS 127

at the end "B." This was done, and I was informed by the chairman of
the committee that the result was very satisfactory. The other conditions
of the room were quite usual, — plastering on wooden lath, wooden floors,
reasonable height of ceiling.

The above incidents seem to demonstrate fairly clearly that
under certain circumstances abrupt irregularities in temperature
may result in marked and, in general, unfavorable acoustical effects.
The explanation of these effects in both cases is somewhat as follows :

Whenever sound passes from one medium to another of different
density, or elasticity, a portion of the sound is reflected. The sound
which enters the second medium is refracted. The effects observed
above were due to these two phenomena, acting jointly.

The first of the two cases was under simpler conditions, and is,
therefore, the easier to discuss. Essentially, it consisted of a large
room with speaker and auditor facing each other at a comparatively
short distance apart, but with a cylindrical column of hot air rising
from a register immediately between. The voice of the speaker,
striking this column of air, lost a part by reflection; a part of the
sound passed on, entered the column of warm air, and came to the
second surface, where a part was again reflected and the remainder
went on to the auditor. Thus, the sound in traversing the column
of hot air lost by reflection at two surfaces and reached the auditor
diminished in intensity. It reached the auditor with diminished
intensity for another reason.

The column of warm air acted like a lens. The effect of the
column of air was not like that of the ordinary convex lens,
which would bring the sound to a focus, but rather as a diverging
lens. The effect of a convex lens would have been obtained had the
column of air been colder than that of the surrounding room. Be-
cause the air was warmer, and, therefore, the velocity of sound
through it greater, the effect was to cause the sound in passing
through the cylindrical colutain to diverge even more rapidly and
to reach the auditor very considerably diminished in intensity.
Which of these two effects was the more potent in diminishing the
sound, whether the loss by reflection or the loss by lens-like disper-
sion was the greater, could only be determined if one knew the tem-
perature of the air in the room, in the column, and the diameter of

128 ARCHITECTURAL ACOUSTICS

the column. It is sufficient, perhaps, to point out on the authority
of such eminent men as Dr. Reid and Mr. Jenney that the phenome-
non is a real one and one to be avoided, and that the explanation is
ready at hand and comparatively simple.

It is, perhaps, worth while pointing out that in both of the above
cases there was a good deal of reverberation in the room, so that
any considerable diminution in the intensity of the sound coming
directly from the speaker to the auditor resulted in its being lost
in the general reverberation. Had the same conditions as to loca-
tion of speaker, auditor, column of warm air and temperature
occurred out of doors or in a room of very slight reverberation the
effect would have been very much less noticeable. Nevertheless,
great irregularity of temperature is to be avoided, as the above
testimony fairly clearly shows.

The above also suggests another line of thought. If, instead of
having a single screen of great temperature difference between
speaker and auditor, there were many such differences in tempera-
ture, though slight in amount, the total effect might be great. This
corresponds, in the effect produced, to what Tyndall calls a "floccu-
lent condition of the atmosphere" in his discussion of the trans-
mission of fog signals. Tyndall points out that if the atmosphere
is in layers alternately warm and cold sound is transmitted with
much more rapid diminution in intensity than when the atmosphere
is of very uniform temperature. This phenomenon is, of course,
much more important with such temperature differences as occur
out of doors than in a room, but it suggests that, in so far as it is a
perceptible effect, the temperature of a room should be homogeneous.
This condition of homogeneity is best secured by that system of
ventilation known as "distributed floor outlets." It has the addi-
tional merit of being, perhaps, the most efficient system of ven-
tilation.

SENSE OF LOUDNESS^

It will be shown here that there is a sense of relative loudness, par-
ticularly of equality of loudness, of sounds differing greatly in pitch,
that this sense of loudness is accurate, that it is nearly the same for
all normal ears, that it is independent of experience, and that, there-
fore, it probably has a physical and physiological basis. This
investigation has been incidental to a larger investigation on the
subject of architectural acoustics. It has bearing, however, on
many other problems, such, for example, as the standardization of
noises, and on the physiological theory of audition.

The apparatus used consisted of four small organs (Proc. Am.
Acad, of Arts and Sciences, 1906) ^ so widely separated from each
other as to be beyond the range of each other's influence. Each
organ carried seven night-horn organ pipes at octave intervals in
pitch, 64, 128, 256, . . . 4096 vibrations per second. The four organs
were so connected electrically to a small console of seven keys that
on pressing one key, any one, any two, any three or all four organ
pipes of the same pitch would sound at once, — the combination of
organ pipes sounding being adjusted by an assistant and unknown
to the observer.

In other parts of the investigation on architectural acoustics the
loudness of the sound emitted by each of the twenty-eight organ
pipes in terms of the minimum audible sound for the corresponding
pitch had been determined. The experiment was conducted in the
large lecture-room of the Jefferson Physical Laboratory, and, in
the manner explained elsewhere, the computation was made for the
loudness of the sound, taking into account the shape of the room
and the materials employed in its construction.

The experiment consisted in adjusting the number of pipes which
were sounding or in choosing from among the pipes until such an
adjustment was accomplished, that, to an observer in a more or less
remote part of the room all seven notes, when sounded in succession,
seemed to have the same loudness. As the pipes of the same pitch

^ Contributions from the Jefferson Physical Laboratory, vol. viii, 1910.
2 See p. 84.

130 SENSE OF LOUDNESS

did not all have the same loudness, it was possible by taking various
combinations to make this adjustment with considerable accuracy.
This statement, however, is subject to an amendment in that all
four pipes of the lowest pitch were not suflficiently loud and the
faintest of the highest pitch was too loud.

There were ten observers, and each observer carried out four in-
dependent experiments. Speaking broadly, in the case of every
observer, the four independent experiments agreed among them-
selves with great accuracy. This was to the great surprise of every
observer, each before the trial doubting the possibility of such adjust-
ment. The results of all ten observers were surprisingly concordant.

After the experiment with the first two observers, it seemed
possible that their very close agreement arose from their familiarity
with the piano, and that it might be that they were adjusting the
notes to the "balance" of that particular instrument. The next
observer, therefore, was a violinist. Among the observers there was
also a 'cellist. Lest the feeling of relative loudness should come
from some subconscious feeling of vocal effort, although it is diffi-
cult to see how this could extend over so great a range as six octaves,
singers were tried whose voices were of very different register. Two
of the observers, including one of the pianists, were women. Two
of the observers were non-musical, one exceedingly so.

The accompanying table gives the results of the observations,
the energy of each sound being expressed in terms of minimum
audible intensity for that particular pitch, after making all correc-
tions for the reenforcement of the sound by the walls of the room.
The observations are recorded in order, the musical characteristic
of the observer being indicated.

PlTCH FkEQTJENCT

Observers

128

256

512

1024

204S

409

1. Piano

7.0(+)XlC< 1.7X10S 4.4X10" S.OXW 15.0X105 9.6X10= 4.5(-

2. Piano

7.0+

1.7

4.4

11.2

9.2

12.0

5.2-

3. Non-musical

7.0-t-

1.7

3.6

8.9

6.3

9.6

4.5-

4. Non-musical

7.0-1-

1.7

3.7

7.7

14.6

14.4

5.6-

5. Violin

7.04-

1.7

3.5

11.7

13.9

8.0

3.5-

6. Violin

7.0-1-

1.7

4.0

11.4

15.6

16.2

5.2-

7. 'Cello

7.0-h

1.7

4.2

12.0

13.4

9.6

5.1-

8. Tenor

7.0-1-

1.7

3.9

13.3

13.5

10.5

4.0-

9. Soprano

7.0+

1.7

4.7

12.9

17.0

9.6

5.4-

10. Piano

7.04-

1.7

3.5

13.2

14.6

8.0

4.9-

7.0(4-) 1.7 4.0 11.0 13.3 10.6 4.8-

ARCHITECTURAL ACOUSTICS^

CORRECTION OF ACOUSTICAL DIFFICULTIES

v/N the completion of the Fogg Art Museum in 1895, I was re-
quested by the Corporation of Harvard University to investigate
the subject of architectural acoustics with the end in view of cor-
recting the lecture-room which had been found impracticable and
abandoned as unusable. Later the planning of a new home for
the Boston Symphony Orchestra in Boston widened the scope of
the inquiry. Since then, over questions raised first by one building
and then another, the subject has been under constant investigation.

In 1900 a series of articles, embodying the work of the first five
years and dealing with the subject of reverberation, was published
in the American Architect and also in the Engineering Record. The
next five years were devoted to the extension of this study over the
range of the musical scale and the results were published in the Pro-
ceedings of the American Academy of Arts and Sciences in 1906.
Since then the investigation has been with reference to interference
and resonance, the effects of peculiarities of form, and the causes
of variation in audibility in different parts of an auditorium. These
results will be published in another article during the ensuing year.

The progress of this experimental investigation has been guided
in practical channels and greatly enriched by the experience gained
from frequent consultation by architects, either for purposes of
correcting completed buildings or in the preparation of plans in
advance of construction. Reserving for a later article the stimu-
lating subject of advance planning, the present article is devoted
to the problems involved in the correction of completed buildings.
It is illustrated by a few examples which are especially typical. I
desire to take this opportunity of expressing my appreciation of
the very cordial permission to use this material given by the archi-
tects, Messrs. McKlm, Mead & White, Messrs. Carrere & Hastings,
Messrs. Cram, Goodhue & Ferguson, and Messrs. Allen & CoUens

1 The Architectural Quarterly of Harvard University, March, 1912.

181

132 ARCHITECTURAL ACOUSTICS

— to these and to the other architects whose confidence in this work
has rendered an extensive experience possible.

The practical execution of this work of correction has recently
been placed on a firmer basis by Mr. C. M. Swan, a former graduate
student in the University and an associate in this work, who has
taken charge of a department in the H. W. Johns-Manville Com-
pany. I am under obligations to him and to this company for some
of the illustrations used below, and to the company, not merely for
having placed at my disposal their materials and technical experi-
ence, but also for having borne the expense of some recent investi^
gations looking toward the development of improved ma,terials,
with entire privilege of my making free publication of scientific
results.

It is proposed to discuss here only such corrective methods as
can be employed without extensive alterations in form. It is not
proposed to discuss changes of dimension, changes in the position
of the wall-surfaces or changes in ceiling height. It is the purpose
to discuss here medicinal rather than surgical methods. Such
treatment properly planned and executed, while not always avail-
able, will in the great majority of cases result in an entire remedy
of the difficulty.

Two old, but now nearly abandoned devices for remedying acous-
tical difficulties are stretched wires and sounding-boards. The
first is without value, the second is of some value, generally shght,
though occasionally a perceptible factor in the final result. The
stretching of wires is a method which has long been employed, and
its disfiguring relics in many churches and court rooms proclaim a
difficulty which they are powerless to reHeve. Like many other
traditions, it has been abandoned but slowly. The fact that it was
wholly without either foundation of reason or defense of argument
made it difficult to answer or to meet. The device, devoid on the
one hand of scientffic foundation, and on the other of successful
experience, has taken varied forms in its application. Apparently
it is a matter of no moment where the wires are stretched or in what
amount. There are theatres and churches in Boston and New
York in which four or five wires are stretched across the middle of
the room; in other auditoriums miles on miles of wire have been

ACOUSTICAL DIFFICULTIES

133

stretched; in both it is equally without effect. In no case can one
obtain more than a qualified approval, and the most earnest nega-
tives come where the wires have been used in the largest amount.
Occasionally the response to inquiries is that "the wires may have
done some good but certainly not much," and in general when even
that qualified approval is given the installation of the wires was

Fig. 1. Ceiling of church, San Jose, CaUfornia, showing an ineffective use of stretched wires.

accompanied by some other changes of form or occupancy to which
the credit should be given. How extensive an endeavor is sometimes
made in the use of stretched wires is shown by the accompanying
illustration which shows a small section of the ceiling of a church
in San Jose, California. In this church between one and two miles
of wire have been stretched with resulting disfigurement, and wholly
without avail. The question is being taken up again by the church
for renewed effort.

134

ARCHITECTURAL ACOUSTICS

Aside from such cumulative evidence of ineffectiveness, it is not
difficult to show that there is no physical basis for the device. The
sound, whose echoes these wires are presumed to absorb, scarcely
affects the wires, giving to them a vibration which at most is of
microscopical magnitude. If the string of a violin were free from
the body of the violin, if the string of a piano were free from the

Fig. 2. Congregational Church, Naugatuck, Connecticut. McKim, Mead and White, Architects.

sounding-board, if the string of a harp did not touch the thin sound-
ing-board which faces its slender back, when plucked they would
not emit a sound which could be heard four feet away. The sound
which comes from each of these instruments is communicated to
the air by the vibration of its special sounding-board. The string
itself cuts through the air with but the slightest communication of
motion. Conversely when the sound is in the room and the string
at rest the vibrating air flows past it, to and fro, without disturbing

ACOUSTICAL DIFFICULTIES

135

it, and consequently without itself being affected by reaction either
for better or worse.

The sounding-board as a device for correcting acoustical diffi-
culties has at times a value; but unless the sounding-board is to
be a large one, the benefit to be expected from its installation may
be greatly overrated. As this particular subject calls for a line of

Fig. 3. Hall of the House of Representatives, Rhode Island State Capitol, Providence, R. I.
McKim, Mead and White, Architects.

argument very different from that of the main body of the present
paper, it will be reserved for a discussion elsewhere, where, space
permitting, it can be illustrated by examples of various forms
accompanied by photographs and by a more or less exhaustive
discussion of their relative merits.

The auditorium in whose special behalf this investigation started
seventeen years ago was the lecture-room of the Fogg Art Museum.

136

ARCHITECTURAL ACOUSTICS

Although this room was in a large measure remedied, it will not be
taken as an example. Its peculiarities of shape were such that its
complete relief was inherently a complicated process. While this
case was chronologically the first, it is thus not suitable for an
opening illustration.

Among a number of interesting problems in advance of con-
struction the firm of McKim, Mead & White has brought some

Fig. 4.

Detail, Hall of the House of Representatives, Rhode Island State Capitol.
McKim, Mead and \\liite, Architects.

interesting problems in correction, of which three will serve ad-
mirably as examples because of their unusual directness. The first
is that of the Congregational Church in Naugatuck, Connecticut,
shown in the accompanying illustration. When built its ceiling
was cylindrical, as now, but smooth. Its curvature was such as to
focus a voice from the platform upon the audience, — not at a point,
but along a focal line, for a cylindrical mirror is astigmatic. The

ACOUSTICAL DIFFICULTIES 137

difficulty was evident with the speaking, but may be described
more efPectually with reference to the singing. The position of the
choir was behind the preacher and across the main axis of the
church. On one line in the audience, crossing the church obliquely
from right to left, the soprano voice could be heard coming even
more sharply from the ceiling than directly from the singer. The
alto starting nearer the axis of the church had for its focus a line
crossing the church less obliquely. The phenomena were similar for
the tenor and the bass voices, but with focal lines crossing the
church obliquely in opposite directions. The difficulty was in a
very large measure remedied by coffering the ceiling, as shown in
the illustration, both the old and the new ceiling being of plaster.
Ideally a larger and deeper coffering was desirable, but the solution
as shown was practical and the result satisfactory.

The hall of the House of Representatives in the Rhode Island
State Capitol illustrated another type of difficulty. In considering
this hall it is necessary to bear in mind that the problem is an essen-
tially different one from that of a church or lecture-room. In these
the speaking is from a raised platform and a fixed position. In a
legislative assembly the speaking is in the main from the floor, and
may be from any part of the floor; the speaker stands on a level
with his fellow members; he stands with his back to a part of the
audience, and often with his back to the greater part of his audience;
in different parts of the house the speaker directs his voice in dif-
ferent directions, and against different wall-surfaces. In this hall
the walls were of stone to approximately half the height of the
room; above that they were of stone and plaster. The ceiling was,
as shown, coffered. The difficulty in this room was with that part
of the voice which, crossing the room transversely, fell on the side
walls. With the speaker standing on the floor, the greater volume
of his voice was directed upward. The sound striking the side wall
was reflected across the room to the opposite wall and back again,
to and fro, mounting gradually until it reached the ceiling. It was
there reflected directly down upon the audience. The ceiling
sloped, and had some curvature, but the curvature was not such
as to produce a distinct focusing of the sound. During these re-
flections the sound met only feebly absorbent surfaces and there-
fore returned to the audience with but little loss of intensity. Its

138

ARCHITECTLTRAL ACOUSTICS

return was at such an interval of time as to result in great confusion
of speech. Onlj' the fact that the voice, rising at different angles,
traveled different paths and therefore returned at varying inter-
vals, prevented the formation of a distinct echo. The difficulty
was remedied in this case by a change in material without change

Fig. 5. Lecture-room, Metropolitan Museum of Art, New York.
McKim, Mead and White, Architects.

of form, by diminishing the reflecting power of the two side walls.
This was done by placing a suitable felt on the plaster walls between
the engaged columns, and covering it with a decorated tapestry.
Fortunately, the design of the room admitted of a charming exe-
cution of this treatment. It is interesting to note that this treat-
ment applied to the lower half of the walls would not have been
acousticallv effective.

ACOUSTICAL DIFFICULTIES

139

The lecture-room of the Metropolitan Museum of Art illus-
trates the next step in complexity. This hall is a semi-circular
auditorium, with the semi-circle slightly continued by short,
straight walls. As shown in the illustrations the platform is nearly,
though not wholly, within a broad but shallow recess. The body

Fig. 6. Lecture-room, Metropolitan Museum of Art, New York.
McKim, Mead and White, Architects.

of the auditorium is surmounted by a spherical ceiling with short
cylindrical extension following the straight side walls. In the
center of the ceiling is a flat skylight of glass. In this room the re-
verberation was not merely excessive, but it resolved itself by focus-
ing into a multiple echo, the components of which followed each
other with great rapidity but were distinctly separable. The

140 ARCHITECTURAL ACOUSTICS

number distinguishable varied in different parts of the hall. Seven
were distinguishable at certain parts. A detailed discussion of this
is not appropriate in the present paper as it concerns rather the
subject of calculation in advance of construction. To improve the
acoustics the ceiling was coffered, the limiting depth and dimensions
of this coffering being determined in large measiu-e by the dimen-
sions of the skylight. The semi-circular wall at the rear of the
auditorium was transformed into panels which were filled with
felt over which was stretched burlap as shown in the second illus-
tration. The result was the result assured, — the reduction of the
disturbance to a single and highly locahzed echo. This echo is
audible only in the central seats — two or three seats at a time —
and moves about as the speaker moves, but in symmetrically opposite
direction. Despite this residual effect, and it should be noted that
this residual effect was predicted, the result is highly satisfactory to
Dr. Edward Robinson, the Director of the Museum, and the room is
now used with comfort, whereas it had been for a year abandoned.

It should be borne in mind that "perfect acoustics" does not
mean the total eUmination of reverberation, even were that possible.
Loudness and reverberation are almost, though not quite, propor-
tional quahties. The result to be sought is a balance between the
two qualities, dependent on the size of the auditorium and the use
to which it is to be apphed.

Geometrically the foregoing cases are comparatively simple. In
each case the room is a simple space bounded by plane, cylindrical
or spherical surfaces, and these surfaces simply arranged with refer-
ence to each other. The simplicity of these cases is obvious. The
complexity of other cases is not always patent, or when patent it is
not obvious to a merely casual inspection how best the problem
should be attacked. A large number of cases, however, may be
handled in a practical manner by regarding them as connecting
spaces, each with its own reverberation and pouring sound into and
receiving soimd from the others. An obvious case of this is the
theatre, where the aggregate acoustical property is dependent on
the space behind the proscenium arch in which the speaker stands,
as well as on the space in front of it. In another sense and to a less
degree, the cathedral, with its chancel, transept and nave may be

Fig. 7. Design for St. Paul'.s Cathedral, Detroit. Cram, Goodhue and Ferguson. Architects.

142 ARCHITECTURAL ACOUSTICS

regarded as a case of connected spaces. The problem certainly takes
on a simpler aspect when so attacked. An extreme and purely hy-
pothetical case would be a deep and wide auditorium with a very
low ceiling, and with a stage recess deep, high and reverberant, in
fact such a case as might occur when for special purposes two very
different rooms are thrown together. In such a case the reverbera-
tion calculated on the basis of a single room of the combined volume
and the combined absorbing power would yield an erroneous value.
The speaker's voice, especially if he stood back some distance from
the opening between the two rooms, would be lost in the production
of reverberation in its own space. The total resulting sound, in a
confused mass, would be propagated out over the auditorium. Of
course this is an extreme case and of unusual occurrence, but by its
very exaggeration serves to illustrate the point. In a less degree
it is not of infrequent occurrence. It was for this reason, or rather
through the experience of this effect, although only as a nice refine-
ment, that the Boston Symphony Orchestra has its special scenery
stage in Carnegie Hall, and for this that Mr. Damrosch in addition
moved his orchestra some little distance forward into the main
auditorium for his concerts in the New Theatre.

A cathedral is a good example of such geometrical complication,
still further complicated by the variety of service which it is to
render. It must be adapted to speaking from the pulpit and to
reading from the lectern. It must be adapted to organ and vocal
music, "and occasionally to other forms of service, though generally
of so minor importance as to be beyond the range of appropriate
consideration. Most cathedrals and modern large chiu-ches have
a reverberation which is excessive not only for the spoken but also
for a large portion of the musical service. The difficulty is not
peculiar to any one type of architecture. To take European ex-
amples, it occurs in the Classic St. Paul in London, the Romanesque
Durham, the Basilican Romanesque Pisa, the Italian Gothic Flor-
ence, and the English Gothic York.

The most interesting example of this type has been Messrs. Cram,
Goodhue & Ferguson's charming cathedral in Detroit, especially
interesting because in the process of correcting the acoustics it was
possible to carry to completion the decoration of the original design.

Fig. 8. St. Paul's Cathedral, Detroit. Cram, Goodhue and Ferguson, Architects.

144 ARCHITECTURAL ACOUSTICS

The nave, moderately narrow in the clerestory, was broad below
through its extension by side aisles. It might fairly be regarded
as two simply connected spaces. The lower space, when there was
a full audience, was abundantly absorbent; the clerestory, though
with wood ceiling, was not absorbent. Although their combined
reverberation was great, it was not so great as alone to produce the
actual effect obtained. Absorbing material in the form of a felt,
highly efficient acoustically, was placed in the panels on the ceiling.
The original architectural design by Mr. Cram (Fig. 7) showed the
ceiling decorated in colors, and this though not a part of the original
construction was carried out on the covering of the felt, with a re-
sult highly satisfactory both acoustically and architecturally. The
transept, also high and reverberant, was similarly treated, as was
also the central tower which was even higher than the rest of the
church. As a matter of fact the results at first attained were satis-
factory only with an audience filling at least three-quarters of the
seats, the condition for which it was planned. The treatment was
subsequently extended to the lower levels in order that the cathedral
might be serviceable not merely for the normal but for the occa-
sionally small audience. The chancel did not need and did not
receive any special treatment. It was highly suitable to the musical
service, and being at the back of both the pulpit and the lectern did
not greatly affect that portion of the service which called for dis-
tinctness of enunciation.

It may be remarked in passing that the lectern is almost invari-
ably a more diflScult problem than the pulpit. This is in part be-
cause reading, with the head thrown slightly forward, is more
difficult than speaking; because, if the lectern is sufficiently high
to permit of an erect position it screens the voice; because a speaker
without book or manuscript, seeing his audience, realizes his dis-
tance and his difficulties; and finally, because the pulpit is generally
higher and against a column whereas the lectern stands out free and
unsupported.

The auditorium which has received the greatest amount of dis-
cussion recently is the New Theatre in New York. Had it been a
commercial proposition its acoustical quality would have received
but passing notice. As an institution of large purpose on the part

ACOUSTICAL DIFFICULTIES 145

of the Founders it received a correspondingly large attention. As
an institution of generous purpose, without hope or desire for finan-
cial return, it was appropriated by the public, and received the
persistent criticism which seems the usual reward for such under-
takings. The writer was consulted only after the completion of
the building, but its acoustical difficulties can be discussed ade-
quately only in the light of its initial programme.

It was part of the original programme submitted to Messrs.
Carrere & Hastings that the building should be used, or at least
should be adapted to use for opera as well as for drama. In this
respect it was to bear to the Metropolitan the position which the
Opera Comique in Paris bears to the Opera. This idea, with its
corollary features, influenced the early design and shows in the
completed structure.

It was also a part of the initial plan that there should be two
rows of boxes, something very unusual in theatre construction.
This was a prodigal use of space and magnified the building in all
its dimensions. Later, but not until after the building was nearly
completed, the upper row of boxes was_ abandoned, and the gallery
thus created was devoted to foyer chairs. As the main walls were
by this time erected, the gallery was limited in depth to the boxes
and their antechambers. It thus resulted that this level, which is
ordinarily occupied by a gallery of great value, is of small capacity.
Notwithstanding this the New Theatre seats twenty-three hun-
dred, while the usual theatre seats but little more than two-thirds
that number.

