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SP-58 
Supplement to 
H.O. Pub. 614 


SPECIAL PUBLICATION 


TABLES OF SOUND SPEED 
IN SEA WATER 


Oceanographic Analysis Division 
| Marine Sciences Department 


AUGUST 1962 


OC 
e 228.8 U.S. NAVAL OCEANOGRAPHIC OFFICE 
3S WASHINGTON, D.C. 
ek. 


| s - 


+ 


SP-58 
Supplement to 
H.O. Pub. 614 


SPECIAL PUBLICATION 


TABLES OF SOUND SPEED 
IN SEA WATER 


Oceanographic Analysis Division 
Marine Sciences Department 


AUGUST 1962 


-8 U.S. NAVAL OCEANOGRAPHIC OFFICE 
WASHINGTON, D.C. 


Mey CO 


ABST RAG. 

Sound speed tables have been computed from W.D. Wilson’s 
equation (Journal of the Acoustical Society of America, Vol. 32, 
No. 10, October 1960). The tables cover temperature, salinity, 
and pressure ranges from —2.5° to 34.9°C, 0 to 41.9°/,., and 
1.03 kg/cm2 to 1260 kg/cm2. A pressure-depth relationship is 
established whereby the tables may be entered with either depth 
in meters or pressure in kilograms per square centimeter. 

A sound speed nomogram developed from values in the table is 

_ presented for purposes of rapid calculation. 


FOREWORD 


It has become increasingly evident that the accuracy of the Kuwahara 
equation for computing sound speeds in sea water is not sufficient for 
present day needs. In situ measurements of sound speed in sea water 
indicate that at some depths the speed calculated by the Kuwahara 
equation is 3 to 4 meters per second too slow. To remedy this inade- 
quacy a conference of interested parties, heldatthe Hydrographic Office 
in May 1961, concluded that the sound speed equation of Kuwahara 
should be replaced by the empirical equation developed at the Naval 
Ordnance Laboratory by Wayne D,. Wilson. Since that time this Office 
has been recomputing available sound speed data onthe basis of Wilson's 
equation, The tables presented here have beendevelopedfrom the Wilson 
equation to facilitate hand computation of sound speeds from tempera- 
ture and salinity data. 


Although continuing research may yield more accurate equations, 
these tables are individually accurate to the nearest 0.1 meter per 
second and the total error in any computation within the normal range 
of oceanographic variables should be less than 0.3 meter per second. 


Rear Admiral, U. S. Navy 
Commander 


sp os oe 
a os 


CONTENTS 


Page 
Part I, Discussion 
AS A Wiel DLS Bie, Mise cle ots Najves oe aintet fects 56 0 6) Opec ay ciated cars 2 
B_sound speed) Nomograrns sg ve eile fe =) eels i ies 3 
RUGS 5 6 6004 ¢ 9906000005 5 Rep Eseiamee 4 
Part II, Sound Speed Tables 
Examples of Use Of Tables c.h jes 6 <i ter = tei (esi te aller 7 
Table 1. Sound Speed, V, (1449.1 m/sec), corrected 
for changes in Pressure (kg/cm4), Vopr cece 8 
Table 2, Sound Speed, V, (1449.1 m/sec), corrected 
for changes in Depth (meters), pressures 
derived assuming 35%, 0°C), Vp Ste hes - 9 
Table 3. Correction to Sound Speed, V, (1449.1 m/sec), 
for changes in Latitude-Depth, Vy .......- ) 
Table 4. Correction to Sound Speed, V, (1449.1 m/sec), 
for changes in, Salinity (%e); Veo 2 5 - =: 2 © = 10 
Table 5. Correction to Sound Speed, V, (1449.1 m/sec), 
for changes in Temperature (°C), Vz. .... ~ 20 
Table 6. Correction to Sound Speed, V, (1449.1 m/sec), 
for simultaneous changes in Salinity, 
Temperature, and Pressure, Vstp AGO 10h Go. co 28 
Table 7. Sound Speed Conversion - Meters/Second 
COSMECENOECONGd Santis se we «hs 5. a aha 47 
FIGURE 
sound Speed INomogram 2.9. i. 656. s+ s « Hap ultée Oh Seon O- Chee 5 