The necessity of providing twenty-three commodious boxes, all
in the first tier, of which none should be so near the stage as to be
distinctly inferior, determined a large circle for their front and for
the front of all the galleries. Thus not merely are the seats, which
are ordinarily the best seats, far from the stage, but the great hori-
zontal scale thus necessitated leads architecturally to a correspond-
ingly great vertical scale. The row of boxes and the foyer balcony
above not merely determined the scale of the auditorium, but also
presented at the back of their shallow depth a concave wall which
focused the reflected sound in the center of the auditorium.

Finally, it should be borne in mind that while the acoustical

146

ARCHITECTURAL ACOUSTICS

demands in a theatre are greater than in almost any other type of
auditorium, because of the great modulation of the voice in dra-
matic action, the New Theatre was undertaking an even more
than usually difficult task, that of presenting on the one hand the
older dramas with their less familiar and more difficult phrasing,
and on the other the more subtle and delicate of modern plays.

Fig. 9. Interior, the New Theatre, New York City. Carrere and Hastings, Architects.

The conventional type of theatre construction is fairly, though
only fairly, well adapted to the usual type of dramatic performance.
The New Theatre, with a verj^ difficult type of performance to
present, was forced by the conditions which surrounded the project
to depart horn the conventional type far more radically than was
perhaps at that time realized.

Here, as usual in a completed building, structural changes and
large changes of form were impossible, and the acoustical difficulties

ACOUSTICAL DIFFICULTIES

147

of the auditorium could be remedied only by indirection. The
method by which a very considerable improvement was attained
is shown by a comparison of the line drawing (Fig. 10) with the pho-
tograph of the interior of the theatre as originally completed. The
boxes were changed from the first to the second level, being inter-
changed with the foyer chairs, while the excessive height of the
main body of the auditorium was reduced by means of a canopy
surrounding the central chandelier. This ingenious and not dis-

FiG. 10. The New Theatre, New York City, showing Canopy and Changed Boxes.

pleasiag substitute for the recommended lowering of the ceiling was
proposed by Mr. Hastings, although of course only as a means to
an end. The canopy is oval in plan, following the outline of the
oval panel in the ceiling, its longer axis being transverse. Its major
and minor horizontal dimensions are 70 feet and 40 feet. Its
effective lowering of the height of the ceiling is 20 feet. A moment's
consideration will show that its effective area in preventing the
ceiling echo is greater than its actual dimensions, particularly in

148 ARCHITECTURAL ACOUSTICS

the direction of its minor axis. The improvem.ent brought about
by this was pronounced and satisfactory to the Founders. The
distances, however, were still too great, even visually, for the type
of dramatic performance for which the theatre was primarily in-
tended, and such use was therefore discontinued. The New Theatre
is much better adapted to opera than to dramatic performances,
and it will be a matter of great regret if, with its charming solution
of many difficult architectural problems, it is not restored to such
dignified purpose.

The last and very satisfactory example is that of the Chapel of
the Union Theological Seminary of Messrs. Allen & Collens. Its
interesting feature is that the corrective treatment was applied in
the process of construction. It is further interesting as an example
of a treatment which is not merely inconspicuous, but is entirely
indistinguishable. The photograph without explanation is the best
evidence of this (p. 149).

The above examples have been chosen from many score as typical
of the principles involved. In each case the nature of the difficulty
has been stated and the method employed in its correction, or at
least its special feature very briefly described. The remainder of
the paper will be devoted to a discussion of the principles involved
in acoustical correction and in presenting the results of some recent
experiments.

In discussing the above examples, especially the first and the
third, the Congregational Church in Naugatuck, and the lecture-
room of the Metropolitan Museum of Art, consideration had to be
given to the effect of the geometrical shape of the room. This
aspect of the problem of architectural acoustics constitutes a sub-
ject so large that a separate paper must be devoted to its adequate
treatment. It involves not merely simple reflection but inter-
ference and diffraction, as well as the far from simple subject of the
propagation of sound parallel to or nearly parallel to the plane of
an audience. It has been the object of special investigation during
the past six years. This investigation has recently come to a suc-
cessful issue and will probably be published in full during the en-
suing year. It is suitable that it should receive separate publication
for, as it concerns shape, it is of more value for calculation in ad-

Fig. 11. Chapel, Union Theological Seminary, New York City. Allen and Collcns, Architects.

150 AECHITECTURAL ACOUSTICS

vance of construction than in the correction of completed buildings.
It must here suffice to merely indicate the nature of the results.

When sound is produced in a confined auditorium it spreads
spherically from the source until it reaches the audience, the walls,
or the ceiling. It is there in part absorbed and in part reflected.
The part which is reflected retraverses the room until it meets
another surface. It is again in part absorbed and in part reflected.
This process continues until, after a greater or less number of
reflections, the sound becomes of negligible intensity. Thus at any
one time and at any one point in the room there are many sounds
crossing each other. In a very simple auditorium, such as a simple
rectangular room with plain walls and ceiling, this process is not
difficult to follow, either step by step, or by large, but entirely
adequate, generalizations. When the conditions are more compli-
cated it is more difficult to analyze; it is also more liable to be a
vitally significant factor in the problem. That it has heretofore
been inadequately discussed has arisen from the failure to take into
consideration the phenomenon of diffraction in the propagation of
a sound nearly parallel to an absorbing audience, the phenomenon
of diffraction in reflection from an irregular surface, and, above all,
the phenomenon of interference. The first of these three considera-
tions is of primary importance in calculating the intensity of the
sound which has come directly from the source, in calculating the
effect of distance in the audience, and in calculating the relative
loudness on the floor and in the gallery, and at the front and at the
back of the gallery. The second consideration enters into the cal-
culation of the path of the soimd after reflection from any broken
or irregular surfaces. The third is a factor of the utmost impor-
tance when the sounds which are crossing at any point in the audi-
torium are of comparable intensity and have traveled paths of so
nearly equal length that they have originated from the same ele-
ment. This latter calls for a more elaborate explanation.

In both articulate speech and in music the source of sound is
rapidly and in general, abruptly changing in pitch, quality, and
loudness. In music one pitch is held during the length of a note.
In articulate speech the unit or element of constancy is the syllable.
Indeed, in speech it is even less than the length of a syllable, for the

ACOUSTICAL DIFFICULTIES 151

open vowel sound which forms the body of a syllable usually has a
consonantal opening and closing. During the constancy of an ele-
ment, either of music or of speech, a train of sound-waves spreads
spherically from the source, just as a train of circular waves spreads
outward from a rocking boat on the surface of still water. Different
portions of this train of spherical waves strike different surfaces of
the auditorium and are reflected. After such reflection they begin
to cross each other's paths. If their paths are so different in length
that one train of waves has entirely passed before the other arrives
at a particular point, the only phenomenon at that point is pro-
longation of the sound. If the space between the two trains of
waves be suflBciently great the effect will be that of an echo. If
there be a number of such trains of waves thus widely spaced, the
effect will be that of multiple echoes. On the other hand if the two
trains of waves have traveled so nearly equal paths that they over-
lap, they will, dependent on the difference in length of the paths
which they had traveled, either reenforce or mutually destroy each
other. Just as two equal trains of water-waves crossing each other
may entirely neutralize each other if the crest of one and the trough
of the other arrive together, so two sounds, coming from the same
soiu-ce in crossing each other may produce silence. This phenom-
enon is called interference and is a common phenomenon in all
types of wave motion. Of course this phenomenon has its comple-
ment. If the two trains of water-waves so cross that the crest of
one coincides with the crest of the other and trough with trough,
the effects will be added together. If the two sound-waves be simi-
larly retarded, the one on the other, their effects will also be added.
If the two trains of waves be equal in intensity, the combined in-
tensity will be quadruple that of either of the trains separately, as
above explained, or zero, depending on their relative retardation.
The effect of this phenomenon is to produce regions in an audito-
rium of loudness and regions of comparative or even complete silence.
It is a partial explanation of the so-called deaf regions in an audi-
torium.

It is not difficult to observe this phenomenon directly. It is
difficult, however, to measure and record the phenomenon in such
a manner as to permit of an accurate chart of the result. Without

152

ARCHITECTURAL ACOUSTICS

going into the details of the method employed the result of these
measurements for a room very similar to the Congregational Church
in Naugatuck is shown in the accompanying chart. The room
experimented in was a simple rectangular room with plain side

Fig. 13. Distribution of intensity on the head level in a room
with a barrel-shaped ceiling, with center of curvature on the
floor level.

walls and ends and with a barrel or cylindrical ceiling. The ceiling
of the room was smooth like the ceiling of the Naugatuck Church
before it was coflFered. The result is clearly represented in Fig. 12,
in which the intensity of the soimd has been indicated by contour
lines in the manner employed in the drawing of the Geodetic Survey

ACOUSTICAL DIFFICULTIES 153

maps. The phenomenon indicated in these diagrams was not
ephemeral, but was constant so long as the source of sound con-
tinued, and repeated itself with almost perfect accuracy day after
day. Nor was the phenomenon one which could be observed merely
instrumentally. To an observer moving about in the room it was
quite as striking a phenomenon as the diagrams suggest. At the
points in the room indicated as high maxima of intensity in the
diagram the sound was so loud as to be disagreeable, at other points
so low as to be scarcely audible. It should be added that this dis-
tribution of intensity is with the source of sound at the center of
the room. Had the source of sound been at one end and on the axis
of the cylindrical ceiling, the distribution of intensity would still
have been bilaterally symmetrical, but not symmetrical about the
transverse axis.

As before stated a full discussion of this phase of the subject is
reserved for another paper which is now about ready for publication.

In the second, in the fourth, and in part in the third of the above
examples the acoustical diflBculty was that of excessive reverberation.

If a sound of constant pitch is maintained in an auditorium,
though only for a very brief time, the sound spreading directly
from the source, together with the sound which has been reflected,
arrives at a steady state. The intensity of the sound at any one
point in the room is then the resultant of all the superposed sounds
crossing at that point. As just shown, the mutual interference of
these superposed sounds gives a distribution of intensity which
shows pronounced maxima and minima. However, the probable
intensity at any point, as well as the aggregate intensity over the
room, is the sum of the components. Whatever the distribution of
maxima and minima the state is a steady one so long as the source
continues to sound. The steady condition in the room is such that
the rate of absorption of the soimd is equal to the rate of emission
by the source.

If after this steady state is established the source is abruptly
checked, the different trains of waves will continue their journey,
the maxima and minima shifting positions. Ultimately, the sound
will cease to be audible, having diminished in intensity until it has
passed below what aurists call the "threshold of audibility." The

154 ARCHITECTURAL ACOUSTICS

duration of audibility after the source has ceased is thus dependent
upon the initial intensity, upon the absorbing material, and upon
the location of that absorbing material with reference to the several
trains of waves. In special cases the position of the absorbing ma-
terial is a matter of the utmost importance, but in many cases the
aggregate result may be computed on the basis of the total absorbing
power in the room.

The prolongation of the sound in an auditorium after the source
has ceased 1 have ventured to call reverberation, and to measure it
numerically by the duration of audibility after the abrupt cessation
of a source which has produced an average intensity of sound in the
room equal to one million times minimum audible intensity. This
is an ordinary condition in actual occurrence.

In the 1900 papers published in the Engineering Record and the
American Architect, this subject of reverberation was discussed at
great length, and it was there shown how it might be measured and
indeed, how it might be calculated in advance of construction. In
addition to the formula many coefficients of absorption were de-
termined, such data being absolutely necessary to the reduction of
the subject to an exact science. This work related to sounds having
a pitch an octave above middle C.

But it was of course obvious that the acoustical quality of an
auditorium is not determined by its character with reference to a
single note. The next series of papers, published in 1906, therefore
extended the investigation over the whole range of the musical scale
giving data for many materials and wall-surfaces, and rendering a
more complete calculation possible. At the conclusion of these
papers it was shown how the reverberation of an auditorium should
be represented by a curve in which the reverberation is plotted
against the pitch and by way of illustration a particular case was
shown, that of the large lecture-room in the Jefferson Physical
Laboratory, both with and without an audience. This curve is
reproduced in the accompanying diagram (Fig. 13).

In the process of investigating an auditorium such a curve
should be drawn as definitive of its initial condition and then in the
determination of the treatment to be employed similar curves
should be drawn representing the various alterations proposed and

ACOUSTICAL DIFFICULTIES

155

taking into consideration the location of the surfaces, their areas
and the nature of the proposed treatment. The diagram (Fig.
14) shows the result of this computation for the more inter-
esting of the above examples, St. Paul's Cathedral, Detroit. In
this diagram curves are drawn plotting the reverberation of the

1-— ==== =

C C,

Fig. 13. Curves showing the reverberation in the lecture-
room of the Jefferson Physical Laboratory without an
audience and with an audience filling all the seats.

cathedral in its original condition, empty, and with a three-quarters
audience, and with a full audience, and again after its acoustical
correction also empty, with a three-quarters audience, and with a
full audience.

Reprints of the papers just mentioned were mailed at the time
to all members of the American Institute of Architects. Duplicates

156

AECHITECTURAL ACOUSTICS

will gladly be sent to any one who may be interested in the further
perusal of the subject.

Brief mention has been made of the dependence, in special cases,
of the eflBciency of an absorbing material on its positions in an au-
ditorium. For example, in the room whose distribution of intensity

\
\
\
\
\

^
•
•

\ \
\ \
\ \

_ •

\
>

\
\

,,'--

***!»

z^y^~

-3 --.

s;N

— -^

-4

^4-

c, o, c, c.

Fig. 14. Curves showing the reverberation in St. Paul's
Cathedral, Detroit, before (1', 2', 3', 4') and after (1, 2,
3, 4) corrections, empty and with a one-quarter, one-
half, three-quarter and full audience.

was shown in Fig. 12, the absorbing material would have much
greater eflSciency in reducing the reverberation if placed so as to
include maxima, than if so placed as to include minima. That this
would be true is obvious. The magnitude of the eflPect, however, is
not so clear, for the maxima and minima shift as the sound dies

ACOUSTICAL DIFFICULTIES

157

away. It was therefore submitted to an accurate experimental
investigation. The results are shown in the adjacent diagram.

.0
a

1
1

1
/

'^\

(

\
3
\

c„ c,

Fig. 15. Showing the relative efficiency of felt in differ-
ent parts of a room having a barrel ceiling. Ciirve 1,
normal absorbing power; Curve 2, absorbing power in
the center of the room; Curve 3, absorbing power at
the side of the room. Ca is middle C, 256.

Fig. 15. In this diagram the curve marked 1 shows by its vertical
ordinates the normal eflSciency of a very highly absorbent felt. If

158

ARCHITECTURAL ACOUSTICS

so placed in the room as to include on its surface the maxima of
intensity of the sound it had an eflfective absorbing power as shown
in Curve 2, a truly remarkable increase over its normal value.
Curve 3 shows the efficiency of the same felt when placed against
the side wall. It there included more maxima than minima for the

1.0

^•.\

^»N

""■

0. c,

Fig. 16. Absorbing power of various kinds of felt as de-
fined in the text. C3 is middle C, 256.

lower notes, but more minima than maxima for the higher notes,
with a resulting efficiency curve which is very irregular.

The following experiments were performed for the H. W. Johns-
Manville Company in the search for an efficient absorbing material
and an effective method of treatment. The absorbing efficiency of
felt is dependent on the flexibility of the mass as a whole and on its
porosity. It is not in large measure dependent on the material

ACOUSTICAL DIFFICULTIES

159

employed, except in so far as the nature of that material determines
the nature, and therefore the closeness, of the felting process. The
same materials, therefore, might very well have either a very high
or a very low absorbing efficiency, depending entirely upon the
process of manufacture. The nature of the material is here specified,

.6
.6

.3
2

c, c.

0, c,

Fig. 17. Effect of air space behind felt. Curve 1, felt in
contact with the wall; Cvirves 2, 3, and 4, felt at dis-
tances of 2, 4, and 6 inches from the wall.

not with the idea that it alone can determine the quality, but merely
as an additional piece of information. In addition to this, in each
case the ratio of the solid material to the free space is given; but
even this does not define in full the essential conditions. The ab-
sorbing power is determined not merely by the ratio of the air space
to the soHd material, but by the size of the pores and by the elas-

160

ARCHITECTURAL ACOUSTICS

ticity and viscosity of the mass as a whole. In Fig. 16 Curve 1 is
a hair felt, the one alluded to above as of exceptional efficiency.
The fraction of its total volume, which is solid material, is 0.12.
Curve 2 is a mixture of hair felt and asbestos, whose solid portion is

1.0

.8
.8
.7
.6

.5
.4
.3

/ 3
\

f A

\ \

"-4^

—

y^'

Fig. 18. Curves showing the effect on absorbing power
of membrane covering. Curve 1, felt; Curve 2, burlap
cemented with silicate of soda; Ciu-ve 3, light mem-
brane as described; Ciurve 4, heavy membrane as de-
scribed; lower Curve 3, light membrane alone; lower
Curve 4, heavy membrane alone.

0.19 of its total volume. Curve 3 is a felt wholly of asbestos
thickness, whose solid portion is 0.33 of its total volume. In this
latter the asbestos fiber is felted to an asbestos cloth which serves
to strengthen it greatly. Curve 4 is for an asbestos felt without
reenforcement. That a considerable fraction of its absorbing power

ACOUSTICAL DIFFICULTIES 161

is due to its elastic yielding as a whole is shown by its rather sharp
maxima.

The curves in Fig. 17 show the effect of holding the felt at differ-
ent distances from the wall. In each case it was held on a wire
grating. Curve 1 is when the felt is as near the wall as the grating
would permit, perhaps within a quarter of an inch of the wall.
Curve 2 is when the felt was held at a distance of two inches; Curve
3 at four inches; and Curve 4 at six inches from the wall. It is
evident that there is a slight gain from an air space behind the felt,
but it is also evident that this gain is so slight as to be entirely
incommensurate with the cost of construction and its loss in dur-
ability.

The Curves in Fig. 18 show the efficiency of various coverings.
Curve 1 is the normal exposed efficiency of the felt above referred
to. Curve 2 is its efficiency when covered by burlap attached by
silicate of soda. This covering was so sized as to be practically
impervious, but was in contact with and a part of the felt. Curves 3
and 4 show the efficiency of coverings which are not in contact with
the felt, but which are stretched. Both coverings are impervious, —
3 relatively light, 4 heavy. Number 3 weighs 0.87 ounces to the
square foot; number 4 weighs 2.58 ounces to the square foot. The
materials of which these coverings are made have no bearing on the
question, and would be misleading if stated. The really significant
factors are their weight, the tension with which they are stretched,
their elasticity, and their viscosity. The weight of the several
coverings has been stated; the other factors can be defined best by
means of their independent absorbing powers. Lower curves 3 and 4
indicate the absorbing power of the membrane coverings alone.
It is interesting to note that the diaphragm which has by itself the
least absorbing power has the greatest absorbing power when
combined with the felt. This is by no means a paradox. It is
exactly the result which could be predicted by application of the
simplest of physical principles.

THEATRE ACOUSTICS^

ViTRtrvitrs, De Architectura, Liber V, Cap. VIII. (De locis con-
sonaniibus ad theatra eligendis.)

" All this being arranged, we must see with even greater care that a
position has been taken where the voice falls softly and is not so reflected
as to produce a confused effect on the ear. There are some positions offer-
ing natural obstructions to the projection of the voice, as for instance the
dissonant, which in Greek are termed KarrixowTes ; the circumsonant, which
with them are named wipirixovvTts ; and again the resonant, which are termed
avrrixovvres. The consonant positions are called by them avvrixovPTes.

The dissonant are those places in which the sound first uttered is carried
up, strikes against solid bodies above, and, reflected, checks as it falls the
rise of the succeeding sound.

The circumsonant are those in which the voice spreading in all direc-
tions is reflected into the middle, where it dissolves, confusing the case
endings, and dies away in sounds of indistinct meaning.

The resonant are those in which the voice comes in contact with some
solid substance and is reflected, producing an echo and making the case
terminations double.

The consonant are those in which the voice is supported and strength-
ened, and reaches the ear in words which are clear and distinct."

This is an admirable analysis of the problem of theatre acoustics.
But to adapt it to modern nomenclature, we must substitute for the
word dissonance, interference; for the word circumsonance, rever-
beration; for the word resonance, echo. For consonance, we have
unfortunately no single term, but the conception is one which is fun-
damental.

It is possible that in the above translation and in the following
interpretation I have read into the text of Vitruvius a definiteness of
conception and an accord with modern science which his language
only fortuitously permits. If so, it is erring on the better side, and is
but a reasonable latitude to take under the circumstances. The only
passage whose interpretation is open to serious question is that re-

* The American Architect, vol. civ, p. 257.
168

164 THEATRE ACOUSTICS

lating to dissonant places. If Vitruvius knew that the superposition
of two sounds could produce silence, and the expression "opprimit
insequentis vocis elationem" permits of such interpretation, it must
stand as an observation isolated by many centuries from the modern
knowledge of the now familiar phenomenon of interference.

Interference

Interference is a phenomenon common to all types of wave motion.
The best introduction to its discussion is by reference to water-waves

Fig. 2. Greek Theatre at the University of Cahfornia. Mr. John Galen Howard, Architect.

and in particular to an interesting example of tidal interference on
the Tongking Peninsula. The tide of the Pacific Ocean enters the
Chinese Sea through two channels, one to the north of the Philippine
Islands, between Luzon and Formosa, and the other through the
Sulu Archipelago between Mindanao and Borneo. The northern
channel is short and deep; and the tide enters with very little re-
tardation. The other channel, although broad, is shallow, tortuous,
and broken by many small islands; and the tide in passing through
is much retarded. The two tides thus entering the Chinese Sea pro-
duce an effect which varies from point to point. At one port on the
Tongking Peninsula, these tides are so retarded relatively to each
other as to be six hours apart. It is high tide by one when it is low
tide by the other. It also so happens that at this point the two tides

THEATRE ACOUSTICS 165

are equal. Being equal and exactly opposite in phase, they neutralize
each other.

Because tidal waves are long in comparison with the bodies of
water in which they are propagated, their interference phenomena
are obscure except to careful analysis. When, however, the waves
are smaller than the space in which they are being propagated, the
interference system becomes more marked, more complicated, and
more interesting. Under such circumstances, there may be regions
of perfect quiet near regions of violent disturbance.

Subjecting the parallel to a more exact statement, whenever two
water-waves come together the resulting disturbance at any instant
is equal to the algebraic sum of the disturbances which each would
produce separately. If their crests coincide, the joint effect is equal
to the sum of their separate effect. If crest and trough coincide, their
joint effect is the difference between them. If their relative retarda-
tion is intermediate, a wave results which is intermediate between
their sum and their difference and whose time of maximum does not
occur simultaneously with the maximum of either of the components.

The phenomenon is one which may be produced accurately on
any scale and with any type of wave motion. Thus sound consists
of waves of alternate condensation and rarefaction in the air. If two
trains of sound-waves cross each other so that at a given point con-
densation in the two trains arrive simultaneously, the rarefactions
will also arrive simultaneously, and the total disturbance is a train
of waves of condensation and rarefaction equal to the sum of the two
components. If one train is retarded so that its condensations coin-
cide with the other's rarefactions, the disturbance produced is the
difference between that which would be produced by the trains of
waves separately. Just as a tidal wave, a storm wave, or a ripple
may be made to separate and recross by some obstacle round which
it diffracts or from which it is reflected, and recombining produce
regions of violent and regions of minimum disturbances, so sound-
waves may be diffracted or reflected, and recombining after travel-
ling different paths, produce regions of great loudness and regions of
almost complete silence. In general, in an auditorium the phenom-
enon of interference is produced not by the crossing of two trains of
waves only, but by the crossing of many, reflected from the various

166 THEATRE ACOUSTICS

walls, from the ceiling, from the floor, from any obstacle whatever
in the room, while still other trains of waves are produced by the
diffraction of the sound around columns and pilasters.

A source of sound on whose steadiness one can rely is all that is
necessary in order to make the phenomenon of interference obvious,
A low note on a pure toned stop of a church organ will serve the
purpose admirably. The observer can satisfy himself that the note
is sounding steadily by remaining in a fixed position. As soon, how-
ever, as he begins to move from this position by walking up and down
the aisle he will observe a great change in loudness. Indeed, he may
find a position for one ear which, if he closes the other, will give al-
most absolute silence, and this not far from positions where the
sound is loud to the extent of being disagreeable. The observer in
walking about the church will find that the phenomenon is compli-
cated. It is, however, by no means random in its character, but
definite, permanent, and accurate in its recurrence, note for note.
The phenomenon, while difficult, is by no means impossible of experi-
mental investigation or of theoretical solution. Indeed, this has been
done with great care in connection with the study of another prob-
lem, — that of the Central Criminal Court Room in London known as
Old Bailey. The full primary explanation of the methods and results
of this general investigation would be inappropriately long in an
article dealing with the acoustics of theatres; for while interference
is a factor in every auditorium, it is on the whole not the most
seriously disturbing factor in theatre design.

The subject of interference would not have been given even so
extended a discussion as this in a paper dealing with tJieatres were
it not that recently there has been proposed in Germany a form of
stage setting known as the Kuppel-horizont for sky and horizon
effects, to accompany the Fortuny system of stage lighting, in which
interference may be a not inconsiderable factor unless guarded
against. The Fortuny system, which in the opinion of some com-
petent judges is an effective form of stage lighting, consists primarily
in the use of indirect illumination, softened and colored by reflection
from screens of silk. As an adjunct to the system, and in an en-
deavor to secure a considerable depth to the stage without either
great height or an excessive use of sky and wing flies, a cupola is

THEATRE ACOUSTICS

167

recommended to go with the Fortuny lighting as shown in the ac-
companying figures taken from the pubhcations of the Berliner Alle-
gemeine Electridtats Gesellschaft. In Figs. 3 and 4, the cupola is
shown in section and in plan. Lights A and B illuminate the interior
of the cupola; C and E light the area of the stage on which the prin-

CUSTAlNORAPeK''-

UNDCe STAdL irACt.

.SECTION

•- PLAN

Figs. 3 and 4. Section and plan of the Kuppel-Horizont
with Fortuny system of lighting.

cipal action occurs. Cloud effects, either stationary or moving, are
projected on the surface of the cupola by a stereopticon. The great
advantage claimed for this form of stage setting is the more natural
arrangement of stage properties which it makes possible, and the
elimination of numerous flies. On the other hand there is some criti-
cism that this lighting results in an unnatural silhouetting.

168

THEATRE ACOUSTICS

So detailed an explanation of the diagrams and the purpose of the
several parts is necessitated by the fact that it is as yet an unfamiliar
device in this country. It has been introduced recently in a number
of theatres in Gennany, although I believe not elsewhere, unless
possibly in one theatre in England. It has been called to my atten-
tion by Professor Baker as a possible equipment of the theatre which

Fig. 5. Interference system for tenor C in the Kuppel-Horizont,
having a thirty-six foot proscenium opening. The intensity
of sound is represented by contour Unes, the maximum vari-
ation being forty-seven fold.

is proposed for the dramatic department of Harvard University, and
it is reasonable to regard it as a probable factor in theatre design in
other countries than Germany.

In Fig. 5 is plotted the interference system established in this
space, on a standing head level of five feet from the floor of the stage,
by a sustained note tenor C in pitch. The intensity of the sound is
indicated by contour lines very much as land elevation is indicated
on the maps of the Geodetic Survey. In this plot, account has been
taken of the sound reflected from the cupola and from the floor. No
account has been taken of the reflection from the walls of the main
auditorium since this would be a factor only for sounds prolonged
beyond the length of any single element in articulate speech. Even
in the case of a very prolonged sound the modification of the inter-

THEATRE ACOUSTICS 169

f erence system of the stage and cupola by the rest of the auditorium
would be very slight.

The interference system on the stage in question being deter-
mined wholly by the floor and cupola, it may be computed, and in
the preparation of the chart was computed, by the so-called method
of images. The sound reflected from the floor comes as from a virtual
image as far beneath the floor as the mouth of the speaker is above
it. Each of these produce real images by reflection from the interior
of the cupola. Bearing in mind that these real images show the
phenomenon of diffraction and some astigmatism, and taking into
account the phase of the sound as determined by reflection and by
distance, the calculation is laborious but not difficult. It involves
but the most familiar processes of geometrical optics.

The disturbing effect of this interference system is not so great
when the speaker is well in front of the center of curvature of the
cupola, and of course it is almost always more or less broken by the
stage properties, as indicated in Figs. 3 and 4. Nevertheless, it is
well to bear in mind that the quarter sphere form, as indicated in the
diagrams, is neither necessary from the standpoint of illumination
nor desirable from the standpoint of acoustics. Acoustically a flatter
back with sharper curvature above and at the sides is preferable.

It should be repeated that the interference system is established
only when the tones are sustained, in this case over one-tenth of a
second, and is more of an annoyance to the actor on the stage than
to the audience. With shorter tones it becomes an echo, and in this
form is quite as annoying to the audience as to the actor. It should
be added that the interference changes with change of pitch, but
preserves extreme maxima and minima for a central position in a
spherical or partly spherical surface. Finally in music, since sus-
tained tones occur more than in speech, the interference is more dis-
turbing. The effect of such spherical stage recesses on music is
shown by those otherwise unusually excellent auditoriums. Orches-
tra Hall in Chicago, and the Concert Hall at Willow Grove Park
near Philadelphia.

170 THEATRE ACOUSTICS

Reverberation

" Circumsonant places" were rare and almost wholly negligible
difficulties in Greek and Roman theatres. However, they were com-
mon in the temples, and were even more pronounced in some of the
older Roman palaces. It must have been in the experience of such
conditions, wholly foreign to the theatre of which he was writing,
that Vitruvius made this portion of his analysis of the acoustical
problem. Given the fundamental form of the Greek theatre, it re-
quired no special consideration and little or no skill to avoid such
difficulties. However, this is not true of the modern theatre, in which
excessive reverberation is more often the defect than any other
factor.

If a sound be produced briefly in a wholly empty, wholly closed
room, having perfectly rigid walls, it will be reflected at each inci-
dence with undiminished intensity, and, travelling to and fro across
the room, will continue audible almost indefinitely. Of course no
theatre, ancient or modem, satisfies these conditions and the sound
loses at each reflection, diminishing in intensity, until in the course of
time it crosses what the experimental psychologist calls the "thresh-
old of audibility." In the Greek theatres the duration of audibility
of the residual sound after the cessation of a source of ordinary loud-
ness was never more than a few tenths of a second; in a modem
theatre it may be several seconds. The rapidity with which the
sound dies away depends on the size of the theatre, on its shape, on
the materials used for its waUs, ceiling, and furnishings, and on the
size and distribution of the audience. The size and shape of the
theatre determines the distance travelled by the sound between
reflections, while the materials determine the loss at each reflec-
tion. No actual wall can be perfectly rigid. Wood sheathing,
plaster on wood lath, plaster on wire lath, plaster apphed directly
to the sohd wall, yield under the vibrating pressure of sound and
dissipate its energy. Even a wall of solid marble yields slightly,
transmitting the energy to external space or absorbing it by its own
internal viscosity.

Absorptions by the walls and other objects in the process of reflec-
tion, including in this transmission through all openings into outer

THEATRE ACOUSTICS 171

space as equivalent to total absorption — boundary conditions in
other words — are practically alone to be credited with the dissolu-
tion of the residual sound. But Vitruvius' statement that the
sound "is reflected into the middle, where it dissolves" challenges
completeness and at least the mention of another factor, which,
because of its almost infinitesimal importance, would otherwise be
passed without comment.

Assuming, what is of course impossible, a closed room of ab-
solutely rigid and perfectly reflecting walls, a sound once started
would not continue forever, for where the air is condensed by the
passing of the wave of sound, it is heated, and where it is rarefied, it
is cooled. Between these unequally heated regions and between
them and the walls, there is a continual radiation of heat, with a re-
sulting dissipation of available energy. In the course of time, but
only in the course of a very long time, the sound would even thus
cease to be of audible intensity. This form of dissipation might well
be caUed in the language of Vitruvius "solvens in medio"; but, in-
stead of being an important factor, it is an entirely negligible factor
in any actual auditorium.

Practically the rapidity with which the sound is absorbed is de-
pendent solely on the nature of the reflecting surfaces and the length
of the path which the sound must traverse between reflections, the
latter depending on the shape and size of the auditorium. It was
shown in a series of papers published in The American Architect in
1900,^ and in another paper published in the Proceedings of the Amer-
ican Academy of Arts and Sciences in 1906,^ that, given the plans of
an auditorium and the material of which it is composed, it is possible
to calculate with a very high degree of accuracy the rate of decay of
a sound in the room and the duration of its audibility. In the first of
the above papers there was given the complete theory of the subject,
together with tables of experimentally determined coefficients of ab-
sorption of sound for practically all the materials that enter into
auditorium construction, for sounds having a pitch one octave above
middle C (vibration frequency 512). In the second of the above
papers there were given the coefficients of absorption of building
materials for the whole range of the musical scale.

1 See page 69. ' Ibid.

172

THEATRE ACOUSTICS

In the careful design of a room for musical purposes, the problem
obviously must include the whole range of the musical scale, at least
seven octaves. It is not so obvious that the study must cover so
great a range when the primary use is to be with the spoken voice.
The nearest study to architectural acoustics is the highly developed
science of telephony, and in this it is apparently sufficient for much
of the work to adapt the theory and design to the single frequency of
800, approximately A in the second octave above middle C. But for

Fig. 6. The Little Theatre, New York. Ingalls and Hoffman, Architects.

some problems the investigation must be extended over a consider-
able range of pitch. Similarly experience in the architectural prob-
lem shows that with some of the materials entering into building con-
struction there occurs a sharp resonance within a not great range of
pitch. It is, therefore, necessary to determine the reverberation even
for the speaking voice, not for a single pitch but for a considerable
range, and the quality of a theatre with respect to reverberation will
be represented by a curve in which the reverberation is plotted
against the pitch.

Without undertaking to give again a complete discussion of the
theory of reverberation, and referring the reader to the earlier (1900)
numbers of The American Architect, it will suffice to give a single

Figs. 7 and 8. Plan and Section of the Little Theatre, New York.
Ingalls and Hoffman, Architects.

174 THEATRE ACOUSTICS

illustration. For this I have selected Mr. Winthrop Ames' "Little
Theatre" in New York, designed by Messrs. Ingalls and HoflFman,
because the purpose and use of this auditorium was defined from the
beginning with unusual precision. The purpose was the production
of plays which could be adequately rendered only by the most deli-
cate shades of expression, which would be lost in considerable meas-
ure if the conditions were such as to necessitate exaggeration of
feature or of voice. The definition of its use was that it should seat
just less than 300, and that all the seats were to be as nearly as
possible of equal excellence, with the important assurance that every
seat would be occupied at every performance.

The final plan and section of the Little Theatre are shown in
Figs. 7 and 8. The initial pencil sketch was of an auditorium differ-
ing in many architectural details, acoustical considerations sharing
in, but by no means alone dictating, the steps leading to the final
solution of the problem. The first calculations, based on the general
lines of the initial sketch, and assuming probable materials and plaus-
ible details of construction (plaster on tile walls, plaster on wire lath
ceiling, solid plaster cornices and moulding), gave a reverberation as
shown in Curve 1 in Fig. 9. This would not have been in excess of
that in many theatres whose acoustical qualities are not especially
questioned. But the unusual requirements of the plays to be pre-
sented in this theatre, and the tendency of the public to criticize
whatever is unconventional in design, led both Mr. Ames and the
architects to insist on exceptional quality. The floor was, therefore,
lowered at the front, the ceiling was lowered, and the walls near the
stage brought in and reduced in curvature, with, of course, corre-
sponding changes in the architectural treatment. The rear wall,
following the line of the rear seats, remained unchanged in curvature.
The side walls near the stage were curved. The net effect of these
changes was to give an auditorium 28 feet high in front, 23 feet high
at the rear, 48 feet long and 49 feet broad, with a stage opening 18
by 31, and having a reverberation as shown by Curve 2. In order to
reduce still further the reverberation, as well as to break acoustically
the curvature of the side and rear walls, "acoustic felt" was applied
in panels. There were three panels, 6 feet by 13 feet, on each of the
side walls, and seven panels, two 4 feet 5 inches by 13 feet, two 5

THEATRE ACOUSTICS

175

feet by 10 feet, two 2 feet by 4 feet, and one 8 feet by 7 feet, on the
rear wall. The resulting reverberation is shown by Curve 3 in the
diagram. Throughout, consideration was had for the actual path of
the sound in its successive reflections, but the discussion of this

■

]

-a

-3 —

Fig. 9. Eeverberation in seconds of the Little Theatre,
for notes of different pitch, C3 being Middle C, Curve 1
for the first design. Curve 2 for the second, and Curve
3 for the third and as built.

phase of the general problem comes in the next section and will be
illustrated by other theatres.

It should be said, parenthetically but none the less emphatically,
that throughout this paper by theatre is meant an auditorium for
the spoken drama.

176

THEATRE ACOUSTICS

Echo

When a source of sound is maintained constant for a suflBciently
long time — a few seconds will ordinarily suffice — the sound be-
comes steady at every point in the room. The distribution of the
intensity of sound under these conditions is called the interference

Fig. 10. Interior, the New Theatre, New York. Carrere and Hastings, Architects.

system, for that particular note, of the room or space in question.
If the source of sound is suddenly stopped, it requires some time for
the sound in the room to be absorbed. This prolongation of sound
after the source has ceased is called reverberation. If the source of
sound, instead of being maintained, is short and sharp, it travels as
a discrete wave or group of waves about the room, reflected from
wall to wall, producing echoes. In the Greek theatre there was ordi-

THEATRE ACOUSTICS

177

narily but one echo, "doubling the case ending," while in the modern
theatre there are many, generally arriving at a less interval of time
after the direct sound and therefore less distinguishable, but stronger
and therefore more disturbing.

This phase of the acoustical problem will be illustrated by two
examples, the New Theatre, the most important structure of the

kind in New York, and the plans of the theatre now building for the
Scollay Square Realty Company in Boston.

Notwithstanding the fact that there was at one time criticism of
the acoustical quality of the New Theatre, the memory of which
still Hngers and still colors the casual comment, it was not worse in
proportion to its size than several other theatres in the city. It is,
therefore, not taken as an example because it showed acoustical de-
fects in remarkable degree, but rather because there is much that
can be learned from the conditions under which it was built, because
such defects as existed have been corrected in large measure, and

178

THEATRE ACOUSTICS

above all in the hope of aiding in some small way in the restoration
of a magnificent building to a dignified use for which it is in so many
ways eminently suited. The generous purpose of its Founders, the
high ideals of its manager in regard to the plays to be produced, and
the perfection otherwise of the building directed an exaggerated and
morbid attention to this feature. Aside from the close scrutiny which

Fig. 12

always centers on a semi-public undertaking, the architects, Messrs.
Carrere and Hastings, suffered from that which probably every archi-
tect can appreciate from some similar experience of his own, — an
impossible program. They were called on to make a large "little
theatre," as a particular type of institution is called in England; and,
through a division of purpose on the part of the Founders and Ad-
visers, for the Director of the Metropolitan Opera was a powerful
factor, they were called on to make a building adapted to both the
opera and the drama. There were also financial diflBculties, although
very different from those usually encountered, a plethora of riches.
This necessitated the provision of two rows of boxes, forty-eight
originally, equally commodious, and none so near the stage as to

THEATRE ACOUSTICS

179

thereby suffer in comparison with the others. Finally, there was a
change of program when the building was almost complete. The
upper row of boxes was abandoned and the shallow balcony thus
created was devoted to foyer chairs which were reserved for the

Fig. 13. Plans and Section of the New Theatre, New York.
Carr&'e and Hastings, Architects.

annual subscribers. As will be shown later these seats were acousti-
cally the poorest in the house.

Encircling boxes are a familiar arrangement, but most of the
precedents, especially those in good repute, are opera houses and
not theatres, the opera and the drama being different in their acous-
tical requirements. In the New Theatre this arrangement exerted a
three-fold pressure on the design. It raised the balcony and gallery 12
feet. It increased both the breadth and the depth of the house. And,
together with the requirement that these boxes should not extend

180 THEATRE ACOUSTICS

near the stage, it led to side walls whose most natural architectural
treatment was such as to create sources of not inconsiderable echo.
The immediate problem is the discussion of the reflections from
the ceiling, from the side walls near the stage, from the screen and
parapet in front of the first row of boxes and from the wall at the
rear of these boxes. To illustrate this I have taken photographs of
the actual sound and its echoes passing through a model of the

Fig. 14. Photograph of a sound-wave, WW, entering a model
of the New Theatre, and of the echoes oi, produced by the
orchestra screen, a^ from the main floor, ns, from the floor
of the orchestra pit, at, the reflection from the orchestra
screen of the wave aa, 05 the wave originating at the edge of
the stage.

theatre by a modification of what may be called the Toeppler-Boys-
Foley method of photographing air disturbances. The details of the
adaptation of the method to the present investigation will be ex-
plained in another paper. It is sufficient here to say that the method
consists essentially of taking off the sides of the model, and, as the
sound is passing through it, illuminating it instantaneously by the
light from a very fine and somewhat distant electric spark. After
passing through the model the light falls on a photographic plate
placed at a little distance on the other side. The light is refracted by
the sound-waves, which thus act practically as their own lens in pro-
ducing the photograph.

In the accompanying illustrations reduced from the photographs
the enframing silhouettes are shadows cast by the model, and all

Fig. 15

Fig. 18

Fig. 16

Fig. 19

, , ' ■ ' vj ^^vsyyjiysWiissfl

^£

Fig. 17

Fig. 20

Two series of photographs of the sound and its reflections in the New Theatre, — 1.5 to 17 before, 18 to 20 after
the installation of the canopy in the ceiling. The effect of the canopy in protecting the balcony, foyer chairs,
boxes, and the orchestra chairs back of row L is shown by comparing Figs. 19 and 20 with Figs. 16 and 17.

182 THEATRE ACOUSTICS

within are direct photographs of the actual sound-wave and its
echoes. For example, Fig. 14 shows in silhouette the principal longi-
tudinal section of the main auditorium of the New Theatre. WW is
a photograph of a sound-wave which has entered the main auditorium
from a point on the stage at an ordinary distance back of the pros-
cenium arch; Ui, is the reflection from the solid rail in front of the
orchestra pit, and a-i, the reflection from the floor of the sound which
has passed over the top of the rail; a^ is the reflection from the floor

Fig. 21. Photograph of the direct sound, WW, and of the
echoes from the various surfaces; 02,2, a wave, or echo, due
to the combination of two waves which originated at the
orchestra pit; Ci from the oval panel in the ceiling; Ca and
C3, from the ceiling mouldings and cornice over the prosce-
nium arch; Cj, a group from the moulding surrounding the
panel; rj, from the proscenium arch; bi, 62, ^6 from the
screens in front, and the walls in the rear of the boxes,
balcony and gallerj'.

of the pit, and 04 the reflection of this reflected wave from the rail;
while as originated at the edge of the stage. None of these reflections
are important factors in determining the acoustical quality of the
theatre, but the photograph affords excellent opportunity for show-
ing the manner in which reflections are formed, and to introduce the
series of more significant photographs on page 181.

Figures 15, 16, and 17 show the advance of the sound through the
auditorium at .07, .10, and .14 second intervals after its departure

THEATRE ACOUSTICS 183

from the source. In Fig. 15, the waves which originated at the
orchestra pit can be readily distinguished, as well as the nascent
waves where the primary sound is striking the ceiling cornice imme-
diately over the proscenium arch. The proscenium arch itself was
very well designed, for the sound passed parallel to its surface.
Otherwise reflections from the proscenium arch would also have
shown in the photograph. These would have been directed toward
the audience and might have been very perceptible factors in deter-
mining the ultimate acoustical quality.

The system of reflected waves in the succeeding photograph in
the series is so complicated that it is diflBcult to identify the several
reflections by verbal description. The photograph is, therefore, re-
produced in Fig. 21, lettered and with accompanying legends. It is
interesting to observe that all the reflected waves which originated
at the orchestra pit have disappeared with the exception of waves
ttj and az. These have combined to form practically a single wave.
Even this combined wave is almost negligible.

The acoustically important reflections in the vertical section are
the waves Ci, C2, and C3. The waves 61 and 62 from the screen in front
of the boxes and from the back of the boxes are also of great impor-
tance, but the peculiarities of these waves are better shown by photo-
graphs taken vertically through a horizontal section.

The waves Ci, C2, Cs, and 61 and 62 show in a striking manner the
fallacy of the not uncommon representation of the propagation of
sound by straight lines. For example, the wave Ci is a reflection from
the oval panel in the ceiling. The curvature of this panel is such
that the ray construction would give practically parallel rays after
reflection. Were the geometrical representation by rays an ade-
quate one the reflected wave would thus be a flat disc equal in area
to the oblique projection of the panel. As a matter of fact, however,
the wave spreads far into the geometrical shadow, as is shown by
the curved portion reaching well out toward the proscenium arch.
Again, waves c^, and C3 are reflections from a cornice whose irregular-
ities are not so oriented as to suggest by, the simple geometrical
representation of rays the formation of such waves as are here clearly
shown. But each small cornice moulding originates an almost hemi-
spherical wave, and the mouldings are in two groups, the position of

184 THEATRE ACOUSTICS

each being such that the spherical waves conspire to form these two
master waves. The inadequacy of the discussion of the subject of
architectural acoustics by the construction of straight lines is still
further shown by the waves reflected from the screens in front of the
boxes, of the balcony, and of the gallery. These reflecting surfaces
are narrow, but give, as is clearly seen in the photograph, highly
divergent waves. This spreading of the wave beyond the geometrical
projection is more pronounced the smaller the opening or the reflect-
ing obstacle and the greater the length of the wave. The phenom-
enon is called diffraction and is, of course, one of the well-known
phenomena of physics. It is more pronounced in the long waves of
sound than in the short waves of light, and on the small areas of an
auditorium than in the large dimensions of out-of-door space. It
cannot be ignored, as it has been heretofore ignored in all discussion
of this phase of the problem of architectural acoustics, with im-
punity. The method of rays, although a fairly correct approximation
with large areas, is misleading under most conditions. For example,
in the present case it would have predicted almost perfect acoustics
in the boxes and on the main floor.

Figures 17 and 20 show the condition in the room when the main
sound-wave has reached the last seat in the top gallery. The wave
Ci has advanced and is reaching the front row of seats in the gallery,
producing the effect of an echo. A little later it will enter the balcony,
producing there an echo greater in intensity, more delayed, and
affecting more than half the seats in the balcony, for it will curve
under the gallery, in the manner just explained, and disturb seats
which geometrically would be protected. Still later it will enter the
foyer seats and the boxes. But the main disturbance in these seats
and the boxes, as is well shown by the photograph, arises from the
wave d, and in the orchestra seats on the floor from the wave C3.

In the summer following the opening of the theatre, a canopy,
oval in plan and slightly larger than the ceiling oval, was hung from
the ceihng surrounding a central chandelier. The effect of this in
preventing these disturbing reflections is shown by a comparison,
pair by pair, of the two series of photographs. Figs. 15 to 17 and
Figs. 18 to 20. It is safe to say that there are few, possibly no
modern theatres, or opera houses, equal in size and seating capacity.

Fig. 22

Fig. 25

Fig. 23

Fig. 26

Fig. 24

Fig. 27

Photographs showing the reflections, in a vertical plane, from the sides of the proscenium
arch, the plain wall below the actors' box, and the rail or screen in l^ront of the boxes.
The photographs taken in numerical sequence show the progress of a single sound-wave
and its reflections.

186 THEATRE ACOUSTICS

which are so free from this particular type of disturbance as the New
Theatre at the present time.

In the study of the New Theatre, photographs were taken through
several horizontal sections. It will be sufficient for the purposes of
the present paper to illustrate the effect of curved surfaces in pro-
ducing converging waves by a few photographs showing the propa-
gation of sound through a single section in a plane passing through
the parapet in front of the boxes. The reflected waves shown in

Fig. 28. A photograph, one of many taken, showing
in vertical section one stage of the reflection bi.
Fig. 21. These reflections were eliminated by the
architects in the summer following the opening
of the theatre, but have been in part restored by
sulisequent changes.

Fig. 22 originating from the edge of the proscenium arch and from
the base of the column can be followed throughout all the succeeding
photographs. In Fig. 23 are shown waves originating from the plain
wall beneath the actor's box and the beginning of some small waves
from the curved parapet. It is easily possible, as it is also interesting
and instructive, to follow these waves through the succeeding photo-
graphs. In Fig. 25 the sound has been reflected from the rear of the
parapet; while in Fig. 26 it has advanced further down the main
floor of the auditorium, narrowing as it proceeds and gaining in in-
tensity. The waves reflected from the parapet outside of the aisles
are here shown approaching each other behind the wave which has
been reflected from the parapet between the aisles. Waves are also
shown in Fig. 26 emerging from the passages between the boxes.

THEATRE ACOUSTICS 187

Indeed, it is possible to trace the waves arising from a second reflec-
tion from the proscenium arch of the sound which, first reflected
from the corresponding surfaces on the other side, has crossed di-
rectly in front of the stage. With a Uttle care, it is possible also to
identify these waves in the last photograph.