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PART I. DISCUSSION 
INTRODUCTION 


The sound speed tables presented in H. O. Pub. No. 614), after 
Kuwahara2, present sound speed as a function of temperature, salinity, 
pressure, and latitude. His tables were developed from mathematical 
analysis of specific volumes rather than empirical sound speed meas- 
urements, Actual measurements of sound speed in sea water indicate 
Kuwahara's speeds are approximately 4 meters per second too slow. 


With the development of progressively more complex weapons 
systems it became necessary to have more accurate sound speed 
information. As a result of this recognized need, a conference? of 
interested parties was held at the Hydrographic Office in May 196l 
for the purpose of resolving whether or not a new equation for the 
calculation of sound speed should be adopted, It was generally agreed 
that Wilson's equation4 (shown below) should be adopted for Naval 
applications. This decision was reached with the knowledge that 
research presently being conducted may yield equations which are 
somewhat more accurate. 


V m/sec. = 1449.14 +Vp +V +Vy +Vetp 


Where: 
Vp") ='160272 > -10=" PhO268"x 107° P24'sH216 « 1059.P8 
— 3.3603 x 10-12 p4 
V, = 1.39799 (S—35) + 1.69202 x 10-3 (S—35)? 
od ss =e ahh og tg 24 
V4 572, Aaba2 se 10e- i = 2 6045. .q 10 1° + 729851 sc 10 ° 1 
Veg = S35) (244 100s 7 7711 XO’ T+ 7.7016,% 10, P 


— 1.2943 x 10-7 P? +3.1580 x 10-8 PT+1.5790 x 10-2 PT?) 
P(2{1e607 10 2 -P a7ae12' 10-8 1 4.4.5 283 a0 BT) 
4+ P*(—2.5204 x 10-” T +1.8563 x 10-9 T*) +P°(—1.9646 x 
Oj. TD: 


The tables presented herein are computed from the above equation 
and should be used in lieu of those in H. O. Pub. No. 614, 1951 edition. 


A. TABLES 


According to Wilson, the mean standard deviation of the error 
between his equation and measured speeds over the range of variables 
(temperature -4°C. to 30°C., salinity 0% to 37%, pressure 1 to 1,000 
kg/cm“) is 0.30 m/sec. With temperature as the dependent variable, 
the maximum standard deviation is 0.74 m/sec at salinity 0.00% and 
surface pressure, and the minimum standard deviation is 0.08 m/sec 
at 36.55% salinity and 420 kg/cm% pressure. 


The accuracy of the equation at values higher than those shown 
above has had some limited evaluation by Wilson. The difference 
between the measured and computed velocities at some sample extreme 
values are: 


Temperature Salinity Pressure Difference 
30 513°C. 42.15% Surface 0.13m/sec 
39.85 34.99 Surface 0.06 
39.85 42.15 Surface 0.85 
39.85 42.15 381 kg/cm2 0.65 
20.11 34.99 1,150 kg/cm2 0.21 


Tables 1 through 6 were developed using the Wilson equation 
programmed for the IBM 7070 computer. The speeds were computed 
to the nearest 0.01 m/sec and for convenience were rounded to the 
nearest 0.1 m/sec for presentation. 