Although many were taken, it will suffice to show a Single photo-
graph. Fig. 28, of the reflections in the plane passing through the
back of the boxes. These disturbing reflections were almost entirely
eliminated in the revision of the theatre by the removal of the boxes
from the first to the second row and by utilizing the space vacated
together with the anterooms as a single balcony filled with seats.

An excellent illustration of the use of such photographs in plan-
ning, before construction and while all the forms are still fluid, is to
be found in one of the theatres now being built in Boston by Mr.
C. H. Blackall, who has had an exceptionally large and successful
experience in theatre design. The initial pencil sketch. Fig. 29, gave
in the model test the waves shown in the progressive series of photo-
graphs. Figs. 31 to 33. The ceiling of interpenetrating cylinders was
then changed to the form shown in finished section in Fig. 30, with
the results strikingly indicated in the parallel series of photographs.
Figs. 34 to 36. It is, of course, easy to identify all the reflections in
each of these photographs, — the reflections from the ceiling and the
balcony front in the first; from the ceiling and from both the balcony
and gallery front in the second; and in the third photograph of the
series, the refiections of the ceiling reflection from the balcony and
gallery fronts and from the floor. But the essential point to be ob-
served, in comparing the two series pair by pair, is the almost total
absence in the second series of the ceiling echo and the relatively
clear condition back of the advancing sound-wave.

Consonance

Consonance is the process whereby, due to suitably placed reflect-
ing walls, "the voice is supported and strengthened." It is the one
acoustical virtue that is positive. It is also the characteristic virtue
of the modern theatre, and that through which this complicated
auditorium surmounts the attendant evils of interference, reverbera-
tion, and echo. Yet such is our modern analysis of the problem that

188

THEATRE ACOUSTICS

we do not even have for it a name. On the other hand, it is the virtue
which the Greek theatre has in least degree. It is, therefore, all the
more interesting that it should have been included in the analysis of
Vitruvius, and should have received a name sO accurately descriptive.
Indeed, one can hardly make explanation of the phenomenon better
than through the very type of theatre in which its lack is the one
admitted defect.

The Greek theatre enjoys a not wholly well-founded reputation
for extremely good acoustics. In most respects it is deserved; but

Fig. 29. Section in pencil sketch of Scollay Square Theatre, Boston.
Mr. C. H. Blackall, Architect.

the careful classical scholar, however gratified he may be by this
praise of a notable Greek invention, regards himself as barred by
contemporaneous evidence from accepting for the theatre unquali-
fied praise. Every traveler has heard of the remarkable quality of
these theatres, and makes a trial wherever opportunity permits, be
it at beautiful Taormina, in the steep sloped theatre at Pompeii, the
great theatre at Ephesus, or the "little theatre" on the top of Tus-
culum, — always with gratifying results and the satisfaction of hav-
ing confirmed a well-known fact. Perhaps it is useless to try to
traverse such a test. But there is not a theatre in Italy or Greece
which is not in so ruined a condition today that it in no way what-
ever resembles acoustically its original form. If its acoustics are

THEATRE ACOUSTICS

189

perfect today, they certainly were not originally. Complete " scaena "
and enclosing walls distinctly altered the acoustical conditions. The
traveler has in general tested what is little more than a depression
in the ground, or a hollow in a quiet country hillside. As a matter of
fact, the theatre in its original form was better than in its ruined
state. Still, with all its excellencies it was not wholly good. Its
acoustical qualities were not wholly acceptable to its contemporaries.

Fig. 30. Finished section of Scollay Square Theatre, Boston.] Mr. C. H. Blackall, Architect.

and would be less acceptable in a modern theatre, and for modern
drama.

The difficulty with such casual evidence is that it is gathered
under wholly abnormal conditions. Not only are the ruins but scant
reminders of the original structure, but the absence of a large audi-
ence vitiates the test, as it would vitiate a test of any modern theatre.
But while in a modern auditorium the presence of an audience almost
always, though not invariably, improves the acoustics, in the classical
theatre the presence of an audience, in so far as it has any effect, is

190 THEATRE ACOUSTICS

disadvantiagebus. The eflPect of an audience is always twofold, — it
diminishes the reverberation, and it diminishes the loudness or in-
tensity of the voice. In general, the one effect is advantageous, the!
other disadvantageous. But in the Greek theatre, occupied or un-
occupied, ruined or in its original form, there was very little rever-
beration. In fact, this was its merit. On the other hand, the very
fact that there was little reverberation is significant that there was
very slight architectural reenforcement of the voice. One might well
be unconvinced by such a priori considerations were there not ex-
cellent evidence that these theatres were not wholly acceptable
acoustically even in their day, and for drama written for and more
or less adapted to them. Excellent evidence that there was insuffi-
cient consonance is to be found in the megaphone mouthpieces used
at times in both the tragic and the comic masks, and in the proposal
by Vitruvius to use resonant vases to strengthen the voice.

The doubt is not as to whether a speaker, turned directly toward
the audience and speaking in a sustained voice, could make himself
heard in remote parts of a crowded Greek theatre. It is almost cer-
tain that he could do so, even in the very large and more nearly level
theatres, such as the one at Ephesus. Better evidence of this than
can be found in the casual test of a lonely ruin is the annual per-
formance by the staff of the Comedie FranQaise in the theatre at
Orange. But even this, the best preserved of either Greek or Roman
theatres, is but a ruin, and its temporary adaptation for the annual
performance is more modern than classical. A much better test is in
the exercises regularly held in the Greek Theatre of the University of
California, designed by Mr. John Galen Howard, of which President
Wheeler speaks in most approving terms. The drama, especially
modern drama, diflFers from sustained speech and formal address in
its range of utterance, in modulation, and above all in the require-;
ment that at times it reaches the audience with great dynamic quality
but without strain in enunciation. Mere distinctness is not sufficient;
It was through a realization of this that the megaphone mouthpiece
was invented, — awkward in use and necessarily destructive of many
of the finer shades of enunciation. That it was only occasionally used
proves that it was not a wholly satisfactory device, but does not dfe^.
tract its evidence of weakness in the acoustics of the theatre.. ' , '[

Fig. 31

Fig. 34

Fig. 32

Fig. 35

Fig. 33

Fig. 36

Two series of photographs showiag, Figs. 31-33, the reflections which would have resulted from the exe-
cution of the first pencil sketch of the Scollay Square Theatre (Fig. 29), and. Figs. 3-t-3G, from the
execution of the second sketch by Mr. Blackall (shown in finished section in Fig. 30).

192 THEATRE ACOUSTICS

The megaphone mouthpiece bears to the acoustics of the Greek
theatre the same evidence, only in a reciprocal form, that the mask
itself bears to the theatre's illumination. It was not possible to see
in bright daylight, particularly in the bright sunlight of the Mediter-
ranean atmosphere, with anything like the accuracy and detail pos-
sible in a darkened theatre with illuminated stage. The pupil of the
eye was contracted, and the sensitiveness of the retina exhausted by
the brilliancy of the general glare. Add to this that the distance from
the stage was very much greater in the Greek than in the modern
theatre, audience for audience, and one can realize the reason for the
utter impossibility of facial expression in Greek dramatization except
by artificial exaggeration. The heaviness and inflexibility of these
devices, and, therefore, their significance as proof of some inherent
diflSculty in dramatic presentation, is emphasized by the delicacy of
line and fine appreciation of the human form shown in other con-
temporaneous art.

Not less significant in regard to the acoustics of the Greek theatre
are the directions given by Vitruvius for the reenforcement of the
voice by the use of resonant vases :

" Accordingly bronze vessels should be made, proportional in size to the
size of the theatre, and so fashioned that when sounded they produce with
one another the notes of the fourth, the fifth, and so on to the double octave.
These vessels should be placed in accordance with musical laws in niches
between the seats of the theatre in such position that they nowhere touch
the wall, but have a clear space on all sides and above them. They should
be set upside down and supported on the side facing the stage by wedges not
less than half a foot high. . . . With this arrangement, the voice, spreading
from the stage as a center, and striking against the cavities of the different
vessels, will be increased in volume and will wake an harmonious note in
unison with itself."

There is good reason for believing that this device was but very
rarely tried. This, and the fact that it could not possibly have ac-
compKshed the purpose as outlined by Vitruvius, is not germane.
The important point is that its mere proposal is evidence that the
contemporaries of the Greek theatres were not wholly satisfied, and
that the defect was in lack of consonance.

It would be inappropriately elaborate and beyond the possible
length of this paper to give in detail the method of calculating the

THEATRE ACOUSTICS 193

loudness of sound in different parts of an auditorium. That subject
is reserved for another paper in preparation, in which will be given
not merely the method of calculation but the necessary tables for its
simplification. It is, however, possible and proper to give a general
statement of the principles and processes involved.

In this discussion I shall leave out as already adequately discussed
the phenomenon of interference, or rather shall dismiss the subject
with a statement that when two sounds of the same pitch are super-
posed in exact agreement of phase, the intensity of the sound is the
square of the sum of the square roots of their separate intensities;
when they are in opposite phases, it is the square of the difference of
the square roots of their intensities; but when several sounds of the
same pitch arrive at any point in the room with a random difference
of phase their probable intensity is the simple numerical sum of their
separate intensities. It is on the assumption of a random difference
of phase and an average probable loudness that I shall here consider
the question. This has the advantage of being the simpler and also a
first approximation in an auditorium designed for articulate speech.

When sound spreads from a spherically symmetrical source it
diminishes as the square of the distance. When the sound is being
propagated, still in space unrestricted by walls or ceiling, but over
the heads of a closely seated audience, the law of the diminution of
the sound is more rapid than the law of the inverse square. This more
rapid diminution of the sound is due to the absorption of the sound
by the audience. It is a function of the elevation of the speaker and
the angle of inclination of the floor, — in other words, the angle be-
tween the sight lines. The diminution of the intensity of the sound
due to distance is less the greater this angle.

If the auditorium be enclosed by not too remote walls, the voice
coming directly from the speaker is reenf orced by the reflection from
the retaining walls. However, it is obvious that the sounds reflected
from the walls and ceilings have traversed greater paths than the
sound of the voice which has come directly. If this difference of path
length is great, the sounds will not arrive simultaneously. If, how-
ever, the path differences are not great, the reflected sounds will
arrive in time to reenforce the voice which has come directly, each
syllable by itself, or, indeed, in time for the self support of the sub-

194

THEATRE ACOUSTICS

syllabic Components. It is to this mutual strengthening of concur-'
rent sounds within each element of articulate speech that Vitruvius
has given the name "consonance."

Thus in the computation of the intensity of the voice which has
come directly from the speaker across the auditorium, it is necessary
to take into consideration not merely the diminution of intensity
according to the law of the inverse square of the distance and the
diminution of the intensity due to the absorption by the clothing of

Fig. 37. The Harris Theatre, Minneapolis, first design.
Chapman and Magney, Architects.

the audience, but also, as a compensating factor for the latter, the
diffraction of the sound from above which is ever supplying the loss
due to absorption, while in computing the intensity of the sound re-
flected from any wall or other surface one must take into considera-
tion all this, and also the coefficient of reflection of the wall and the
diffraction due to the restricted area of the reflecting element.

Abstract principles are sometimes tedious to follow even when
not difficult. In Fig. 38 is shown a photograph taken in an investiga-
tion for the architects, Messrs. Chapman and Magney, of the Harris
Theatre, to be erected in Minneapolis, which affords an excellent
example of both favorable and unfavorable conditions in respect to
consonance. The initial sketch for this theatre offered no problems

THEATRE ACOUSTICS 195

either of interference or reverberation, and of echo only in the hori-
zontal section. The only very considerable question presented by the
plans was in respect to consonance and there in regard only to the
more remote parts of the floor and of the balcony. The particular
photograph here reproduced records the condition of the sound in
the room at such an instant as to bring out this aspect of the problem
in marked degree.

The forward third of the balcony in this theatre affords an ex-
cellent example of consonance, for the reflection from the ceiling-
arrives so nearlv simultaneously with the sound which has come

Fig. 38. Showing the consonance in the balcony of the Harris
Theatre. This relates only to consonance in the vertical
section.

directly from the stage as to "strengthen and support" it and yet
"leave the words clear and distinct." The interval between the two,
the direct and the reflected voice, varies from .01 second to .03
second. Back of the first third, however, the consonance from the
ceiling gradually diminishes and is practically imperceptible beyond
the middle of the gallery. Back of that point the direct voice di-
minishes rapidly since it is passing in a confined space over the highly
absorbent clothing of the audience. The loss of intensity at the rear
of the gallery is increased by the carrying of the horizontal portion
of the ceiling so far rearward. While the effect of this is to throttle
the rear of the gallery it obviously strengthens the voice in the for-
ward third. Although there is thus some compensation, on the
whole the forward part of the gallery does not need this service so

196 THEATRE ACOUSTICS

much as the rear seats. The photograph shows this process clearly:
the main sound-wave can be seen advancing after having passed the
angle in the ceiling. The wave reflected from the ceiling can be seen
just striking the gallery seats. It is evident that at the instant at
which the photograph was taken the sound-wave was receiving the
last of this support by the sound reflected from the ceiling.

The photograph also shows how the sound after passing the ceil-
ing angle spreads into the space above, thus losing for the moment
thirty per cent of its intensity, a loss, however, to be regained in
considerable part later.

On the main floor the reflection from the ceiling strengthens the
direct voice only for the long syllabic components. Nevertheless, in
comparison with other theatres the forward part of the floor of this
theatre will be excellent. There will be just a trace of echo immedi-
ately under the front of the balcony, but this will be imperceptible
beyond the first four rows of seats under the balcony. It is obvious
from the photograph that there is no consonance in the rear of the
main floor of the auditorium under the balcony.

A not unnatural, certainly a not uncommon, inquiry is for some
statement of the best height, the best breadth, and the best depth for
a theatre, for a list of commended and a list of prohibited forms and
dimensions. A little consideration, however, will show that this is
neither a possible nor the most desirable result of such an inves-
tigation.

For a simple rectangular auditorium of determined horizontal
dimensions there is a best height. When, however, the horizontal
dimensions are changed the desirable height changes, although by no
means proportionally. When the floor is inclined, when the walls are
curved, when there are galleries and connection corridors, when the
material of construction is varied in character, the problem becomes
somewhat more intricate, the value of each element being dependent
on the others. Moreover it is futile to attempt to formulate a stand-
ard form even of a single type of auditorium. How greatly the
design must vary is well illustrated in the four theatres which have
been taken as examples, — the Little Theatre with all the seats on
the main floor, the Harris Theatre, very long, very broad, and with

THEATRE ACOUSTICS 197

but a single gallery, the ScoUay Square Theatre with two galleries,
and the New Theatre with two rows of boxes and two galleries.
The fundamental conditions of the problem, not the entirely free
choice of the architect, determined the general solution in each
case. Acoustical quality is never the sole consideration; at best it
is but a factor, introduced sometimes early, sometimes late, into
the design.

8
BUILDING MATERIAL AND MUSICAL PITCH ^

Ihe absorbing power of the various materials that enter into
the construction and furnishing of an auditorium is but one phase
in the general investigation of the subject of architectural acoustics
which the writer has been prosecuting for the past eighteen years.
During the first five years the investigation was devoted almost
exclusively to the determination of the coeflScients of absorption
for sounds having the pitch of violin C (512 vibrations per second).
The results were published in the American Architect and the En-
gineering Record in 1900.^ It was obvious from the beginning that
an investigation relating only to a single pitch was but a preliminary
excursion, and that the complete solution of the problem called for
an extension of the investigation to cover the whole range in pitch
of the speaking voice and of the musical scale. Therefore during
the years which have since elapsed the investigation has been ex-
tended over a range in pitch from three octaves below to three
octaves above violin C. That it has taken so long is due to the fact
that other aspects of the acoustical problem also pressed for solu-
tion, such for example as those depending on form, — interference,
resonance, and echo. The delay has also been due in part to the
nature of the investigation, which has necessarily been opportunist
in character and, given every opportunity, somewhat laborious and
exhausting. Some measure of the labor involved may be gained
from the fact that the investigation of the absorption coefficients
for the single note of violin C required every other night from twelve
until five for a period of three years.

While many improvements have been made in the methods of
investigation and in the apparatus employed since the first paper
was published fourteen years ago, the present paper is devoted solely
to the presentation of the results. I shall venture to discuss, al-
though briefly, the circumstances under which the measurements

1 The Brickbuilder, vol. xxiii, no. 1, January, 1914. ^ No. 1, p. 1.

199

200 BUILDING MATERIAL

were made, my object being to so interest architects that they will
call attention to any opportimities which may come to their notice
for the further extension of this work; for, while the absorbing
powers of many materials have already been determined, it is
evident that the list is still incomplete. For example, the coeflScient
of glass has been determined only for the note first studied, C, an
octave above middle C. In 1898 the University had just com-
pleted the construction of some greenhouses in the Botanical
Gardens, which, before the plants were moved in, fulfilled admirably
the conditions necessary for accurate experimenting. Glass formed
a very large part of the area of the enclosing surfaces, all, in fact,
except the floor, and this was of concrete whose coefficient of absorp-
tion was low and had already been determined with accuracy. By
this good fortune it was possible to determine the absorbing power
of single-thickness glass. But at that time the apparatus was adapted
only to the study of one note; and as the greenhouse was soon fully
occupied with growing plants which could not be moved without
danger, it was no longer available for the purpose when the scope
of the investigation was extended. Since then no similar or nearly
so good opportunity has presented itself, and the absorbing power
of this important structural siu-face over the range of the musical
scale has not as yet been determined. There was what seemed for
the moment to be an opportunity for obtaining this data in an in-
door tennis court which Messrs. McKim, Mead and White were
erecting at Rhinebeck on the Hudson, and the architects undertook
to secure the privilege of experimenting in the room, but inquiry
showed that the tennis court was of turf, the absorption of which
was so large and variable as to prevent an accurate determination
of the coefficients for the glass. The necessary conditions for such
experiments are that the material to be investigated shall be large
in area, and that the other materials shall be small in area, low in
power of absorption, and constant in character; while a contribut-
ing factor to the ease and accuracy of the investigation is that the
room shall be so located as to be very quiet at some period of the
day or night. The present paper is, therefore, a report of progress
as well as an appeal for further opportunities, and it is hoped that
it will not be out of place at the end of the paper to point out some

MUSICAL PITCH 201

of the problems which remain and ask that interested architects
call attention to any rooms in which it may be possible to complete
the work.

The investigation does not wholly wait an opportunity, A
special room, exceptionally well adapted to the purpose in size,
shape, and location, has been constantly available for the research
in one form or another. This room, initially lined with brick set
in cement, has been lined in turn with tile of various kinds, with
plaster, and with plaster on wood lath, as well as finished from time
to time in other surfaces. This process, however, is expensive, and
carried out in completeness would be beyond what could be borne
personally. Moreover, it has further limitations. For example, it
is not possible in this room to determine the absorbing power of
glass windows, for one of the essential features of a window is that
the outside space to which the sound is transmitted shall be open
and unobstructed. An inner lining of glass, even though this be
placed several inches from the wall, would not with certainty repre-
sent normal conditions or show the effect of windows as ordinarily
employed in an auditorium. Notwithstanding these limitations,
this room, carefully studied in respect to the effects of its pecu-
liarities of form, especially such as arise from interference and reso-
nance, has been of great service.

Wall and Ceiling-Surfaces

It is weU to bear in mind that the absorption of sound by a wall-
surface is structural and not superficial. That it is superficial is one
of the most widespread and persistent fallacies. When this investi-
gation was initially undertaken in an endeavor to correct the
acoustics in the lecture-room of the Fogg Art Museum, one of the
first suggestions was that the walls were too smooth and should be
roughened. The proposal at that time was that the walls be re-
plastered and scarred with the toothed trowel in a swirling motion
and then painted, a type of decoration common twenty years ago.
A few years later inquiries were received in regard to sanded sur-
faces, and still later in regard to a rough, pebbly surface of un-
troweled plaster; while within the past three years there have been
many inquiries as to the eflBciency of roughened brick or of rough

202 BUILDING MATERIAL

hewn stone. On the general principle of investigating any proposal
so long as it contained even a possibility of merit, these suggestions
were put to test. The concrete floor of a room was covered with a
gravel so sifted that each pebble was about one-eighth of an inch
in diameter. This was spread over the floor so that pebble touched
pebble, making a layer of but a single pebble in thickness. It
showed not the slightest absorbing power, and there was no per-
ceptible decrease in reverberation. The room was again tried with
sand. Of course, it was not possible in this case to insure the thick-
ness of a single grain only, but as far as possible this was accom-
plished. The result was the same. The scarred, the sanded, the
pebbly plaster, and the rough hewn stone are only infinitesimally
more efficient as absorbents than the same walls smooth or even
polished. The failure of such roughening of the wall-smiaces to
increase either the absorption or the dispersion of sound reflected
from it is due to the fact that the soimd-waves, even of the highest
notes, are long in comparison with the dimensions of the irregu-
larities thus introduced.

The absorption of sound by a wall is therefore a structural
phenomenon. It is almost infinitely varied in the details of its
mechanism, but capable of classification in a few simple modes.
The fundamental process common to all is an actual yielding of the
wall-surface to the vibrating pressure of the sound. How much the
wall yields and what becomes of the motion thus taken up, depends
on the nature of the structure. The simplest type of wall is obvi-
ously illustrated by concrete without steel reenforcement, for in
this there is the nearest approach to perfect homogeneity. The
amount that this wall would yield would depend upon its dimen-
sions, particularly its thickness, and upon the density, the elasticity,
and the viscosity of the material. It is possible to calculate this
directly from the elements involved, but the process would be
neither interesting nor convincing to an architect. It is in every
way more satisfactory to determine the absorbing power by direct
experiment. A concrete wall was not available. In its stead, the
next more homogeneous wall was investigated, an eighteen-inch
wall of brick set in cement. This wall was a very powerful re-
flector and its absorbing power exceedingly slight. Without going

MUSICAL PITCH 203

into the details of the experiment, it will suffice here to say that
this wall absorbed one and one-tenth per cent of the lowest note
investigated, a C two octaves below middle C, having a vibration
frequency of sixty-four per second; one and two-tenths per cent
of sounds an octave in pitch higher; one and four-tenths per cent
of sounds of middle C; one and seven-tenths per cent for violin C;
two per cent for sounds having a pitch one octave above; two and
three-tenths for two octaves above; and two and one-half per cent
for sounds having a pitch three octaves above violin C, that is to
say, 4094 vibrations per second, the highest note investigated.
These may be written as coefficients of absorption thus :

Ci, .011; Cs, .012; Cs, .014; C4, .017; C^, .020; C„ .023; Cj, .025.

There is a graphical method of presenting these results which is
always employed in physics, and frequently in other branches of
science, when the phenomenon under investigation is simply pro-
gressive and dependent upon a single variable. Whenever these
conditions are satisfied — and they are usually satisfied in any
well conducted investigation — the graphical representation of
the results takes the form of a diagram in which the results of the
measurements are plotted vertically at horizontal distances de-
termined by the variable condition. Thus in the following diagram
(Curve 1, Fig. 1) the coefficients of absorption are plotted vertically,
the varying pitch being represented by horizontal distances along the
base hne. Such a diagrammatic representation serves to reveal the
accuracy of the work. If the phenomenon is a continuous one,
the plotted points should lie on a smooth curve; the nearness with
which they do so is a measure of the accuracy of the work if the
points thus plotted are determined by entirely independent experi-
ments. This form of diagrammatic representation serves another
purpose in permitting of the convenient interpolation for values
intermediate between observed values. The coefficients for each
type of wall-surface will be given both numerically and diagram-
matically. In order to avoid confusion, the observed points have
been indicated only on the cuxve for wood sheathing in Fig. 1. It
will suffice to say merely that the other curves on this diagram
are drawn accurately through the plotted observations.

204

BUILDING MATERIAL

The next wall-surface investigated was plaster on hollow terra
cotta tile. The plaster coat was of gypsum hard plaster, the rough
plaster being five-eighths of an inch in thickness. The result shows
a slightly greater absorption due to the greater flexibility of a hollow

— ,-a:^ — —I .^

^^2= ==^ L^^P ^ 1— S=_i^ =£==-

C, C, C3 c. c, c„ c,

Fig. 1. Absorbing power for sounds varying in pitch
from C = 64 to C = 4,096: 1, brick wall; 2, plaster
on terra cotta hollow tile; 3, plaster on wire lath;
4, same with skim coat; 5, wood sheathing.

tile wall rather than to any direct effect of the plaster. The differ-
ence, however, is not great. The numerical results are as follows
(Curve 2, Fig. 1):

Ci, .012; C2, .013; C3, .015; C4, .020; Cj, .028; Ce, .040; C7, .050.

Ci is the lowest note, 64 vibrations per second; C7, the highest,
4,096 per second; the other notes at octave intervals between.

MUSICAL PITCH 205

Plaster on an otherwise homogeneous sustaining wall is a first
step in the direction of a compound wall, but a vastly greater step
is taken when the plaster instead of being applied directly to the
sustaining wall is furred to a greater or less distance. In a homo-
geneous wall, the absorption of sound is partially by communication
of the vibration to the material of the wall, whence it is telephoned
throughout the structure, and partly by a yielding of the wall as a
whole, the sound being then communicated to outside space. In
a compound wall in which the exposed surface is furred from the
main structure of the wall, the former vibrates between the furring
strips like a drum. Such a surface obviously yields more than would
a surface of plaster applied directly to tile or brick. The energy
which is thus absorbed is partly dissipated by the viscosity of the
plaster, partly by transmission in the air space behind it, and partly
through the furring strips to the main wall. The mechanism of
this process is interesting in that it shows how the free standing
plaster may absorb a great amount of sound and may present a
greater possibility of resonance and of selective absorption in the
dififerent registers of pitch. It is obvious that we are here dealing
with a problem of more complicated aspect. It is conceivable
that the absorption coeflScient should depend on the nature of the
supporting construction, whether wood lath, wire lath, or expanded
metal lath; on the distance apart of the studding, or the depth of
the air space; or, and even more decidedly, on the nature of the
plaster employed, whether the old lime plaster or the modern quick
setting gypsum plaster. A start has been made on a study of this
problem, but it is not as yet so far advanced as to permit of a system-
atic correlation of the results. It must suffice to present here the
values for a single construction. The most interesting case is that
in which lime plaster was applied to wood lath, on wood studding
at foiirteen-inch spacing, forming a two-inch air space. The co-
efficients of absorption before the finishing coat was put. on were
(Curve 3, Fig. 1) :

Ci, .048; C2, .020; C3, .024; C4, .034; d, .030; Ce, .028; C7, .043.

The values after the finishing coat was put on were as follows
(Curve 4, dotted. Fig. 1) :

Ci, .036; C2, .012; C3, .013; C4, .018; d, .045; Ce, .028; Cj, .055.

206 BUILDING MATERIAL

It should be remarked that the determination of these coeflScients
was made within two weeks after the plaster was applied and also
that the modern lime is not the same as the lime used thirty years
ago, either in the manner in which it is handled or in the manner
in which it sets and dries. It is particularly interesting to note in
these observations, more clearly in the plotted curves, the phe-
nomenon of resonance as shown by the maxima, and the effect of
the increased thickness produced by the skim coat in increasing the
rigidity of the wall, decreasing its absorbing power, and shifting the
resonance.

The most firmly established traditions of both instrumental and
architectural acoustics relate to the use of wood and excite the
liveliest interest in the effect of wood sheathing as an interior sur-
face for auditoriums ; nor are these expectations disappointed when
the phenomenon is submitted to exact measurement. It was not
easy to find satisfactory conditions for the experiment, for not
many rooms are now constructed in which plaster on studding, and
suflBciently thin, forms a very considerable factor. After long waiting
a room suitable in every respect, except location, became available.
Its floor, its whole wall, indeed, its ceiling was of pine sheath-
ing. The only other material entering into its construction was
glass in the two windows and in the door. Unfortunately, the room
was on a prominent street, and immediately adjacent was an all-
night lunch room. Accurate experiments were out of the question
while the lunch room was in use, and it was, therefore, bought out
and closed for a few nights. Even with the freedom from noise
thus secured, the experiments were not totally undisturbed. The
traffic past the building did not stop sufficiently to permit of any
observations until after two o'clock in the morning, and began again
by four. During the mtervening two hours, it was possible to
snatch periods for observation, but even these periods were dis-
turbed through the curiosity of passers and the more legitimate
concern of the police.

Anticipating, the phenomenon of resonance in wood in a more
marked degree than m any other material, new apparatus was
designed permitting of measurements at more frequent intervals
of pitch. The new apparatus was not available when the work

MUSICAL PITCH 207

began and the coefficients for the wood were determined at octave
intervals, with results as follows :

Ci, .064; Ca, .098; C3, .112; C4, .104; Cb, .081; Ce, .082; C7, .113.

These results when plotted showed clearly a very marked reso-
nance. The more elaborate apparatus was hastened to completion
and the coefficients of absorption determined for the intermediate
notes of E and G in each of the middle four octaves. The results of
both sets of experiments when plotted together give Curve 5 in
Fig. 1. The accuracy with which these fourteen points fall on a
smooth curve drawn through them is all that could be expected in
view of the conditions under which the experiment was conducted
and the limited time available. Only one point falls far from the
cvu-ve, that for middle C (C3, 256). The general trend of the curve,
however, is established beyond reasonable doubt. It is interesting
to note the very great differences between this curve and those
obtained for sohd walls, and even for plastered walls. It is espe-
cially interesting to note the great absorption due to the resonance
between the natural vibration of the walls and the sound, and to
observe that this maximum point of resonance lies in the lower part,
although not in the lowest part, of the range of pitch tested. The
pitch of this resonance is determined by the nature of the wood, its
thickness, and the distance apart of the studding on which it is
supported. The wood tested was North Carolina pine, five-eighths
of an inch in thickness and on studding fourteen inches apart. It
is, perhaps, not superfluous to add at this time that a denser wood
would have had a lower pitch for maximum resonance, other con-
ditions being alike ; an increased thickness would have raised the
pitch of the resonance; while an increased distance between the
studding would have lowered it. Finally it should be added that
the best acoustical condition both for music and for speaking would
have been with the maximum resonance an octave above rather
than at middle C.

Even more interesting is the study of ceramic tile made at the
request of Messrs. Cram, Goodhue, and Ferguson. The investiga-
tion had for its first object the determination of the acoustical
value of the tile as employed in the groined arches of the Chapel of

208 BUILDING MATERIAL

the United States Military Academy at West Point. The investi-
gation then widened its scope, and, through the skill and great
knowledge of ceramic processes of Mr. Raphael Guastavino, led to
really remarkable results in the way of improved acoustical effi-
ciency. The resulting construction has not only been approved by
architects as equal, if not better, in architectiu-al appearance to
ordinary tile construction, but it is, so far as the writer knows, the
first finished structural surface of large acoustical efficiency. Its
random use does not, of course, guarantee good acoustical quality
in an auditorium, for that depends on the amount used and the
surface covered.

The first investigation was in regard to tile used at West Point,
with the following result :

Ci, .012; C2, .013; C3, .018; C4, .029; d, .040; Cg, .048; C7, .053.

These are plotted in Curve 1, Fig. 2. The first endeavors to im-
prove the tile acoustically had very slight results, but such as they
were they were incorporated in the tile of the ceiling of the First
Baptist Church in Pittsburgh (Curve 2, Fig. 2).

Ci, .0^8; C2, .030; C3, .038; C4, .053; d, .080; Ce, .102; C7, .114.

There was no expectation that the results of this would be more
than a very slight ameUoration of the difficulties which were to be
expected in the church. In consequence of its use, the tile may be
distinguished for purposes of tabulation as Pittsburgh Tile. With-
out following the intermediate steps, it is sufficient to say that the
experiments were continued nearly two years longer and ultimately
led to a tile which for the conveniences of tabulation we will call
Acoustical Tile. The resulting absorbent power is far beyond what
was conceived to be possible at the beginnmg of the investigation,
and makes the construction in which this tile is incorporated unique
in acoustical value among rigid structures. The coefficients for this
construction are as follows:

Ci, .064; C2, .068; Cg, .117; C*, .188; d, .250; Cg, .258; C7,

graphically shown in Curve 3, Fig. 2. It is not a panacea. There
is, on the other hand, no question but that properly used it will very
greatly ameliorate the acoustical difficulties when its employment

MUSICAL PITCH

209

is practicable, and used in proper locations and amounts will render
the acoustics of many auditoriums excellent which would otherwise
be intolerable. It has over sixfold the absorbing power of any exist-
ing masonry construction and one-third the absorbing power of the

" -^

- — '

s--^

*■

C, Cj Cj Ci C, 0^ c,

Fig. 2. Absorbing power: 1, West Point tile; 2, Pitts-
burgh tile; 3, acoustical tile; 4, best felt.

best known felt plotted on the same diagram for comparison (Curve
4). It is a new factor at the disposal of the architect.

Chairs and Audience

Equally important with the wall and ceiling-surfaces of an
auditorium are its contents, especially the seats and the audience.

In expressing the coeflScients of absorption for objects which are
themselves units and which cannot be figured as areas, the coeffi-

210

BUILDING MATERIAL

cients depend on the system of measurement employed, Metric or
English. While the international or metric system has become
universal except in English speaking countries, and even in England
and America in many fields, it has not yet been adopted by the

^■^

.^^

■^^

^^2

^ \

z^"^

Fig. 3. Absorbing power: 1, bent wood chairs; 2, 3, 4,
and 5, various kinds of pew cushions as described in
text; 6, audience per person.

architectural profession and by the building trades, and therefore
these coefficients will be given in both systems.

Ash settees or chairs, such as are ordinarily to be found in a
college lecture-room, have exceedingly small absorbing powers.
Such furniture forms a very small factor in the acoustics of any
auditorium in which it is employed. The coefficients for ash chairs
are as follows (Curve 1, Fig. 3) :

MUSICAL PITCH 211

Metric
Ci, .014; Ca, .014; Ca, .015; C4, .016; Cs, .017; Ce, .019; C7, .021.

English
Ci, .15; C2, .15; C3, .16; C4, .17; d, .18; Ce, .20; C7, 23.

The coefficients for settees were also determined, but differ so little
from those for chairs that this paper will not be burdened with
them. When, however, the seats are upholstered, they immediately
become a considerable factor in the acoustics of an empty, or par-
tially empty, auditorium. Of course the chairs either upholstered
or unupholstered are not a factor in the acoustics of the auditorium
when occupied. The absorbing power of cushions depends in con-
siderable measure upon the nature of the covering and upon the
nature of the padding. The cushions experimented upon were such
as are employed in church pews, but the coefficients are expressed
in terms of the cushion which would cover a single seat. The co-
efficients are as follows :

Cushions of wiry vegetable fiber covered with canvas and a thin
damask cloth (Curve 2, Fig. 3) :

Metric
Ci, .060; C2, .070; C3, .097; C4, .135; d, .148; Ce, .132; C7, .115.

English
Ci, .64; C2, .75; C3, 1.04; C4, 1.45; Cb, 1.59; Ce, 1.42; C7, 1.24.

Cushions of long hair covered with canvas and with an outer
covering of plush (Curve 3, Fig. 3) :

Metric
Ci, .080; C2, .092; C3, .105; C4, .165; C„ .155; Ce, .128; C7, .085.

English
Ci, .86; C2, .99; C3, 1.13; C4, 1.77; Cj, 1.67; Ce, 1.37; C7, .91.

Cushions of hair covered with canvas and an outer covering of
thm leatherette (Curve 4, Fig. 3) :

Metric
Ci, .062; C2, .105; C3, .118; C4, .180; Ce, .118; Ce, .068; C7, .040.

212 BUILDING MATERIAL

English
Ci, .67; C2, I.IS; Cs, 1.27; C4, 1.93; Ce, 1.27; Cg, .73; C7, .43.

Elastic felt cushions of commerce, elastic cotton covered with
canvas and a short nap plush (Curve 5, Fig. 3) :

Metric
Ci, .092; Ci!, .155; C3, .175; C4, .190; Cs, .258; Cs, .182; C7, 120.

English
Ci, .99; C2, 1.66; C3, 1.88; C4, 2.04; C5, 2.77; Cs, 1.95; C7, 1.29.

Of all the coefficients of absorption, obviously the most difficult
to determine are those for the audience itself. It would not at all
serve to experiment on single persons and to assume that when a
number are seated together, side by side, and in front of one an-
other, the absorbing power is the same. It is necessary to make the
experiment on a full audience, and to conduct such an experiment
requires the nearly perfect silence of several hundred persons, the
least noise on the part of one vitiating the observation. That the
experiment was ultimately successful beyond aU expectation is due
to the remarkable silence maintained by a large Cambridge audi-
ence that volunteered itself for the pm^ose, not merely once, but
on four separate occasions. The coefficients of absorption thus de-
termined lie, with but a single exception, on a smooth curve (Curve 6,
Fig. 3). The single exception was occasioned by the sound of a
distant street car. Correcting this observation to the ciu-ve, the
coefficients for an audience per person are as follows :

Metric
Ci, .160; C2, .332; C3, .395; C4, .440; Cb, .455; Ce, .460; C7, .460.

English
Ci, 1.72; C2, 3.56; C3, 4.25; C4, 4.72; d, 4.70; Cs, 4.95; C7, 4.95.

Fabrics

It is evident from the above discussion that fabrics are high
absorbents of sound. How eflFective any particular fabric may be,
depends not merely on the texture of its surface and the material.

MUSICAL PITCH

213

but upon the weave or felting throughout its body, and of course,
also upon its thickness. An illuminating study of this question
can be made by means of the curves in Fig. 4. In this figure are
plotted the coefficients of absorption for varying thicknesses of felt.
Curve 1 is the absorption curve for felt of one-half inch thickness.

1
/

Fig. 4. Absorbing power of felt of varying thickness, from
one-half to three inches, showing by extrapolation the
absorption by thin fabrics of the upper register only.

Curve 2 of felt of one inch thickness, and so on up to Curve 6, which
is for felt of three inches in thickness. It is interesting to contem-
plate what the result of the process would be were it continued to
greater thickness, or in the opposite direction to felt of less and less
thickness. It is inconceivable that felt should be used more than
three inches in thickness and, therefore, extrapolation in this direc-

214 BUILDING MATERIAL

tion is of academic interest only. On the other hand, felt with de-
creasing thickness corresponds more and more to ordinary fabrics.
If this process were carried to an extreme, it would show the effect
of cheesecloth or bunting as a factor in the acoustics of an audito-
rium. It is obvious that very thin fabrics absorb only the highest
notes and are negligible factors in the range of either the speaking
voice or of music. On the other hand, it is evident that great thick-
ness of felt absorbs the lower register without increasing whatever
its absorption for the upper register. Sometimes it is desirable to
absorb the lower register, sometimes the upper register, but far more
often it is desirable to absorb the sounds from C3 to Ce, but espe-
cially in the octave between C4 and Ce.

The felt used in these experiments was of a durable nature and
largely composed of jute. Because wool felt and ordinary hair felt
are subject to rapid deterioration from moths, this jute felt was the
only one which could be recommended for the correction of audi-
toriums until an interested participator in these investigations de-
veloped an especially prepared hair felt, which is less expensive than
jute felt, but which is much more absorbent. Its absorption curve
is plotted in Fig. 2.

Location

Such a discussion as this should not close without pointing out
the triple relation between pitch, location, and apparent power of
absorption. This is shown in Fig. 5. Curve 1 shows the true co-
efficient of absorption of an especially effective felt. Curve 2 is its
apparent absorption when placed in a position which is one of loud-
ness for the lower register and of relative silence for the upper
register. Curve 3 is the apparent coefficient of absorption of the
same felt when placed in a position in the room of maximum loud-
ness for all registers. It is evident from these three curves that in
one position a felt may lose thirty per cent and over of its efficiency
in the most significant register, or may have its efficiency nearly
doubled. These curves relate to the efficiency of the felt in its effect
on general reverberation. Its efficiency in the reduction of a dis-
crete echo is dependent to an even greater degree on its location
than on pitch.

MUSICAL PITCH

215

The above are the coefficients of absorption for most materials
usually occurring in auditorium construction, but there are certain
omissions which it is highly desirable to supply, particularly notice-
able among these is the absorption curve for glass and for old plaster.

Pig. 5. Double dependence of absorbing power on pitch
and on location, showing one of the sources of error
which must be guarded against in the determination of
coefficients of absorption and in the use of absorbing
materials.

216 BUILDING MATERIAL

It is necessary for such experiments that rooms practically free from
furniture should be available and that the walls and ceiling of the
room should be composed in a large measure of the material to be
tested. The author would appreciate any opportunity to carry out
such experiments. The opportimity would ordinarily occur in the
construction of a new building or in the remodeling of an old one.

It may be not wholly out of place to point out another modern
acoustical difficulty and to seek opportunities for securing the neces-
sary data for its solution. Coincident with the increased use of
reenforced concrete construction and some other building forms
there has come increased complaint of the transmission of sound
from room to room, either through the walls or through the floors.
Whether the present general complaint is due to new materials and
new methods of construction, or to a greater sensitiveness to un-
necessary noise, or whether it is due to greater sources of disturbance,
heavier traffic, heavier cars and wagons, elevators, and elevator
doors, where elevators were not used before, — whatever the cause
of the annoyance there is urgent need of its abatement in so far as
it is structurally possible. Moreover, several buildings have shown
that not infrequently elaborate precautions have resulted disas-
trously, sometimes fundamentally, sometimes through the oversight
of detaOs which to casual consideration seem of minor importance.
Here, as in the acoustics of auditoriums, the conditions are so com-
plicated that only a systematic and acciu-ately quantitative investi-
gation will yield safe conclusions. Some headway, perhaps half a
year's work, little more than a beginning, was made in this investi-
gation some years ago. Methods of measurements were developed
and some results were obtained. Within the past month the use of
a room in a new building, together with that of the room immedi-
ately below it, has been seciu-ed for the period of two years. Be-
tween these rooms the floor will be laid in reenforced concrete of two
thicknesses, five inches and ten inches, in hollow tile, in brick arch,
in mill construction, and with hung ceiling, and the transmission of
sound tested in each case. The upper surface of the floor will be
laid in tile, in hardwood, with and without soimd-deadening lining,
and covered with linoleum and cork, and its noise to the tread
measured.

MUSICAL PITCH 217

However, such experiments but lay the foundation. What is
needed are tests of the walls and floors of rooms of various sizes, and
of the more varied construction which occurs in practice, in rooms
connecting with offsets and different floor levels, — the complicated
condition of actual building as against the simplified conditions of
an orderly experiment. The one will give numerical coefficients,
the other, if in sufficiently full measure, will give experience leading
to generalization which may be so formulated as to be of wide value.
What is therefore sought is the opportunity to experiment in rooms
of varied but accurately known construction, especially where the
insulation has been successful. Unfortunately, with modern build-
ing materials acoustical difficulties of all sorts are very numerous.

ARCHITECTURAL ACOUSTICS^

IJECAUSE familiarity with the phenomena of sound has so far out-
stripped the adequate study of the problems involved, many of them
have been popularly shrouded in a wholly unnecessary mystery.
Of none, perhaps, is this more true than of architectural acoustics.
The conditions surrounding the transmission of speech in an en-
closed auditorium are complicated, it is true, but are only such as
will yield an exact solution in the light of adequate data. It is, in
other words, a rational engineering problem.

The problem of architectural acoustics is necessarily complex,
and each room presents many conditions which contribute to the
result in a greater or less degree, according to circumstances. To
take justly into account these varied conditions, the solution of the
problem should be quantitative, not merely qualitative; and to
reach its highest usefulness and the dignity of an engineering science
it should be such that its application can precede, not merely follow,
the construction of the building.

In order that hearing may be good in any auditorium it is neces-
sary that the sound should be sufficiently loud, that the simulta-
neous components of a complex sound should maintain their proper
relative intensities, and that the successive sounds in rapidly moving
articulation, either of speech or of music, should be clear and distinct,
free from each other and from extraneous noises. These three are
the necessary, as they are the entirely sufficient, conditions for good
hearing. Scientifically the problem involves three factors: rever-
beration, interference, and resonance. As an engineering problem
it involves the shape of the auditorium, its dimensions, and the
materials of which it is composed.

Sound, being energy, once produced in a confined space, will
continue until it is either transmitted by the boundary walls or is
transformed into some other kind of energy, generally heat. This
process of decay is called absorption. Thus, in the lecture-room of

' The Journal of the Franklin Institute, January, 1915.
»9

220 ARCHITECTURAL ACOUSTICS

Harvard University, in which, and in behalf of which, this investi-
gation was begun, the rate of absorption was so small that a word
spoken in an ordinary tone of voice was audible for five and a half
seconds afterwards. During this time even a very deliberate speaker
would have uttered the twelve or fifteen succeeding syllables. Thus
the successive enunciations blended into a loud sound, through
which and above which it was necessary to hear and distinguish the
orderly progression of the speech. Across the room this could not
be done; even near the speaker it could be done only with an effort
wearisome in the extreme if long maintained. With an audience
filling the room the conditions were not so bad, but still not tolerable.
This may be regarded, if one so chooses, as a process of multiple re-
flection from walls, from ceiling, and from floor, flrst from one and
then another, losing a little at each reflection imtil ultimately in-
audible. This phenomenon will be called reverberation, including,
as a special case, the echo. It must be observed, however, that, in
general, reverberation results in a mass of sound filling the whole
room and incapable of analysis into its distinct reflections. It is
thus more difficult to recognize and impossible to locate. The term
"echo" will be reserved for that particular case in which a short,
sharp sound is distinctly repeated by reflection, either once from a
single surface, or several times from two or more surfaces. In the
general case of reverberation we are concerned only with the rate of
decay of the sound. In the special case of the echo we are concerned
not merely with its intensity, but with the interval of time elapsing
between the initial sound and the moment it reaches the observer.
In the room mentioned as the occasion of this investigation no dis-
crete echo was distinctly perceptible, and the case will serve ex-
cellently as an illustration of the more general type of reverberation.
After preliminary gropings, first in the literature and then with
several optical devices for measuring the intensity of soimd, all
established methods were abandoned. Instead, the rate of decay
was measured by measuring what was inversely proportional to it,
— the duration of audibility of the reverberation, or, as it will be
called here, the duration of audibility of the residual sound. These
experiments may be explained to advantage here, for they will give
more clearly than would abstract discussion an idea of the nature

ARCHITECTURAL ACOUSTICS

221

of reverberation. Broadly considered, there are two, and only two,
variables in a room, — shape (including size) and materials (includ-
ing furnishings). In designing an auditorium an architect can give
consideration to both; in repair work for bad acoustic conditions it
is generally impracticable to change the shape, and only variations
in materials and furnishings are allowable. This was, therefore,
the line of work in this case. It was evident that, other things being
equal, the rate at which the reverberation would disappear was
proportional to the rate at which the sound was absorbed. The
first work, therefore, was to determine the relative absorbing power

Fig. 1.

80 100 ISO 140 160 180 200 220 S40 260 280 300

Length of cushions in meters
Curve showing the relation of the duration of the residual

sound to the added absorbing material.

of various substances. With an organ pipe as a constant source of
soimd, and a suitable chronograph for recording, the duration of
audibihty of a sound after the source had ceased in this room when
empty was found to be 5.62 seconds. All the cushions from the
seats in Sanders Theatre were then brought over and stored in the
lobby. On bringing into the lecture-room a number of cushions,
having a total length of 8.2 meters, the duration of audibility fell to
5.33 seconds. On bringing in 17 meters the sound in the room after
the organ pipe ceased was audible for but 4.94 seconds. Evidently
the cushions were strong absorbents and rapidly improving the
room, at least to the extent of diminishing the reverberation. The
result was interesting and the process was continued. Little by
little the cushions were brought into the room, and each time the

222

ARCHITECTUBAL ACOUSTICS

duration of audibility was measured. When all the seats (436 in
number) were covered, the sound was audible for 2.03 seconds.
Then the aisles were covered, and then the platform. Still there
were more cushions, — almost half as many more. These were
brought into the room, a few at a time, as before, and draped on a
scaffolding that had been erected around the room, the duration of
the sound being recorded each time. Finally, when all the cushions
from a theatre seating nearly fifteen hundred persons were placed
in the room — covering the seats, the aisles, the platform, the rear
wall to the ceiling — the duriation of audibility of the residual sound

240 320 400

Cushions

Fig. 2. Curve 5 plotted as part of its corresponding rectangular
hyperbola. The solid part was determined experimentally;
the displacement of this to the right measures the absorbing
power of the walls of the room.

was 1.14 seconds. This experiment, requiring, of course, several
nights' work, having been completed, all the cushions were removed
and the room was in readiness for the test of other absorbents. It
was evident that a standard of comparison had been estabhshed.
Curtains of chenille, 1.1 meters wide and 17 meters in total length,
were draped in the room. The duration of audibility was then 4.51
seconds. Turning to the data that had just been collected, it ap-
peared that this amount of chenille was equivalent to 30 meters of
Sanders Theatre cushions. Oriental rugs (Herez, Demirjik, and
Hindoostanee) were tested in a similar manner, as were also cretonne
cloth, canvas, and hair felt. Similar experiments, but in a smaller

ARCHITECTURAL ACOUSTICS 223

room, determined the absorbing power of a man and of a woman,
always by determining the number of running meters of Sanders
Theatre cushions that would produce the same effect. This process
of comparing two absorbents by actually substituting one for the
other is laborious, and it is given here only to show the first steps
in the development of a method. Without going into details, it is
suflScient here to say that this method was so perfected as to give
not merely relative, but absolute, coefficients of absorption.