Although Wilson's equation is entered with pressure as a variable, 
by assuming a uniform water column of 0°C. temperature and 35% 
salinity, a depth-pressure relationship is established; therefore, the 
tables are presented so that they canbe entered with depth or pressure. 
A convenient depth interval from 1 meter to 11,500 meters in the depth 
(pressure) correction, Table 2, is used in order to minimize interpo- 
lation; however, if it is desired to use in situ pressure to obtain the 
pressure correction, Table 1 is to be used, Table 3, converted from the 
original Kuwahara table, is to be applied to correct the sound speeds 
for variations in gravity with latitude and depth. Tables 4 and 5 may be 
entered with salinity to the nearest 0.01% and temperature to the 
nearest 0.01°C., thus eliminating interpolation. The simultaneous cor- 
rections for temperature, salinity, and depth (pressure) are presented 


in Table 6 at standard oceanographic station depths assuming the above 
pressure-depth relationship. Again, if it is desired to use in situ 
pressures instead of depth to make the simultaneous correction, the 
pressure value is presented at each depth. Some interpolation may be 
required in these tables; however, for depths less than 3,000 meters, 
the difference between tables for identical temperature and salinity 
values is usually less than 0.2m/sec. Table 7 is presented for ease 
of conversion of meters/second to feet/second if desired. 


The assumption that the sound speed at a particular depthisa 
weak function of the temperature and salinity structure above that 
depth is supported by NEL”. Inaddition, direct comparisons were made 
at the Hydrographic Office between the speeds presented here and 
those computed by using the actual pressures. Sound speeds were 
computed at standard depths, in one case using computed in situ 
pressures and in the other using computed pressures resulting from 
an assumed water column at 0°C. temperature and 35% salinity. 
In the Gulf of Alaska and the Philippine Trench, this method indicated 
differences of less than 0.1 m/sec or less above 4,000 meters depth. 
In the Philippine Trench at 8,000 meters, the difference was less 
than 0.2 m/sec. These computations indicated that the change in 
pressure attributed to differences in temperature and salinity from 
0°C. and 35% have only a minor effect on the sound speed at any depth. 


B. SOUND SPEED NOMOGRAM 


The sound speed nomogram and structure form was drawn from the 
values of sound speed giveninthe tables. As in the tables, the pressure- 
depth relationship is based on a 0°C. and 35% water column, The main 
body of the nomogram presents sound speed as a function of tempera- 
ture and depth with salinity held at 35%. Values are plotted to the 
nearest tenth of a meter per second and can probably be read to the 
nearest 0.5 m/sec. An inset is provided to correct for salinities other 
than 35%; for salinities less than 35% the correction is negative, for 
salinities greater than 35% the correction is positive. For the normal 
range of salinity, temperature, and depth for oceanic and nearshore 
waters the salinity correction is accurate to the nearest 0.1 m/sec. 
For anomalous oceanographic conditions but within the range of 
variables covered by the tables, the error may increase to 0,3 to 
0.4m/sec; i.e., for fresh water at 2,000 meters depth or 32% (or 38%o) 
salinity at 11,000 meters. 


Sound speeds from the nomogram can be determined to within one 
meter per second; if greater accuracy is desired, the tables should be 
used, 


The temperature structure at an oceanographic station may be 
plotted on the nomogram to determine an approximate sound speed 
structure. Large errors in absolute speed will occur in nearshore 
areas or enclosed seas where the salinity may deviate radically from 
35%0; the general shape of the speed structure may be easily determined 
for the normal oceanographic environment, 


REFERENCES 


1. U. S. HYDROGRAPHIC OFFICE. Processing oceanographic data,by 
E. C. LaFond, H. O. Pub. No. 614. 114p., 1951. 


2. KUWAHARA, S. Velocity of sound in sea water and calculation of the 
velocity for use in sonic sounding. Hydrographic Review, vol. 16, 
no, 2, pp. 123-140, 1939. 


3. U. S. HYDROGRAPHIC OFFICE. Summary of the conference on 
sound speed equations. Enclosure to HO ltr ser 9233 of 24 Oct. 
1961. 


4, WILSON, W. D. Equation for the speed of sound in sea water, 
Journal of the Acoustical Society of America, vol. 32, no. 10, 
pp. 1357, Oct. 1960. 