In this manner a number of coefficients of absorption were de-
termined for objects and materials which could be brought into
and removed from the room, for sounds having a pitch an octave
above middle C. In the following table the numerical values are
the absolute coefficients of the absorption:

Oil paintings, inclusive of frames 28

Carpet rugs 20

Oriental rugs, extra heavy 29

Cheesecloth 019

Cretonne cloth 15

Shelia curtains 23

Hair felt, 2.5 cm. thick, 8 cm. from wall 78

Cork, 2.5 cm. thick, loose on floor 16

Linoleum, loose on floor 12

When the objects are not extended surfaces, such as carpetsor

rugs, but essentially spacial units, it is not easy to express the

absorption as an absolute coefficient. In the following table the

absorption of each object is expressed in terms of a square meter of

complete absorption :

Audience, per person 44

Isolated woman 54

Isolated man 48

Plain ash settees 039

Plain ash settees, per single seat 0077

Plain ash chairs, "bent wood" 0082

Upholstered settees, hair and leather 1-10

Upholstered settees, per single seat 28

Upholstered chairs similar in style ■ • ■ • -30

Hair cushions, per seat 21

Elastic felt cushions, per seat 20

Of even greater importance was the determination of the co-
efficient of absorption of floors, ceilings, and wall-surfaces. The

224

ARCHITECTURAL ACOUSTICS

accomplishment of this called for a very considerable extension of
the method adopted. If the reverberation in a room as changed
by the addition of absorbing material be plotted, the resulting
curve will be foimd to be a portion of an hyperbola with displaced
axes. An example of such a curve, as obtained in the lectiu-e-
room of the Fogg Art Museum, in Cambridge, is plotted in the
diagram. Fig. 1. If now the origin of this curve be displaced so
that the axes of coordinates are the asymptotes of the rectangular
hyperbola, the displacement of the origin measures the initial ab-

10 20 30 40 so 60 TO 80 90 100 110 120 130 140 ISO
120 180 240 300 360 420
540 720 900 1080 1260

Total absorbing material

Pig. 3. The curves of Figs. 8 and 9 entered as parts of their corre-
sponding rectangular hyperbolas. Three scales are employed for
the volumes, by groups 1-7, 8-11, and 12.

sorbing power of the room, its floors, walls, and ceilings. Such
experiments were carried out in a large number of rooms in which
the different component materials entered in very different degrees,
and an elimination between these different experiments gave the
following coefficient of absorption for different materials :

Open window 1.000

Wood sheathing (hard pine) 061

Plaster on wood lath 034

Plaster on wire lath 033

Glass, single thickness 027

Plaster on tile 025

Brick set in Portland cement 025

ARCHITECTURAL ACOUSTICS

225

If the experiments in these rooms are plotted in a single dia-
gram, the result is a family of hyperbolae showing a very interesting
relationship to the volumes of the rooms. Indeed, if from these
hyperbolas the parameter, which equals the product of the co-
ordinates, be determined, it will be found to be linearly propor-
tional to the volume of the room. These results are plotted in
Fig. 4, showing how strict the proportionality is even over a very
great range in volume. We have thus at hand a ready method of

ISO

11 fid

300

oil

wsr-

IwAo

' 12800

^ 100

•/

H 50

IZOO

WO 241

DO 3000

8600

4200

°y

olun

les c

f ro

3ms

1400

Fig. 4. The parameter, k, plotted against the volumes of the
rooms, showing the two proportional.

calculatmg the reverberation for any room, its volume and the
materials of which it is composed being known.

The first five years of the investigation were devoted to violin
C, the C an octave above middle C, having a vibration frequency
of 512 vibrations per second. This pitch was chosen because, in
the art of telephony, it was regarded at that time as the character-
istic pitch determining the conditions of articulate speech. The
planning of Symphony Hall in Boston forced an extension of this
investigation to notes over the whole range of the musical scale,
three octaves below and three octaves above violin C.

In the very nature of the problem, the most important datum
is the absorption coeflacient of an audience, and the determination
of this was the first task undertaken. By means of a lecture on

226 AECHITECTURAL ACOUSTICS

one of the recent developments of physics, wireless telegraphy, an
audience was thus drawn together and at the end of the lecture
requested to remain for the experiment. In this attempt the effort
was made to determine the coefficients for the five octaves from
C2I28 to C62048, including notes E and G in each octave. For
several reasons the experiment was not a success. A threatening
thunderstorm made the audience a small one, and the sultriness of
the atmosphere made open windows necessary, while the attempt
to cover so many notes, thirteen in all, prolonged the experiment
beyond the endurance of the audience. While this experiment
failed, another the following summer was more successful. In the
year that had elapsed the necessity of carrying the investigation
further than the limits intended became evident, and now the ex-
periment was carried from Ci64 to C74096, but included only the
C notes, seven notes in all. Moreover, bearing in mind the experi-
ences of the previous smnmer, it was recognized that even seven
notes would come dangerously near overtaxing the patience of the
audience. Inasmuch as the coefficient of absorption for Ci512 had
already been determined six years before, in the investigations
mentioned, the coefficient for this note was not redetermined. The
experiment was therefore carried out for the lower three and the
upper three notes of the seven. The audience, on the night of this
experiment, was much larger than that which came the previous
siumner, the night was a more comfortable one, and it was possible
to close the windows during the experiment. The conditions were
thus fairly satisfactory. In order to get as much data as possible, and
in as short a time, there were nine observers stationed at different
points in the room. These observers, whose kindness and skill it is
a pleasure to acknowledge, had prepared themselves, by previous
practice, for this one experiment. The results of the experiment
are shown on the lower cm:ve in Fig. 5. This ciu've gives the co-
efficient of absorption per person. It is to be observed that one of
the points falls clearly off the smooth curve drawn through the other
points.^ The observations on which this point is based were, how-
ever, much disturbed by a street car passing not far from the build-
ing, and the departure of this observation from the curve does not

^ This point, evidently on the ordinate Cs, is omitted in the original cut. — Editor.

AECHITECTURAL ACOUSTICS 227

indicate a real departure in the coefficient, nor should it cast much
doubt on the rest of the work, in view of the circumstances under
which it was secured. Counteracting the, perhaps, bad impression

u
8

c. c.

Fig. 6. The absorbing power of an audience for different
notes. The lower curve represents the absorbing power
of an audience per person. The upper curve represents
the absorbing power of an audience per square meter
as ordinarily seated. The vertical ordinates are ex-
pressed in terms of total absorption by a square meter
of surface. For the upper curve the ordinates are thus
the ordinary coefficients of absorption. The several
notes are at octave intervals, as follows: Ci64, CzlSS,
Ca (middle C) 256, C<512, C61024, Ca2048, C74096.

which this point may give, it is a considerable satisfaction to note
how accurately the point for QSiYJt, determined six years before by
a different set of observers, falls on the smooth curve through the

228 ARCHITECTURAL ACOUSTICS

remaining points. In the audience on which these observations
were taken there were 77 women and 105 men. The courtesy of
the audience in remaining for the experiment and the really re-
markable silence which they maintained are gratefully acknowl-
edged.

The next experiment was on the determination of the absorp-
tion of sound by wood sheathing. It is not an easy matter to find
conditions suitable for this experiment. The room in which the
absorption by wood sheathing was determined in the earlier ex-
periments was not available for these. It was available then only
because the building was new and empty. When these more elabo-
rate experiments were under way the room became occupied, and
in a manner that did not admit of its being cleared. Quite a little
searching in the neighborhood of Boston failed to discover an en-
tirely suitable room. The best one available adjoiaed a night
lunch room. The night lunch was bought out for a couple of
nights, and the experiment was tried. The work of both nights
was much disturbed. The traffic past the building did not stop
until nearly two o'clock, and began again at four. The interest of
those passing on foot throughout the night, and the necessity of
repeated explanations to the police, greatly interfered with the
work. This detailed statement of the conditions under which the
experiment was tried is made by way of explanation of the irregu-
larity of the observations recorded on the curve, and of the failure
to carry this particular line of work further. The first night seven
points were obtained for the seven notes Ci64 to C74096. The re-
duction of these results on the following day showed variations
indicative of maxima and minima, which, to be accurately located,
would require the determination of intermediate points. In the
experiment the following night points were determined for the E
and G notes in each octave between C2I28 and C62048. Other
points would have been determined, but time did not permit. It
is obvious that the intermediate points in the lower and in the
higher octave were desirable, but no pipes were to be had on such
short notice for this part of the range, and in their absence the data
could not be obtained. In the diagram. Fig. 6, the points lying on
the vertical lines were determined the first night. The points lying

ARCHITECTURAL ACOUSTICS 229

between the vertical lines were determined the second night. The

accuracy with which these points fall on a smooth curve is, perhaps,

.12

.U
.10
.09
.08
.07
.06
.05
.04
.03
.02
.01

Fig. 6. The absorbing power of wood sheathing, two centi-
meters thick. North Carolina pine. The observations
were made under very unsuitable conditions. The
absorption is here due almost wholly to yielding of the
sheathing as a whole, the surface being shellacked,
smooth, and non-porous. The curve shows one point
of resonance within the range tested, and the prob-
ability of another point of resonance above. It is not
possible now to learn as much in regard to the framing
and arrangement of the studding in the particular room
tested as is desirable. Ca (middle C) 256.

230 ARCHITECTTIRAL ACOUSTICS

all that could be expected in view of the diflSculty under which the
observations were conducted and the limited time available. One
point in particular falls far oflF from this curve, the point for C3256,
by an amount which is, to say the least, serious, and which can be
justified only by the conditions under which the work was done.
The general trend of the curve seems, however, established beyond
reasonable doubt. It is interesting to note that there is one point
of maximum absorption, which is due to resonance between the
walls and the sound, and that this point of maximum absorption
lies in the lower part, though not in the lowest part, of the range of
pitch tested. It would have been interesting to determine, had the
time and facilities permitted, the shape of the curve beyond C74O96,
and to see if it rises indefinitely, or shows, as is far more likely, a
succession of maxima.

The experiment was then directed to the determination of the
absorption of sound by cushions, and for this purpose return was
made to the constant-temperature room. Working in the manner
indicated in the earlier papers for substances which could be carried
in and out of a room, the curves represented in Fig. 7 were obtained.
Ciu-ve 1 shows the absorption coefficient for the Sanders Theatre
cushions, with which the whole investigation was begim ten years
ago. These cushions were of a particularly open grade of packing,
a sort of wiry grass or vegetable fiber. They were covered with
canvas ticking, and that, in turn, with a very thin cloth covering.
Curve 2 is for cushions borrowed from the PhiUips Brooks House.
They were of a high grade, filled with long, curly hair, and covered
with canvas ticking, which was, in turn, covered by a long nap
plush. Curve 3 is for the cushions of Appleton Chapel, hair covered
with a leatherette, and showing a sharper maximum and a more
rapid diminution in absorption for the higher frequencies, as would
be expected under such conditions. Curve 4 is probably the most
interesting, because for more standard commercial conditions ordi-
narily used in churches. It is to be observed that all four curves
fall oflf for the higher frequencies, all show a maximmn located
within an octave, and three of the curves show a curious hump in
the second octave. This break in the curve is a genuine phenomenon,
as it was tested time after time. It is perhaps due to a secondary

ARCHITECTURAL ACOUSTICS

231

resonance, and it is to be observed that it is the more pronounced in
those curves that have the sharper resonance in their principal
maxima.

.7
ft

sVv

•V

■x

c, c.

c, c,

Fig. 7. The absorbing power of cushions. Curve 1 is
for "Sanders Theatre" cushions of wiry vegetable
fiber, covered with canvas ticking and a thin cloth.
Curve 2 is for "Brooks House" cushions of long hair,
covered with the same kind of ticking and plush.
Curve 3 is for "Appleton Chapel" cushions of hair,
covered with ticking and a thin leatherette. Curve 4
is for the elastic felt cushions of commerce, of elastic
cotton, covered with ticking and short nap plush. The
absorbing power is per square meter of surface.
Ca (middle C) 266.

In both articulate speech and in music the source of sound is
rapidly and, in general, abruptly changing in pitch, quality, and
loudness. In music one pitch is held during the length of a note.

232 ARCHITECTURAL ACOUSTICS

In articulate speech the unit or element of constancy is the syllable.
Indeed, in speech it is even less than the length of a syllable, for
the open vowel sound which forms the body of a syllable usually
has a consonantal opening and closing. During the constancy of
an element, either of music or of speech, a train of sound-waves
spreads spherically from the source, just as a train of circular
waves spreads outward from a rocking boat on the surface of still
water. Different portions of this train of spherical waves strike
different surfaces of the auditorium and are reflected. After such
reflection they begin to cross each other's paths. If their paths
are so different in length that one train of waves has entirely passed
before the other arrives at a particular point, the only phenomenon
at that point is prolongation of the sound. If the space between
the two trains of waves be suflSciently great, the effect will be that
of an echo. If there be a number of such trains of waves thus widely
spaced, the effect will be that of multiple echoes. On the other
hand, if two trains of waves have traveled so nearly equal paths
that they overlap, they will, dependent on the difference in length
of the paths which they had traveled, either reenforce or mutually
destroy each other. Just as two equal trains of water-waves cross-
ing each other may entirely neutralize each other if the crest of one
and the trough of the other arrive together, so two sounds, coming
from the same source, in crossing each other may produce silence.
This phenomenon is called interference, and is a common phenom-
enon in all types of wave-motion. Of course, this phenomenon has
its complement. If the two trains of water-waves so cross that the
crest of one coincides with the crest of the other and trough with
trough, the effects will be added together. If the two sound-waves
be similarly retarded, the one on the other, their effects will also
be added. If the two trains of waves be equal in intensity, the
combined intensity will be quadruple that of either of the trains
separately, as above explained, or zero, depending on their relative
retardation. The effect of this phenomenon is to produce regions
in an auditorium of loudness and regions of comparative or even
complete silence. It is a partial explanation of the so-called deaf
regions in an auditorium.

ARCHITECTURAL ACOUSTICS

233

It is not difficult to observe this phenomenon directly. It is
difficult, however, to measure and record the phenomenon in such
a manner as to permit of an accurate chart of the result. Without
going into the details of the method employed, the result of these

.vJ/T""""^

-^v^ ^-^^

Fio. 8. Distribution of intensity on the head level in a room
with a barrel-shaped ceiling, with center of curvature on the
floor level.

measurements for a room very similar to the Congregational Church
in Naugatuck, Connecticut, is shown in the accompanying chart.
The room experimented in was a simple, rectangular room with
plain side walls and ends and with a barrel or cylindrical ceiling.
The result is clearly represented in Fig. 8, in which the intensity

234

ARCHITECTUKAL ACOUSTICS

of the sound has been indicated by contour hnes in the manner
employed in the drawing of the geodetic survey maps. The phenom-
enon indicated in these diagrams was not ephemeral, but was con-
stant so long as the source of sound continued, and repeated itself
with almost perfect accuracj^ day after day. Nor was the phenom-

FlG. 9

Fig. 11

*SEt. '^'r^.,'

^-■■■^'"^'

^.iVv: /■

'■-.'' ■ , ;. > ^ .

" ^L

""""'"'■■'""k.

Fig. 10

Fig. 12

enon one which could be observed merely instrumentally. To an
observer moving about in the room it was quite as striking a phenom-
enon as the diagrams suggest. At the points in the room indicated
as high maxima of intensity in the diagram the sound was so loud
as to be disagreeable, at other points so low as to be scarcely audible.
It should be added that this distribution of intensity is with the
source of sound at the center of the room. Had the source of sound
been at one end and on the axis of the cylindrical ceiling, the dis-

ARCHITECTURAL ACOUSTICS

235

tribution of intensitj' would still have been bilaterally symmetrical,
but not symmetrical about the transverse axis.

When a source of sound is maintained constant for a sufficiently
long time — a few seconds will ordinarily suffice — the sound becomes
steady at every point in the room. The distribution of the intensity

Fig. 13

Fig. 15

Fig. 14

Fig. 16

of sound under these conditions is called the interference system,
for that particular note, of the room or space in question. If the
source of sound is suddenly stopped, it requires some time for the
sound in the room to be absorbed. This prolongation of sound after
the source has ceased is called reverberation. If the source of sound,
instead of being maintained, is short and sharp, it travels as a dis-
crete wave or group of waves about the room, reflected from wall to

236 ARCHITECTURAL ACOUSTICS

wall, producing echoes. In the Greek theatre there was ordinarily
but one echo, "doubling the case ending," while in the modem
auditorium there are many, generally arriving at a less interval of
time after the direct sound and therefore less distinguishable, but
stronger and therefore more disturbing.

The formation and the propagation of echoes may be admirably
studied by an adaptation of the so-called schlieren-Methode device
for photographing air disturbances. It is suflScient here to say that
the adaptation of this method to the problem in hand consists in
the construction of a model of the auditorium to be studied to
proper scale, and investigating the propagation through it of a
proportionally scaled sound-wave. To examine the formation of
echoes in a vertical section, the sides of a model are taken off and,
as the sound is passing through it, it is illuminated instantaneously
by the light from a very fine and somewhat distant electric spark.
In the preceding illustrations, reduced from the photographs,
the enframing silhouettes are shadows cast by the model, and all
within are direct photographs of the actual sound-wave and its
echoes. The four photographs show the sound and its echoes at
different stages in their propagation through the room, the particu-
lar auditorium imder investigation being the New Theatre in New
York. It is not difficult to identify the master wave and the vari-
ous echoes which it generates, nor, knowing the velocity of sound,
to compute the interval at which the echo is heard.

To show the generation of echoes and their propagation in a
horizontal plane, the ceiling and floor of the model are removed and
the photograph taken in a vertical direction. The photographs
shown in Figs. 13 to 16 show the echoes produced in the horizontal
plane passing through the marble parapet in front of the box.

While these several factors, reverberation, interference, and
echo, in an auditorium at all compUcated are themselves compU-
cated, nevertheless they are capable of an exact solution, or, at
least, of a solution as accurate as are the architect's plans in actual
construction. And it is entirely possible to calculate in advance of
construction whether or not an auditorium will be good, and, if not,
to determine the factors contributing to its poor acoustics and a
method for their correction.

THE INSULATION OF SOUND ^

1 HE insulation of sound as an unsolved problem in architectural
acoustics was first brought to the writer's attention by the New
England Conservatory of Music, immediately after its completion
in 1904, and almost simultaneously in connection with a private
house which had just been completed in New York. A few years
later it was renewed by the Institute of Musical Art in New York.
In the construction of all three buildings it had been regarded as
particularly important that communication of sound from room to
room should be avoided, and methods to that end had been em-
ployed which were in every way reasonable. The results showed
that in this phase of architectural acoustics also there had not been
a sufficiently searching and practical investigation and that there
were no experimental data on which an architect could rely. As
these buildings were the occasion for beginning this investigation,
and were both instructive and suggestive, they are, with the con-
sent of the architects, discussed here at some length.

The special method of construction employed in the New England
Conservatory of Music was suggested to the architects by the Trus-
tees of the Conservatory. The floor of each room was of semi-fire-
proof construction, cement between iron girders, on this a layer of
plank, on this paper lining, and on top of this a floor of hard pine.
Between each room for violin, piano, or vocal lessons was a com-
poimd wall, constructed of two partitions with an unobstructed air
space between them. Each partition was of two-inch plaster block
set upright, with the finishing plaster applied directly to the block.
The walls surrounding the organ rooms were of three such partitions
separated by two-inch air spaces. In each air space was a con-
tinuous layer of deadening cloth. The scheme was carried out con-
sistently and with full regard to details, yet lessons conducted in
adjacent rooms were disturbing to each other.

' The Brickbuilder, vol. xxiv, no. 2, February, 1915.

83T

238 THE INSULATION OF SOUND

It is always easier to explain why a method does not work than
to know in advance whether it will or will not. It is especially easy
to explain why it does not work when not under the immediate neces-
sity of correcting it or of supplying a better. This lighter role of the
irresponsible critic was alone invited in the case of the New England
Conservatory of Music, nor will more be ventured at the present
moment.

There is no question whatever that the fundamental considera-
tion on which the device hinged was a soimd one. Any discontinuity
diminishes the transmission of soimd; and the transition from
masonry to air is a discontinuity of an extreme degree. Two solid
masonry walls entirely separated by an air space furnish a vastly
better sound insulation than either wall alone. On the other hand,
the problem takes on new aspects if a masonry wall be replaced by
a series of screen walls, each light and flexible, even though they
aggregate in massiveness the soUd wall which they replace. More-
over, such screen walls can rarely be regarded as entirely insulated
from each other. Granting that accidental commimication has
nowhere been established, through, for example, the extrusion of
plaster, the walls are of necessity in commimication at the floor, at
the ceiling, at the sides, or at the door jambs; and the connection at
the floor, at least, is almost certain to be good. Further, and of ex-
treme importance, given any connection at all, the thinness of the
screen walls renders them like drumheads and capable of large
response to small excitation.

It may seem a remote parallel, but assume for discussion two
buildings a quarter of a mile apart. With the windows closed, no
ordinary soimd in one building could be heard in the other. If,
however, the buildings were connected by a single metal wire
fastened to the centers of window panes, it would be possible not
merely to hear from within one building to within the other, but
with care to talk. On the other hand, had the wires been connected
to the heavy masonry walls of the two buildings, such communica-
tion would have been impossible. This hypothetical case, though
extreme, indeed perhaps the better because of its exaggeration, will
serve to analyze the problem. Here, as in every case, the transmis-
sion of sound involves three steps, — the taking up of the vibration,

THE INSULATION OF SOUND 239

the function of the nearer window pane, its transmission by the wire,
and its communication to the air of the receiving room by the remote
window. The three functions may be combined into one when a
solid wall separates the two rooms, the taking up, transmitting, and
emitting of the sound being scarcely separable processes. On the
other hand, they are often clearly separable, as in the case of multiple
screen walls.

In the case of a solid masonry wall, the transmission from surface
to surface is almost perfect; but because of the great mass and
rigidity of the wall, it takes up but little of the vibration of the inci-
dent sound. It is entirely possible to express by a not very compli-
cated analytical equation the amount of sound which a wall of
simple dimensions will take up and transmit in terms of the mass
of the wall, its elasticity, and its viscosity, and the frequency of
vibration of the sound. But such an equation, while of possible
interest to physicists as an exercise, is of no interest whatever to
architects because of the difficulty of determining the necessary
coefficients.

In the case of multiple screen walls, the communication from
wall to wall, through the intermediate air space or around the edges,
is poor compared with the face to face communication of a solid
wall. But the vibration of the screen wall exposed to the sound, the
initial step in the process of transmission, is greatly enhanced by its
light and flexible character. Similarly its counterpart, the screen
wall, which by its vibration communicates the sound to the receiv-
ing room, is light, flexible, and responsive to relatively small forces.
That this responsiveness of the walls compensates or more than
compensates for the poor communication between them, is the
probable explanation of the transmission between the rooms in the
New England Conservatory.

The Institute of Musical Art in New York presented interesting
variations of the problem. Here also the rooms on the second and
third floors were intended for private instruction and were designed
to be sound proof from each other, from the corridor, and from the
rooms above and below. The walls separating the rooms from the
corridors were double, having connection only at the door jambs
and at the floor. The screen wall next the corridor was of terra

240

THE INSULATION OF SOUND

cotta block, finislied on the corridor side with plaster applied directly
to the terra cotta. The wall next the room was of gypsum block,
plastered and finished in burlap. In the air space between the two
walls, deadening sheet was hung. The walls separating the rooms
were of gypsum block and finished in hard plaster and burlap. As
shown on the diagram (Fig. 1), these walls were cellular, one

SECTION THRO coauiooft.
PAOTITION WALL

EiG. 1. Details of Construction, Institute of Musical Art,
New York, N. Y.

of these cells being entirely enclosed in gypsum block, the others
being closets opening the one to one room, the other to the other.
The closets were lined with wood sheathing which was separated
from the enclosing wall by a narrow space in which deadening sheet
was himg in double thickness with overlapping joints. In the en-
tirely enclosed cell, deadening sheet was also htmg in double thick-
ness.

THE INSULATION OF SOUND 241

It is not difficult to see, at least after the fact, why the deadening
sheet in such positions was entirely without effect. The transverse
masonry webs afforded a direct transmission from side to side of the
compound wall that entirely overwhelmed the transmission through
the air spaces. Had there been no necessity of closets, and therefore,
no necessity of transverse web and had the two screen walls been
truly insulated the one from the other, not merely over their area,
but at the floor, at the ceiling, and at the edges, the insulation would
have been much more nearly perfect.

The means which were taken to secure insulation at the base of
the screen walls and to prevent the transmission of sound from floor
to floor are exceedingly interesting. The floor construction con-
sisted in hollow terra cotta tile arches, on top of this cinder concrete,
on this sawdust mortar, and on the top of this cork flooring. Below
the reenforced concrete arches were hung ceilings of plaster on wire
lath. This hung ceiling was supported by crossed angle bars which
were themselves supported by the I beams which supported the
hollow terra cotta tile arches. In the air spaces between the tile
arches and the hung ceilings, and resting on the latter, was deaden-
ing sheet. This compound floor of cork, sawdust mortar, cinder
concrete, terra cotta tile, air space, and hung ceiling, with deadening
sheet in the air spaces, has the air of finality, but was not successful
in securing the desired insulation.

It is interesting to note also that the screen walls were separated
from the floor arches on which they rested below and on which they
abutted above by deadening sheet. It is possible that this afforded
some insulation at the top of the wall, for the arch was not sustained
by the wall, and the pressure at that point not great. At the bottom,
however, it is improbable that the deadening sheet carried imder the
base offered an insulation of practical value. Under the weight of
the wall it was probably compressed into a compact mass, whose
rigidity was still further increased by the percolation through it of
the cement from the surrounding concrete.

Finally, after the completion of the building, Mr. Damr&sch, the
director, had tried the experiment of cove^)^g the walls of one of the
rooms to a depth of two inches with standard hair felt, with some,
but almost negligible, effect on the transmission of soimd.

242 THE INSULATION OF SOUND

Deadening sheet has been mentioned frequently. All indication
of the special kind employed has been purposely omitted, for the
discussion is concerned with the larger question of the manner of its
use and not with the relative merits of the different makes.

The house in New York presented a problem even more interest-
ing. It was practically a double house, one of the most imperative
conditions of the building being the exclusion of sounds in the main
part of the house from the part to the left of a great partition wall.
This wall of sohd masonry supported only one beam of the main
house, was pierced by as few doors as possible — two — and by
no steam or water pipes. The rooms were heated by independent
fireplaces. The water pipes connected independently to the main.
It had been regarded as of particular importance to exclude sounds
from the two bedrooms on the second floor. The ceilings of the
rooms below were, therefore, made of concrete arch; on top of this
was spread three inches of sand, and on top of this three inches of
lignolith blocks; on this was laid a hardwood floor; and finally,
when the room was occupied, this floor was covered by very heavy
and heavily padded carpets. From the complex floor thus con-
structed arose interior walls of plaster on wire lath on independent
studding, supported only at the top where they were held from the
masonry walls by iron brackets set in lignolith blocks. Each room
was, therefore, practically a room within a room, separated below
by three inches of sand and three inches of lignolith and on all sides
and above by an air space. Notwithstanding this, the shutting of a
door in any part of the main house could be heard, though faintly,
in either bedroom. In the rear bedroom, from which the best results
were expected, one could hear not merely the shutting of doors in
the main part of the house, but the working of the feed pump, the
raking of the furnace, and the coaling of the kitchen range. In the
basement of the main dwelling was the servants' dining room. Rap-
ping with the knuckles on the wall of this room produced in the bed-
room, two stories up and on the other side of the great partition wall,
a sound which, although hardly, as the architect expressed it, magni-
fied, yet of astonishing loudness and clearness. In this case, the
telephone-like nature of the process was even more clearly defined
than in the other cases, for the distances concerned were much

THE INSULATION OF SOUND 243

greater. The problem had many interesting aspects, but will best
serve the present purpose if for the sake of simplicity and clearness
it be held to but one, — the transmission of sound from the servants'
dining room in the basement along the great eighteen-inch partition
wall up two stories to the insulated bedroom above and opposite.

It is a fairly safe hazard that the sound on reaching the bedroom
did not enter by way of the floor, for the combination of reenforced
concrete, three inches of sand, three inches of lignolith block, and
the wood flooring and carpet above, presented a combination of
massive rigidity in the concrete arch, inertness in the sand and
lignolith block, imperviousness in the hardwood floor, and absorp-
tion in the padded carpet which rendered insulation perfect, if per-
fect insulation be possible. No air ducts or steam or water pipes
entered the room. The only conceivable communication, therefore,
was through the walls or ceiling. The communication to the inner
walls and ceiling from the surrounding structural walls was either
through the air space or through the iron angle bars, which, set in
lignolith blocks in the structural wall, retained erect and at proper
distance the inner walls. Of the two means of communication, the
air and the angle bars, the latter was probably the more important.
It is interesting and pertinent to follow this line of communication,
the masonry wall, the angle bars, and the screen walls, and to en-
deavor to discover if possible, or at least to speculate on the reason
for its exceptional though unwelcome efl&ciency.

From the outset it is necessary to distinguish the transverse and
the longitudinal transmission of sound in a building member, that
is, to distinguish as somewhat different processes the transmission
of sound from one room to an adjacent room through a separating
wall or ceiling, from the transmission of sound along the floors from
room to room, or along the vertical walls from floor to floor. Broadly,
although the two are not entirely separable phenomena, one is
largely concerned in the transmission of the sound of the voice, or
the violin, or of other sources free from solid contact with the floor,
and the other in the transmission of the sound of a piano or cello — in-
struments in direct communication with the building structure — or
of noises involved in the operation of the building, dynamos, eleva-
tors, or the opening and closing of doors. In the building under con-

244 THE INSULATION OF SOUND

sideration, the disturbing sounds were in every case communicated
directly to the structure at a considerable distance and transmitted
along the walls until ultimately communicated through the angle
bars, if the angle bars were the means of commimication, to the thin
plaster walls which constituted the inner room. The special features
thus emphasized were the longitudinal transmission of vibration by
walls, floors, and structural beams, and the transformation of these
longitudinal vibrations into the sound-producing transverse vibra-
tions of walls and ceilings bounding the disturbed room. Many
questions were raised which at the time could be only tentatively
answered.

What manner of walls conduct the sound with the greater readi-
ness .'' Is it true, as so often stated, that modem concrete construc-
tion has contributed to the recent prevalence of these difficulties ?
If so, is there a difference in this respect between stone, sand, and
cinder concrete ? In this particular building, the partition wall was
of brick. Is there a difference due to the kind of brick employed,
whether hard or soft ? Or does the conduction of sound depend on
the kind of mortar with which the masonry is set .'' If this seems
trivial, consider the number of joints in even a moderate distance.
Again, is it possible that sotmd may be transmitted along a wall
without producing a transverse vibration, thus not entering the
adjacent room ? Is it possible that in the case of this private house
had there been no interior screen wall the sound communicated to
the room would have been less .'' We know that if the string of a
string telephone passes through a room without touching, a conver-
sation held over the Une will be entirely inaudible in the room. Is
it possible that something like this, but on a grand scale, may happen
in a building ? Or, again, is it possible that the iron brackets which
connected the great partition wall to the screen wall magnified the
motion and so the sound, as the lever on a phonograph magnifies its
motion ? These are not unworthy questions, even if ultimately the
answer be negative.

The investigation divides itself into two parts, — the one dealing
with partition walls especially constructed for the test, the other
with existing structures wherever found in interesting form. The
experiments of the former type were conducted in a special room.

THE INSULATION OF SOUND

245

mentioned in some of the earlier papers (The Brickbuilder, January,
1914)/ and having peculiar merits for the work. For an under-
standing of these experiments and an appreciation of the conditions
that make for their accuracy, it is necessary that the construction of
this room be explained at some length. The west wing of the Jeffer-
son Physical Laboratory is in plan a large square in the center of
which rises a tower, which, for the sake of steadiness and insulation

Fig. 3. Testing Room and Apparatus

from all external vibration, is not merely of independent walls but
has an entirely separate foundation, and above is spanned without
touching by the roof of the main building. The sub-basement room
of this tower is below the basement of the main building, but the
walls of the latter are carried down to enclose it. The floor of the
room is of concrete, the ceiling a masonry arch. There is but one
door which leads through a small anteroom to the stairs mounting
to the level of the basement of the main building. Through the

■ See page 199, chapter 8.

246 THE INSULATION OF SOUND

ceiling there are two small openings for which special means of closing
are provided. The larger of these openings barely permits the
passage of an observer when raised or lowered by a block and tackle.
It is necessary that there be some such entrance in order that obser-
vations may be taken in the room when the door is closed by the wall
construction undergoing test.

Of prime importance, critical to the whole investigation, was the
insulation between the rooms, otherwise than through the partition
to be tested. The latter closed the doorway. Other than that the
two rooms were separated by two eighteen-inch walls of brick,
separated by a one-inch air space, not touching through a five-story
height and carried down to separate foundations. Around the outer
wall and around the antechamber was solid ground. It is difl&cult
to conceive of two adjacent rooms better insulated, the one from
the other, in all directions, except in that of their immediate con-
nection.

The arrangement of apparatus, changed somewhat in later experi-
ments, consisted primarily, as shown in the diagram, of a set of
organ pipes, winded from a bellows reservoir in the room above,
this in turn being charged from an air pump in a remote part of the
building, — remote to avoid the noise of operation. In the center
of the room two reflectors revolved slowly and noiselessly on roller
bearings, turned continuously by a weight, under governor control,
in the room above. The chair of the observer was in a box whose
folding lids fitted over his shoulders. In the box was the small organ
console and the key of the chronograph. The organ and chrono-
graph had also console and key connection with the antechamber.
The details of the apparatus are not of moment in a paper written
primarily for architects.

Broadly, the method of measuring the transmission of sound
through the partitions consisted in producing in the larger room a
sound whose intensity in terms of threshold audibility was known,
and reducing this intensity at a determinable rate until the soimd
ceased to be audible on the other side of the partition. The intensity
of the sound at this instant was numerically equal to the reciprocal
of the coefficient of transmission. This process involved several
considerations which should at least be mentioned.

THE INSULATION OF SOUND 247

The sound of known intensity was produced by organ pipes of
known powers of emission, allowance being made for the volume of
the room, and the absorbing power of the walls. The method was
fully explained in earlier papers.^ It is to be borne in mind that
there was thus determined merely the average of intensity. The
intensity varied greatly in different parts of the room because of
interference. In order that the average intensity of sound against
the partition in a series of observations should equal the average
intensity in the room, it was necessary to continuously shift the in-
terference system. This was accomplished by means of revolving
reflectors. This also rendered it possible to obtain a measure of
average conditions in the room from observations taken in one
position. Finally the observations in the room were always made
by the observer seated in the box, as this rendered his clothing a
neghgible factor, and the condition of the room the same with or
without his presence. Consideration was also given to the acoustical
condition of the antechamber.

Two methods of reducing the sound have been employed. In
the one the sound was allowed to die away naturally, the source
being stopped suddenly, and the rate at which it decreased deter-
mined from the constants of the room. In another type of experi-
ment the source, electrically maintained, was reduced by the addition
of electrical resistance to the circuit. One method was suitable
to one set of conditions, the other to another. The first was em-
ployed in the experiments whose results are given in this paper.

The first measurements were on felt, partly suggested by the ex-
periments of Dr. Damrosch with felt on the walls of the Institute of
Musical Art, partly because it offered the dynamically simplest prob-
lem on which to test the accuracy of the method by the concurrence
of its results. The felt used was that so thoroughly studied in other
acoustical aspects in the paper published in the Proceedings of the
American Academy of Arts and Sciences in 1906. The door separat-
ing the two rooms was covered with a one-half inch thickness of this
felt. The intensity of sound in the main room just audible through
the felt was 3.7 times threshold audibility. Another layer of felt
of equal thickness was added to the first, and the reduction in the

^ See Beverberation, page 1.

248

THE INSULATION OF SOUND

intensity of sound in passing through the two was 7.8 fold. Through
three-thickness, each one-half, the reduction was 15.4 fold, through
four 30.4, five 47.5, and six 88.0. This test was for sounds having the
pitch of vioHn C, first C above middle C, 512 vibrations per second.
There is another way of stating the above results which is perhaps
of more service to architects. The ordinary speaking intensity of

■'.

^2^

12 3 4 6 6

Fig. 3

the voice is — not exactly, of course, for it varies greatly — but
of the order of magnitude of 1,000,000 times minimiun audible in-
tensity. Assume that there is a sound of that intensity, and of the
pitch investigated, in a room in one side of a partition of half-inch
felt. Its intensity on the other side of the partition would be
270,000 times minimiun audible intensity. Through an inch of felt

THE INSULATION OF SOUND 249

its intensity would be 128,000. Through six layers of such felt, that
is, through three inches, its intensity would be 11,400 times mini-
mum audible intensity, — very audible, indeed. The diminishing
intensity of the sound as it proceeds through layer after layer of
felt is plotted in the diagram (Curve 1, Fig. 3), in which all the
points recorded are the direct results of observations. The intensity
inside the room is the full ordinate of the diagram. The curve drawn
is the nearest rectangular hyperbola fitting the observed and calcu-
lated points. The significance of this will be discussed later. It is
sufficient for the present purpose to say that it is the theoretical
curve for these conditions, and the close agreement between it and
the observed points is a matter for considerable satisfaction.

The next partition tested was of sheet iron. This, of course, is
not a normal building material and it may therefore seem disap-
pointing and without interest to architects. But it is necessary to
remember that these were preliminary investigations establishing
methods and principles rather than practical data. Moreover, the
material is not wholly impractical. The writer has used it in recom-
mendations to an architect in one of the most interesting and suc-
cessful cases of sound insulation so far undertaken — that in an
after-theatre restaurant extending underneath the sidewalk of Broad-
way and 42d Street in New York.

The successive layers of sheet iron were held at a distance, each
from the preceding, of one inch, spaced at the edges by a narrow
strip of wood and felt, and pressed home by washers of felt. After
the practical cases cited at the beginning of the paper, it requires
courage and some hardihood to say that any insulation is good. It
can only be said that every care was taken to this end. The results
of the experiments can alone measure the efficiency of the method
employed, and later they will be discussed with this in view.

The third series of experiments were with layers of sheet iron
with one-half inch felt occupying part of the air space between them.
The iron was that used in the second series, the felt that used ia the
first. The air space was unfortunately slightly greater than in the
second series, being an inch and a quarter instead of an inch. The
magnitude of the effect of this difference in distance was not
realized at the time, but it was sufficient to prevent a direct com-

250 THE INSULATION OF SOUND

parison of the second and third series, and an attempt to deduce
the latter from the former with the aid of the first. When this was
realized, other conditions were so different as to make a repetition
of the series difficult.

In the following table is given the results of these three series of
experiments in such form as to admit of easy comparison. To this
end they are all reduced to the values which they would have had
with an intensity of sound in the inner room of 1,000,000. In the
first column each succeeding figure is the intensity outside an addi-
tional half inch of felt. In the second column, similarly, each suc-
ceeding figure is the intensity outside an additional sheet of iron.
In the third column, the second figure is the intensity outside a
single sheet of iron, and after that each succeeding figure is the
intensity outside of an additional felt and iron doublet with air space.

1,000,000

270,000

22,700

23,000

128,000

8,700

3,300

65,000

4,880

700

33,000

3,150

220

21,500

2,060

150

11,400

1,520

The sound transmitted in the second and third series is so much
less than in the first that when an attempt is made to plot it on the
same diagram (Curves 2 and 3, Fig. 3) it results in lines so low as to
be scarcely distinguishable from the base line. Magnifying the scale
tenfold (Fig. 4) throws the first series off the diagram for the earlier
values, but renders visible the second and third.

The method of representing the results of an investigation
graphically has several ends in view: it gives a visual impression of
the phenomenon; it shows by the nearness with which the plotted
values^ lie to a smooth curve the accuracy of the method and of the
work; it serves to interpolate for intermediate values and to ex-
trapolate for points which lie beyond the observed region, forward
or backward; finally, it reveals significant relations and leads to a

'■ In reproducing from the plotted diagrams tor Pigs. 3, 4, and 5, the dots, in some cases,
which indicated the plotted values of the observed points, do not clearly appear in distinction
on the lines. The greatest divergence, in any case, from the line drawn was not more than
twice the breadth of the line itself.

THE INSULATION OF SOUND

251

more effective discussion. It is worth while thus examining the
three curves.

Attention has already been called to the curve for felt, to its ex-
trapolation, and to the close approximation of the observed points
to an hyperbola. The latter fact indicates the simplest possible law

.09

.08

.07

.06

.05

.04

.03

.02

,01

\ 1

2 3

Fig. 4

of absorption. It proves that all layers absorb the same proportion
of the sound; that each succeeding layer absorbs less actual sound
than the preceding, but less merely because less sound reaches it to
be absorbed. In the case in hand the sound in passing through the
felt was reduced in the ratio 1.88 in each layer, 3.53 in each inch.
It is customary to test such curves by plotting them on a special
kind of coordinate paper, — one on which, while horizontal dis-

252

THE INSULATION OF SOUND

tances are uniformly scaled as before, vertical distances are scaled
with greater and greater reduction, tenfold for each unit rise. On
such coordinate paper the vertical distances are the power to which
10 must be raised to equal the number plotted — in other words, it
is the logarithm of the number. Plotted on such paper the curve for

10'

10"

■----..

■^

■~~~~-

^v^

2 3

Fig. 5

felt will result in a straight line, if the curve in the other diagram
was an hyperbola, and if the law of absorption was as inferred. How
accurately it does so is shown in Curve 1, Pig. 5.

When the observations for iron, and for felt and iron, are similarly
plotted (Curves 2 and 3, Pig. 5), the lines are not straight, but
strongly curved uipward, indicating that the corresponding curves
in the preceding diagram were not hyperbolas, and that the law of

THE INSULATION OF SOUND 253

constant coefficient did not hold. This must be explained in one or
the other of two ways. Either there was some by-pass for the sound,
or the efficiency of each succeeding unit of construction was less.

The by-pass as a possible explanation can be quickly disposed of.
Take, for example, the extreme case, that for felt and iron, and make
the extreme assumption that with the completed series of six screens
all the sound has come by some by-pass, the surrounding walls, the
foundations, the ceiling, or by some solid connection from the inner-
most to the outermost sheet. A calculation based on these assump-
tions gives a plot whose curvature is entirely at the lower end and
bears no relationship to the observed values. In the other case, that
of the iron only, a similar calculation gives a similar result; more-
over, the much lower limit to which the felt and iron screens reduced
the sound wholly eliminates any by-pass action as a vital factor in
the iron-only experiment.

The other explanation is not merely necessary by elimination,
but is dynamically rational. The screen walls such as here tested,
as well as the screen walls in the actual construction described by
way of introduction, do not act by absorption, as in the case of the
felt; do not act by a process which is complete at the point, but
rather by a process which in the first screen may be likened to re-
flection, and in the second and subsequent screens by a process which
may be more or less likened to reflection, but which being in a con-
fined space reacts on the screen or screens which have preceded it.
In fact, the process must be regarded not as a sequence of inde-
pendent steps or a progress of an independent action, but as that of
a structure which must be considered dynamically as a whole.

When the phenomenon is one of pure absorption, as in felt, it is
possible to express by a simple formula the intensity of the sound I,
at any distance x, in terms of the initial intensity lo,

I = I„Rk-',

where R represents the factor of surface discontinuity, and k the
ratio in which the intensity is reduced in a unit distance. In the case
of the felt tested, R is .485 and k is 3.53, the distance into the
felt being measured in inches. As an application of this formula,
one may compute the thickness of felt which would entirely ex-

254 THE INSULATION OF SOUND

tinguish a sound of the intensity of ordinary speech, — 10.4 inches.
It is not possible to express by such a formula the transmission of
sound through either of the more complex structures. However, it
is possible to extrapolate empirically and show that 10.4 inches of
neither would accomplish this ideal result, although they are both
far superior to felt for thicknesses up to three inches in one case and
five and one-half inches in the other.

A number of other experiments were tried during this preliminary
stage of the investigation, such, for example, as increasing the
distance between the screen walls, but it is not necessary to recount
them here. Enough has already been given to show that a method
had been developed for accurately measuring the insulating value of
structures; more would but confuse the purpose. At this point the
apparatus was improved, the method recast, and the investigation
begun anew, thenceforward to deal only with standard forms of
construction, and for soimds, not of one pitch only, but for the
whole range of the musical scale.

WHISPERING GALLERIES

It is probable that all existing whispering galleries, it is certain that
the six more famous ones, are accidents; it is equally certain that all
could have been predetermined without difficulty, and like most
accidents could have been improved upon. That these six, the
Dome of St. Paul's Cathedral in London, Statuary Hall in the Capi-
tol at Washington, the vases in the Salle des Cariatides in the Louvre
in Paris, St. John Lateran in Rome, The Ear of Dionysius at Syra-
cuse, and the Cathedral of Girgenti, are famous above others is in a
measure due to some incident of place or association. Four are fa-
mous because on the great routes of tourist travel, one because of
classical traditions, and one, in an exceedingly inaccessible city and
itself still more inaccessible, through a curious story perpetuated by
Sir John W. Herschel in the Encyclopedia Metropolitana. However,
all show the phenomenon in a striking manner and merit the interest
which they excite, an interest probably enhanced by the mystery
attaching to an unpremeditated event in the five more modern cases,
and none the less enhanced in the other by the tradition of its inten-
tional design and as evidence of a "lost art."

The whispering gallery in the Capitol at Washington is of the
simplest possible type.

The Capitol as first built was but the central portion of the present
building, the Senate Chamber and the Hall of the House of Repre-
sentatives being at that time immediately adjacent to the rotunda.
With the admission of new states, and with the general increase in
population, the Senate and the House outgrew their quarters, and in
.1851 the great wings which now complete the building were con-
structed for their accommodation. The old Hall of the House, which
in its day must have been acoustically an exceedingly poor assembly
room, was transformed into the present Hall of Statues and became,
or rather remained, one of the most perfect of whispering galleries.

The ceiling of the Hall of Statues, with the exception of a small
circular skylight, is a portion of an exact sphere with its center very

WHISPERING GALLERIES 257

nearly at head level. As shown in the illustrations the ceiling is cof-
fered. As originally constructed, and as it remained until 1901, the
ceiling was perfectly smooth, being of wood, papered and painted in
a manner to represent coffering. In 1901, a fire in the Chamber of
the Supreme Court, also in the Capitol, led to a general overhauling
of the building, and among other dangerous constructions the ceiling
of wood in the Hall of Statues was replaced by a fireproof construc-
tion of steel and plaster. Instead of being merely painted, the new
ceiling had recessed panels with mouldings and ribs in relief
(Fig. 1). In consequence of this construction, the whispering
gallery lost a large part of its unique quality.

During the years preceding the remodeling of the ceiling, the
whispering gallery had been of great interest to tourists and deep
hollows were worn in the marble tile where the observers stood. The
experiment was usually tried in either one of two ways. The visitor
to the gallery was placed at the center of curvature of the ceiling and
told to whisper, when the slightest sounds were returned to him
from the ceiling. The effect was much more striking than one would
suppose from this simple description. The slight lapse of time re-
quired for the sound to travel to the ceiling and back, together with
one's keen sense of direction, gave the effect of an invisible and mock-
ing presence. Or the guide would place the tourists at symmetrical
points on either side of the center, when they could with the help of
the ceiling whisper to each other across distances over which they
could not be heard directly. The explanation of this particular
whispering gallery is exceedingly simple.

Speech, whether whispered or full toned, consists of waves or
trains of waves of greatly varied character. The study, to its last
refinement, of whispering gallery phenomena involves a considera-
tion of this complicated character of speech, but a rough study, and
one which serves most purposes, can be made by following the path
and the transformation of a single wave. This can be illustrated by
two series of photographs. In the one (Fig. 2), the wave is shown in
the different stages of its advance outward, — spherical, except
where it strikes the floor, the wall, or the repressed transverse arch
of the ceihng. In the second series of photographs (Fig. 3), the
wave has struck the spherical ceiling everywhere at the same instant.

WHISPERING GALLERIES 259

and, reversed in direction, gains in intensity as it gathers together
toward the point from which it issued. The sound reflected from
the other surfaces may be seen dividing and subdividing in multiple
reflection and losing in intensity, while the sound reflected from the
spherical ceiling gains through its rapid convergence.

These and other similar photographs used in this investigation
were taken in a small sectional model, one-sixteenth of an inch to
the foot in scale, made of plaster of Paris or of other convenient ma-
terial, and the impulsive report or wave was produced either by the
explosion of fulminate of mercury or directly by an electric spark.
The flash by which the exposure was taken had a duration of less
than a millionth of a second. It is wholly unnecessary for the pur-
poses of this present discussion to go into the details of this process.
It is sufficient to state that the illustrations are actual photographs
of real sound-waves in the air and reproduce not merely the main
but the subordinate phenomena.