5. PEDERSEN, M. A. NEL sound velocity program. Informal draft 
enclosure to NEL ltr to USNHO SF001 03 01 (NEL L15) 2233-13 
of 10 May 1961. 


DEPTH (THOUSANDS OF FEET) 


SP 58 
4700 4800 4900 5000 5100 5200 FEET/SEC 
1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS /SEC 
0 
;, 100 
0.5 as at aoe =a 40° 45° 50° 55% 60" 65° 70' 75% 80% 85'y TEMPERATURE (°F) 
200 
| al i 
1.0 300 
T | 
400 
nes 0°! > 4 6° 8° 10° 12° 14° 16° 18° 20°)-KY-22°-\ 24°-h+ 26° 28°] 30°} TEMPERATURE (°C) 
1.5 ! 
64 300 
2 - 
3 1000 
| 
4 BB | | 
: | 
4 | T ! 
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T . 2000 
7 | Tt | 
| T 
8 if it it i ; | | = 
h im @ | 1 wn 
i 1 i-4 
| w 
9 | + t Ww 
10. - i - i 3000 = 
t col & 
11 SALINITY CORRECTION t t Le 
3 
‘a SALINITY (°/, ,) a Fa) 
} 
an a 
13 30 5 | LI 4000 
t = 
14 t 
40 ie om ta T 
15 H ~ 5 Eo 
16 = | i H | a It i | 
£ 50 - {31 $3345] 37439f 41 10 O ‘ C 5000 
179] wo Z LAS 
5 ots 10 155 20 25++11 30} 32}34136}38}40 2 i 
18K] = pie 
& 60 a 
if rH 1) Fi ; t 
19 = : Lue i 4 + I 
a - t i 6000 
20 
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T T 
21 ea | 
25 CI i 
22 80 [ | 
| 
[ i 7000 
23 —50 —45 —40 —35 —30 —25 —20 —I5 —10 —5 0 5 Tom ~ T 
METERS /SEC + 
24 ol or ro ott 
~150—140 -130 -120 -110 -100 -90 —80 -70 -60 -50 -40 -30 -20 -10 fo) 10 20 30 
25 FEET/SEC 
SOUND SPEED CORRECTION FOR SAUNITY it }_} 
26 T 


SOUND SPEED NOMOGRAM 
(BASED ON WILSON’S EQUATION) 


HO.N29167@2-c35 


FEET/SEC 


: 8000 
1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS/SEC 
4700 4800 4900 5000 5100 5200 


5 


DEPTH (THOUSANDS OF FEET) 


SOUND SPEED NOMOGRAM 
(BASED ON WILSON’S EQUATION) 


SP 58 
4700 4900 5000 5100 5200 FEET/SEC 
1430 1490 1500 1530 1540 1550 1560 1600 METERS/SEC 
i) 
| 100 
0.5 +-|50° 55 70 804 85%¢ TEMPERATURE ("F) 
200 
1.0 300 
T 400 
15 105 12° 18° 20° aay 24° 26° 28° 4; 30°} TEMPERATURE (°C) 
64 500 
2 =: 
sh 
3 if 
1000 
4 
5 
I l I 
6 + 
2000 
i, if if if T 
| 1 | 
8 t t an 
T T a 
T 
9 ; w 
w 
10 3000 = 
7 oh a = 
* SALINITY CORRECTION f a 
196; qf S 
12 25 October ) y) SALINITY eZ. ) ~ : : uw 
ie c | 4000 
14 ri i 
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16 L h f —+— 
o - 5000 
17 = iz t = It 
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23 7000 
25. —20 
24 METERS /SEC 
25 -160 —150—140 —130-120-110-100 ~90 -80 ~—70 -60 -50 -40 -30 -20 -10 © 10 20 30 ~ 
FEET/SECOND | 
SOUND SPEED CORRECTION FOR SAUNITY 1 
26 ; I 8000 
1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 METERS/SEC 
4700 4800 4900 5000 5100 5200 FEET/SEC 


HO.N916782-C35 


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TABLE 4. CORRECTION TO SOUND SPEED, Vo (1449.1 m/sec), FOR CHANGES IN SALINITY (%o), V, - Continued 


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© METERS 
(1.03 kg/cm?) 