In citing this gallery in an article on Whispering Galleries in Stur-
gis' Dictionary of Architecture, the writer made the statement that
" The ceiling, painted so that it appears deeply panelled, is smooth.
Had the ceiling been panelled the reflection would have been irregu-
lar and the effect very much reduced." A year or so after this was
written the fire in the Capitol occurred, and in order to preserve the
whispering gallery, which had become an object of unfailing interest
to visitors to the Capitol, the new ceiling was made "to conform
within a fraction of an inch " to the dimensions of the ceiling which
it replaced. Notwithstanding this care, the quality of the room
which had long made it the best and the best known of whispering
gaUeries was in large measure lost. Since then this occurrence has
been frequently cited as another of the mysteries of architectural
acoustics and a disproof of the possibilities of predicting such phe-
nomena. As a matter of fact, it was exactly the reverse. Only the part
between the panels was reproduced in the original dimensions of the
dome. The ceiling was no longer smooth, the staff was paneUed in
real recess and rehef, and the result but confirmed the statement
recorded nearly two years before in the Dictionary of Architecture.

The loss of this fine whispering gallery has at least some compen-
sation in giving a convincing illustration, not merely of the condi-

260 WHISPERING GALLERIES

tions which make towards excellence in the phenomenon, but also of
the conditions which destroy it. The effect of the paneling is obvi-
ous. Each facet on the complex ceiling is the source of a wavelet and
as these facets are of different depths the resulting wavelets do not
conspire to form the single focusing wave that results from a per-
fectly smooth dome. In a measure of course in this particular case
the wavelets do conspire, for the reflecting surfaces are systemati-
cally placed and at one or the other of two or three depths. The dis-
persion of the sound, and the destruction of the whispering gallery is,
therefore, not complete.

An instructive parallel may be drawn between acoustical and
optical mirrors :

Almost any wall-surface is a much more perfect reflector of
sound than the most perfect silver mirror is to light. In the former
case, the reflection is over 96 per cent, in the latter case rarely
over 90.

On the surfaces of the two mirrors scratches to produce equally
injurious effects must be comparable in their dimensions to the
lengths of the waves reflected. Audible sounds have wave lengths
of from half an inch to sixty feet; visible light of from one forty-
thousandth to one eighty-thousandth of an inch. Therefore while
an optical mirror can be scratched to the complete diffusion of the
reflected Hght by irregularities of microscopical dimensions, an
acoustical mirror to be correspondingly scratched must be broken
by irregularities of the dimensions of deep coffers, of panels, of
engaged columns or of pilasters.

Moreover, just as remarkable optical phenomena are produced
when the scratches on a mirror are parallel, equal, equal spaced, or of
equal depth, as in mother of pearl, certain bird feathers, and in the
optical grating, so also are remarkable acoustical phenomena pro-
duced when, as is usually the case in architectural construction, the
relief and recess are equal, equally spaced, or of equal depth. The
panels in the dome of the Hall of Statues of course diminish to-
ward the apex of the dome and are thus neither equal nor equally
spaced, but horizontally they are and produce corresponding phe-
nomena. The full details of these effects are a matter of common
knowledge in Physics but are not within the scope of the present

WmSPERlNG GALLERIES 261

discussion. It is sufficient to say that the general result is a disper-
sion or a distortion in the form of the focus and that the general
effect is to greatly reduce the efficiency of the whispering gallery,
but to by no means wholly destroy it, as would be the case with
complete irregularity.

By the term whispering gallery is usually understood a room,
either artificial or natural, so shaped that taint sounds can be heard
across extraordinary distances. For this the Hall of Statues was ill-
adapted, partly because of a number of minor circumstances, but
primarily because a spherical surface is accurately adapted only to
return the sound directly upon itself. When the two points between
which the whisper is to be conveyed are separated, the correct form
of reflecting surface is an ellipsoid having the two points as foci.
When the two points are near together, the ellipsoid resembles more
and more a sphere, and the latter may be regarded as the limiting
case when the two points coincide. On the other hand, when the
two foci are very far apart the available part of the ellipsoid near one
of the foci resembles more and more a paraboloid, and this may be
regarded as the other extreme limiting case when one of the foci is at
an infinite or very great distance. I know of no building a consider-
able portion of whose wall or ceiling surface is part of an exact ellip-
soid of revolution, but the great Mormon Tabernacle in Salt Lake
City is a near approximation. Plans of this remarkable building do
not exist, for it was laid out on the ground without the aid of formal
drawings soon after the settlers had completed their weary pilgrim-
age across the Utah desert and settled in their isolated valley. It was
bmlt without nails, which were not to be had, and held together
merely by wooden pins and tied with strips of buffalo hide. Not-
withstanding this construction, and notwithstanding the fact that it
spans 250 feet in length, and 150 feet in breadth, and is without any
interior columns of any sort, it has been free from the necessity of
essential repair for over fifty years. As the photograph (Fig. 5)
shows, taken at the time of building, the space between the ceiling
and the roof is a wooden bridge truss construction. These photo-
graphs, given by the elders of the church, are themselves inter-
esting considering the circumstances under which they were taken,
the early date and the remote location.

Fig. 4. Exterior, Mormon Tabernacle, Salt Lake Citj', Utah.

5^^ -'--^^,7

Fig. 5. Photograph showing Construction, Mormon Tabernacle, Salt Lake City, Utah.

Fig. 6

264 WHISPERING GALLERIES

It is difficult for an interior photograph of a smooth ceiling to give
an impression of its shape. An idea of the shape of the interior of the
Tabernacle may be obtained, however, from a photograph of its ex-
terior. It obviously somewhat resembles an ellipsoid of revolution.
It is equally obvious that it is not exactly that. Nevertheless there
are two points between which faint sounds are carried with remark-
able distinctness, — the reader's desk and the front of the balcony in
the rear.

The essential geometrical property of an ellipsoid of revolution is
that lines drawn to any point of the surface from the two foci make
equal angles with the surface. It follows that sound diverging
from one focus will be reflected toward the other. The preceding
photographs (Fig. 6) show the progress of a sound-wave in the
model of an idealized whispering gallery of this type in which the
reflecting surface is a portion of a true ellipsoid of revolution.

The most notable whispering gallery of this type is that described
by Sir John Herschel in one of the early scientific encyclopedias, the
Encyclopedia Metropolitana as follows :

In the Cathedral of Girgenti in Sicily, the slightest whisper is borne with
perfect distinctness from the great western floor to the cornice behind the
high altar, a distance of 250 feet. By a most unlucky coincidence the pre-
cise focus of divergence at the former station was chosen for the place of the
confessional. Secrets never intended for the public ear thus became known,
to the dismay of the confessor and the scandal of the people, by the resort
of the curious to the opposite point, which seems to have been discovered
by accident. . . .

Aside from the great distance between the foci, the circumstances
related had many elements of improbability and the final discussion
of this subject was postponed from year to year in the hope that the
summer's work, which has usually been devoted to the study of Eu-
ropean auditoriums, would carry the writer near Girgenti, an inter-
esting but rather inaccessible city on the southwestern coast of
Sicily. Finally, failing any especially favorable opportunity, a flying
trip was made from the north of Europe with the study of this gallery
and of the Ear of Dionysius at Syracuse as the sole objective. On
the way down the perplexity of the case was increased by finding in
Baedeker the statement that there is a noteworthy whispering gal-

Fig. 7. Interior, Cathedral of Girgenti, Sicily.

266 WHISPERING GALLERIES

lery between the west entrance of the Cathedral and "the steps of
the high altar." Such a whispering gallery is wholly inconceivable.
The facts showed a whispering gallery between the foci as described
by Herschel, although the accompanying story is rendered improb-
able by the extreme inaccessibility of the more remote focus, and its
very conspicuous position. Nor is the distance so great as stated by
Herschel, being a little over 100 feet instead of 250 feet. However,
the interest in this whispering gallery arises not because of any inci-
dent attending its discovery, but because it illustrates, albeit rather
crudely, the form of surface giving the best results for whispering
between two very widely separated points.

As already stated the strictly correct form of surface for a whisper-
ing gallery is an ellipsoid of revolution whose foci coincide with the
two points between which there is to be communication. In the
whispering gallery in the Cathedral of Girgenti (Fig. 7), the focusing
surface consists of a quarter of a sphere prolonged in the shape of a
half cylinder forming the ceiling over the chancel. This is obviously
not a true paraboloid, and, such as it is, it is interrupted by an arch
of slight reveal where the cylinder joins the sphere; moreover, the
two points of observation do not lie on the axis of revolution as they
should for the best result. But a hemisphere and a continuing cylin-
der make a fair approach to a portion of a paraboloid; and while the
two points of observation are not on the axis of revolution, they are
on a secondary axis, the station by the door being below, and the
focus in the chancel being at a corresponding distance above the
principal axis.

In all the preceding galleries, there is but a single reflection be-
tween the radiant and the receiving foci. There are others in which
there are several such reflections. Well-known examples are the
church of St. John Lateran in Rome and in the Salle des Cariatides
in the Louvre.

In the Church of St. John Lateran (Fig. 8), each bay in the great
side aisles is a square having a ceiling which is approximately a por-
tion of a sphere. At best, the approximation of the ceiling to a sphere
is not close and the ceiling varies from bay to bay, not intentionally
but merely as a matter of variation in construction. In one bay more
closely than in the others the ceiling, regarded as an acoustical

268 WHISPERING GALLERIES

mirror, has its foci nearly at head level. In consequence of this, two
observers standing at opposite corners can whisper to each other
with the ceiling as a reflecting surface. The curvature even in this
bay is not ideal for the production of a whispering gallery, so that
thus used the gallery is far from notable. It so happens, however,
that the great square columns which form the corners of each bay
have, instead of sharp corners, a reentering cove or fljating in the arc
of a circle and over twelve inches across in opening. If the observers,
instead of attempting to speak directly to the ceiling, turn back to
back and face the columns standing close to them, this great fluting
gathers the sound from the speaker and directs it in a concentrated
cone to the ceiling; this returning from the ceiling to the opposite
angle of the bay is concentrated by the opposite fluting on the other
observer. In more scientific language, borrowed from the nomencla-
ture of the makers of optical instruments, the flutings increase the
angular aperture of the system.

An almost exact duplicate of this whispering gallery is to be found
in the vestibule of the Conservatoire des Arts et Metiers in Paris.
This vestibule, itseK also an exhibition room but called since the dis-
covery of its peculiar property La Salle-Echo, is square with rounded
corners and a low domical ceiling. Here, as in St. John Lateran, the
observers face the corners and the whisper undergoes three reflec-
tions between the foci. The fact that the two observers are back to
back diminishes the sound which would otherwise pass directly be-
tween them and makes the whispering gallery more pronounced and
the phenomenon much more striking. In both galleries it is the cus-
tom for the observers to take their positions in a somewhat random
manner. The correct position is at a distance from the concave
cylindrical surface a little less than half the radius of curvature.

In these whispering galleries the surfaces are not theoretically cor-
rect and the phenomenon is far from perfect. This failure of loud-
ness and distinctness in most of the multiple reflection galleries arises
not from any progressive loss in the many reflections, for the loss of
energy in reflection is practically negligible. Indeed, given ideally
shaped surfaces, multiple reflection whispering galleries are capable
of producing exceptional effect; for if two of the surfaces be very
near the observers they may, even though they themselves be of

Fig. 9. Salle des Cariatides, the Louvre, Paris.

270 WHISPERING GALLERIES

small dimensions, gather into the phenomenon very large portions of
the emergent and of the focused whisper. In both St. John Lateran
and La Salle-Echo, the condensing mirrors are cylindrical and gather
the sound horizontally only. In the vertical plane, they are wholly
without effect.

It is not difficult to determine the correct forms for the extreme
mirrors. If the ceiling be flat, the reflecting surfaces near the two
observers should be parabolic with the axis of the paraboloid di-
rected toward the center of the ceiling, the correct position for the
mouth of the speaker and the ear of the auditor being at the foci of
the two paraboloids. If the ceiling be curved, the simplest design is
when the first and last reflectors are portions of an ellipsoid, each
with one focus at the center of the ceiling and the other at one of the
foci of the system as a whole. Finally, if the ceiling be curved, there
is still another theoretical shape for the end reflectors, determined by
the curvature of the ceiling; in this case the ideal surface is not a
conic surface, nor otherwise geometrically simple, but is such that the
converging power of the end mirror with half the converging power
of the middle mirror will give a plane wave.

It is obvious that the accurate fulfilling of these conditions by acci-
dent is improbable, but they are at least approached in the whisper-
ing gallery in the Salle des Cariatides in the Louvre (Fig. 9). Along
the axis of the room, and at no inconsiderable distance apart, are two
large shallow antique vases. A whisper uttered a little within the rim
of one is partially focused by it, is still further focused by the barrel-
shaped ceiling, and is brought to a final focus symmetrically within
the rim of the further vase. It is evident that the effect is dependent
on only a portion of each vase, but this portion satisfies the necessary
conditions to a first approximation in both longitudinal and in trans-
verse section. When the correct foci are found this whispering gallery
is very distinct in its enunciation. It would be even more distinct if
the ceiling of the room were slightly lower, or, keeping the height the
same, if its radius of curvature were slightly greater. It would be
still better if the vases were sUghtly deeper.

The whispering gallery which has received the greatest amount of
discussion, and a discussion curiously inadequate in view of the emi-
nence of the authorities engaged, is the circular gallery at the base of

Fig. 10. Section through Dome of St. Paul's Cathedral, London.

272 WHISPERING GALLERIES

the dome of St. Paul's Cathedral in London. This gallery was first
brought into scientific consideration by Sir John Herschel, who in
describing it stated that "the faintest sound is faithfully conveyed
from one side to the other of the dome, but is not heard at any inter-
mediate point." According to Lord Rayleigh, whose reference, how-
ever, I am unable to verify, and either in page or edition must be in
error, an early explanation of this was by Sir George Airy, the Astron-
omer Royal, who " ascribed it to the reflection from the surface of the
dome overhead." Airy could have been led into such error only by
the optical illusion whereby a dome seen from within seems lower
than it is in reality. A moment's inspection of the preceding
illustration (Fig. 10), which the Clerk of the Works kindly had re-
produced from an old engraving in the possession of the cathedral,
shows that this explanation would be incorrect. The guide who does
the whispering usually occupies the position marked "A"; the other
focus is in the position marked "B." The focus accounted for by Airy
would be high up in the dome. Lord Rayleigh taking exception both
to the statement of fact by Herschel and the explanation by Airy
wrote "I am disposed to think that the principal phenomenon is to be
explained somewhat differently. The abnormal loudness with which
a whisper is heard is not confined to the position diametrically oppo-
site to that occupied by the whisperer, and therefore, it would appear,
does not depend materially upon the symmetry of the dome. The
whisper seems to creep around the gallery horizontally, not neces-
sarily along the shorter arc, but rather along that arc toward which
the whisperer faces. This is in consequence of the very unequal
audibility of a whisper in front of and behind the speaker, a phe-
nomenon which may easily be observed in the open air." Lord
Rayleigh's explanation of the phenomenon in this case as due to the
"creeping" of the sound around the circular wall immediately sur-
rounding the narrow gallery accessible to visitors is unquestionably
correct. It is but another way qf phrasing this explanation to say
that the intensification of the sound is due to its accumulation when
turned on itself by the restraining wall. It is obvious that the main
intensification arises from the curved wall returning on itself. Verti-
cally, the sound spreads almost as it would were the curved wall
developed on a plane. This vertical spreading of the sound is in a

WHISPERING GALLERIES 273

measure restricted by the circular floor gallery and by the overhang-
ing ledge of the cornice moulding. The cornice can be made to con-
tribute most to the effect by making the curve of its lines below the
principal projecting ledge, that which corresponds to the drip mould-
ing of an exterior cornice, relatively smooth and simple.

But even Lord Rayleigh's explanation does not fully account for
the truly remarkable qualities of this whispering gallery. There are
many circular walls as high, as hard, and as smooth as that in St.
Paul's Gallery but in which the whispering gallery is not to be com-
pared in quality. The rear walls of many semi-circular auditoriums
satisfy these conditions without producing parallel results, for ex-
ample in the Fogg lecture-room at Harvard University before it was
altered, and in the auditorium just completed at Cornell University.
A feature of the whispering gallery in St. Paul's, contributing not a
little to its efficiency, is the inclination of its wall, less noticeable per-
haps in the actual gallery than in the architectural " Section." The
result is that all the sound which passes the quarter point of the
gallery, the point half way around between the foci, is brought down
to the level of the observer, and, combined with the reflection from
the ledge which constitutes the broad seat running entirely around
the gallery, confines and intensifies the sound. This feature is of
course of unusual occurrence.

It may not be out of place to give the dimensions of this gallery.
The distance from focus to focus, if indeed in this type of gallery
they can be called foci, is 150 feet. The wall has a height of 20 feet,
and is not moulded in panels as shown in the engraving, but is smooth
except for eight shallow niches. While the inclination of the wall in
the gallery of St. Paul's is a contributing factor, an even more efficient
wall would have been one very slightly, indeed almost imperceptibly,
curved, the section being the arc of a circle struck from the center of
the dome on a level with the observers. Such a gallery will be in the
dome of the Missouri State Capitol, a gallery unique in this respect
that it will have been planned intentionally by the architects."^

A discussion of noted whispering galleries would not be complete

' The building is now complete One of the architects, Mr. Edgerton Swartwout, reports
that the whispering gallery in the dome exactly fulfills Professor Sabine's prediction, and
has been the cause of much curiosity and astonishment. — Editor.

274

WHISPERING GALLERIES

without mention of the famous Ear of Dionysius at Syracuse. A
mile out from the present city of Syracuse, on the slope of the terrace

occupied by the Neapolis of
the ancient city, are the re-
mains of a quarry entered
on one side on the level but
cut back to perpendicular
walls from a hundred to a
hundred and thirty feet in
height. This old quarry,
now overgrown by a wild
and luxurious vegetation, is
known as the Latomia del
Paradiso. At its western
angle is a great grotto,
shaped somewhat like an
open letter S, 210 feet in
winding length, 74 feet high,
35 feet in width at the base
and narrowing rapidly to-
ward the top. The inner-
most end of this grotto is
nearly circular, and the
rear wall slopes forward as
it rises preserving in revolu-
tion the same contour that
characterizes the two sides
throughout their length.
The top is a narrow channel
of a uniform height and but
a few feet in width. At the
innermost end of this chan-
nel, at the apex of the half
cone which forms the inner
end of the grotto, is a verti-

FiG. 11. Plan and Elevation, with Sectional
Indication, of Ear of Dionysius, Syracuse,
Sicily.

cal opening four or five feet square, scarcely visible, certainly not
noticeable, from below. This opening is into a short passageway

Fig. 12. View of Outer Opening, the So-called Ear of Dionysius, Syracuse, Sicily.

276 WHISPERING GALLERIES

which leads to a flight of steps and thence to the ground above (Fig.
11). The grotto is noted for two somewhat inconsistent acoustical
properties. When being shown the grotto from below, one's atten-
tion is called to its very remarkable reverberation. When above,
one's attention is called to the ability to hear what is said at any
point on the floor.

It is related that Tyrant Dionysius, the great builder of Syracuse,
so designed his prisons that at certain concealed points of observation
he could not merely see everything that was done, but, through re-
markable acoustical design, could hear every word which was spoken,
even when whispered only (Fig. 12). There is a tradition, dating
back however only to the sixteenth century, that this grotto, since
then called the Ear of Dionysius, was such a prison. Quarries were
plausible prisons in which captives of war might have been com-
pelled to work, and there are, surrounding this quarry, traces of a
wall and sentry houses, but there is no direct evidence associating
this grotto with Dionysius, unless indeed one regards its interesting
acoustical properties taken in connection with classical tradition as
such evidence.

In its acoustical property this grotto resembles more a great ear
trumpet than a whispering gallery in the ordinary sense of the word.
It is, of course, in no sense a focusing whispering gallery of the type
represented by the vases and curved ceiling in the Louvre. It more
nearly resembles the gallery in St. Paul's Cathedral, but the sound
is not spoken close to the deflecting wall, one of the essentially
characteristic conditions of a true whispering gallery of that type,
and the wall is not continuously concave. In fact, in other ways also
its acoustical property is not very notable, for distinctness of enun-
ciation is blurred by excessive reverberation.

It is conceivable that whispering galleries should be of use and
purposeful, but it is more probable that they will remain architectural
curiosities. When desired, they may be readily woven into the design
of many types of monumental buildings.

APPENDIX

NOTE ON MEASUREMENTS OF THE INTENSITY OF SOUND AND
ON THE REACTION OF THE ROOM UPON THE SOUND

IvuRiNG one of the early lectures given at the Sorbonne in the spring
of 1917, Professor Sabine referred to the difficulties inherent in ex-
periments on sound intensities. The following is a free translation
from the notes, in French, which he prepared for this lecture:

In no other doman have pihysicists disregarded the conditions in-
troduced by the surrounding materials, but in acoustics these do not
seem to have received the least attention. If measurements are made
in the open air, over a lawn, as was done by Lord Rayleigh in certain
experiments, is due consideration given to the fact that the surface
has an absorbing power for sound of from 40 to 60 per cent.? Or, if in-
side a building, as in Wien's similar experiments, is allowance made
for the fact that the walls reflect from 93 to 98 per cent of the sound?
We need not be surprised if the results of such experiments differ
from one another by a factor of more than a hundred.

It would be no more absurd to carry out photometric measure-
ments in a room where the walls, ceiling, and even the floor and tables
consisted of highly polished mirrors, than to make measurements on
the intensity, or on the quantitative analysis of sound, under the con-
ditions in which such experiments have almost invariably been exe-
cuted. It is not astonishing that we have been discouraged by the
results, and that we may have despaired of seeing acoustics occupy
the position to which it rightly belongs among the exact sciences.

The length of the waves of light is so small compared with the
dimensions of a photometer that we do not need to concern ourselves
with the phenomena of interference while measuring the intensity of
light. In the case of sound, however, it must be quite a different
matter.

In order to show this in a definite manner, I have measured the
intensity of the sound in all parts of a certain laboratory room. For
simplicity, a symmetrical room was selected, and the source, giving a
very pure tone, was placed in the center. It was found that, near the

278 APPENDIX

source, even at the source itself, the intensity was in reality less than
at a distance of five feet from the source. And yet, the clever experi-
menter, Wien, and the no less skillful psychologists Wxmdt and
Miinsterberg have assumed under similar conditions the law of varia-
tion of intensity with the inverse square of the distance. It makes
one wonder how they were able to draw any conclusions from their
measurements .

Not only do the walls reflect sound in such a way that it becomes
many times more intense than it otherwise would be; and not only
does the interference of soimd exist to such an extent that we find
regions of maximum and regions of minimum of sound in a room; but
even the total quantity of sound emitted by the source itself may he
greatly affected by its position with regard to the interference system
of the room.

This will be more readily understood if illustrated by an incident
drawn from the actual experiments. A special sort of felt, of strong
absorbing power, was brought into the room and placed on the floor.
The effect was two-fold. First, the introduction of the felt increased
the absorption of the sound, and thus tended to diminish the total
intensity of sound in the room, theoretically to a third of its previous
value. But actually it had the contrary effect; the soimd became
much louder than before. The felt was so placed on the floor as to
shift the interference system in the room, and thus the reaction of the
soimd vibrations in the room upon the source itself was modified.
The source was a vibrating diaphragm situated at the base of a res-
onating chamber. In its first location, the source was at a node of
condensation, where the motion of the sound which had accumulated
in the room coincided with that of the diaphragm. It was thus diffi-
cult for the diaphragm to impart any additional motion to the air.
In the second case, however, the vibrations of the two were opposite;
the diaphragm was able to push upon the air, and although the am-
plitude of its motion was somewhat reduced by the reaction of the air
upon it, the emitted soimd was louder. When imder these conditions
the diaphragm was forced to vibrate with the same amplitude as at
first, the emitted sound became eight times louder.

Naturally these two positions in the interference system were de-
signedly selected, and they show exceptional reactions on the source.

APPENDIX 279

However, in the case of a very complex sound, a comparable diver-
gence in the reaction of the room on the different components of the
sound would be probable.

It is thus necessary in quantitative research in acoustics to take
account of three factors: the effect of reflection by the walls on the
increase of the total intensity of sound in the room; the effect of inter-
ference in greatly altering the distribution of this intensity; and the
effect of the reaction of the sound vibjrations in a room upon the
source itself. . . .

In choosing a source of sound, it has usually been assumed that a
source of fixed amplitude was also a source of fixed intensity, e. g., a
vibrating diaphragm or a tuning fork electrically maintained. On the
contrary, this is just the sort of source whose emitting power varies
with the position in which it is placed in the room. On the other
hand, an organ pipe is able within certain limits to adjust itself auto-
matically to the reaction due to the interference system. We may
say, simply, that the best standard source of sound is one in which the
greatest percentage of emitted energy takes the form of sound.

PRINTED AT

THE HABVABD UNIVBBSITY PRESS

CAMBRIDGE, MASS., U.S.A.

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