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6.3 


9-9}10.7 JIT.4% 112.2 113.0 113.7 
9-8/10.5 J11.3 ]12.0 [12.8 }13.5 
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9-7 [10.4 J11.1 11128 )12.5 
9-6 110.3 J11.0 111.6 112.3 
8.8} 9.4 10.1 [10.8 [11.4 {12.1 
9-9 110.6 |1123 J11.9 

9 

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8.6] 9.3 


9.3 
9.0 
8.9 


9.2 
9.0 
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TABLE 6, CORRECTION TO SOUND SPEED, V, (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN 


9.9 
9.7 
6.5 
6.3 


9-5 |10.1 


9.7 |10.3 |10.9 
9.5 |10.1/10.7 
9.3 | 9.9 /10.5 
9.2) 9-7 (10.3 

9.3 

9.2 

6.1 

5.9 

5.3 

Sa2 || 55 


6.5 | 6.9 


8 
6 
el 

8.6 

7.0 

5.7 

5.6 

5.2 


8.9 


Ail 


5-9 | 6.3 


e 


8.2] 8.8 


8.8 

8.6 

8.1 

Te) 

6.6 

6.4 

5-4 

5.2 

5.1 

4.9 
4.4] 4.7] 5.0 
4.2), 4.5 14.8 


9.1 
9.0 
7.9 | 8.5 
8.3 
8.2 
8.0 
7.9 | 8.4 | 9.0 
te 
7.5 
6.6 
el 
6.0 
5.8 
5.7 
sry) 
S108) 
5.2 
5.0 
4.9 
4.7 
4.6 


t.7 
726 
To4 
1-3 
7.1 
7.0 
6.1 
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5-4 
5.3 
SI 1 
4.8 
4.5 
ue 
4.2 
4.1 
3.9 


0 


otf 6.3 6-9 


7.8| 8.5 
T.7| 8.3 


6.7 
6.6 
6.5 
Bet 
5.3 
5-0 
4.4 | 4.8 
4.3 | 4.7 
4.6 
44 
4.2 
4.0 
3.9 


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6.2 
6.0 
5.9 
4.6 
Toe | 
Sie! 


6.5 
5.6 
5.5 
4.0 
Sid, 
3-8 | 4.2 
3.7 
364 
3.3 | 3-6 


5.9 
5.8 
See 
5.1 
4.9 
3.5 
3.4 
3.3 
3.0 
2.9 


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3.3 
3.2 
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360 
2.9 
2.7 


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369 | 4.5 
3-8 | 4.4 


4.0 | 4.6 
2.9 
2.8 
2.7 
2.7 
2-2 | 2.6 
2.5 
2.4 
2.4 
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3.4 
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-0.0 
-0.0 
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-0.8 
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-0.7 
-0.7 
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28 


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-0.6 
-0.8 


-0.4 


-0.8 


-0.7|-0.7|-0.8 


-0.8|/-0.9 


-0.5/-0.5/-0.6 


-0.4 
-0.6/-0.7 


-0.4 


-1.0 


-0.7 -0.9 


-0.5 -0.6 


1.4 


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-1.6 
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-1.9 


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0.2 
0.1 
0.1 


1 
1 
1 
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0. 
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0.8 
0.7 
0.6 
0.5 
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0. 
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0.2 
0.2 
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0.1 
0.0 


0.6 
0.5 
0.4 
O.4 
0.3 
0.3 
0.2 
0.2 
0.2 
0.1 
0 
0.1 
0.0 
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-0 
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0.5 
O4 
0.4 
0.3 
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0.2 
0.2 
0.2 
0.0 
0.0 


0.1 
0.1 


1 
1 
1 


2 
2 
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0.2 
0.2 
0.0 
0.0 
0.0 
0.0 


0 
0 
0.1 
0 
0 
0 
0.1 
0.1 
0.1 


-0.0 
-0.0 
0. 
0. 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0} 0.1 

-0.0 
-0.0 
-0.0 
=O. 
-0. 
-0.0 

0 

0 

0 


-0.6/-0.3 
-0.6|-0.3/-0.0 
-0.5 -0.3 
Si- 
Si- 
-0.5/-0.2 
-0.4/-0.2 
-0.4)-0.2 
-0.3/-0.2 
-0.3/-0.2 
-0.3/-0.1 
-0.3/-0.1 
. 0 
° 0 
-0.2/-0.1 
-0.2/-0.1 
-0.2 -0.1 
=O |—Olen 
-0.1/-0.1 
-0.1 
-0.1/-0.0 
-0.0/-0.0 
-0.0]-0.0 
0.0] 0.0 


22.0 
22.5 
23.0 
23 

24 

24 

25.0 
26.5 
27.0 
27.5 
28.0 
28.5 
29.0 
29.5 
30 

30.5 
31.0 
31.5 
32.0 
32.5 
33.0 
33-5 
34.0 
3425 
35.0 
35.5 


29 


-0.1 
-0.2 


0.0}-0.0/-0.1 
-0.2 


0.0 
0.1 


0.1 


-0.3|-0.3}-0.4/-0.4 


=0.2 


-0.1/-0.1 


0.0 


0.1 


37.5 


O.1] 0.1 


38.0 


0.0/-0.1/-0.2]-9.2)-0.3|-0.4/-0.5/-0.6)-0.6 


0.1 


0.2 


38.5 


39.0 


-0.7/-0.8 


-0.2|-0.3/-0.4|-0.5|-0.6 
-0.2}-0.3})-0.5|/-0.6/-0.7/-0.8|/-0.9 


0.0/-0.1 


0.2} 0.1 


39.5 


0.0/-0.1 


0.1 


0.2 
0.2 
0.3 
0.3 


40.0 


40.5 
41.0 


-0.3}-0.4|-0.5|-0.7 


-0.1 


0.0 


0.1 


41.5 
42.0 


0.0/-0.2|-0.3|-0.5/-0.6|-0.8|]-0.9]|-1.1 


0.2 


0.3 


TABLE 6. CORRECTION TO SOUND SPEED, V,, (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN 


500 METERS 
(52.47 kg/cm?) 


SALINITY, TEMPERATURE, AND PRESSURE, Vetp - Continued 


Se eee EEE: 


36 


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3.5 


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2.6 
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3.3 
3.2 
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3.5 


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1.9 
1.8 
1.7 


1.6 
1.5 
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0.3 

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0.1 0.3 
0.1 0.3 
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-0.0 
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0.0 
0.0 
0.0 
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0.0 
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0.0 
0.0 


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0.2 
0.3 
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0.3 
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28.5 
29.0 
29.5 
32.0 
32.5 
33.0 
33.5 
34.0 
34.5 
35.0 
35.5 
38.0 
38.5 
39.0 
39.5 
40.0 
40.5 
41.0 
41.5 
42.0 


TABLE 6. CORRECTION TO SOUND SPEED, Nia (1449.1 m/sec), FOR SIMULTANEOUS CHANGES IN 


1000 METERS 
(104.09 kg/cm?) 


- Continued 


SALINITY, TEMPERATURE, AND PRESSURE, Vetp 


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9.5 
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4.7 
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6.8 
6.7 
6.6 
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6.3 
6.2 
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5.8 
5.6 
5.5 
5-4 
5.2 
5.1 
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4.7 
4.6 
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3.9 
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6.7 
6.6 
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5.8 
5.7 
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3.5 
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5.8 
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4.8 
4.7 
4.6 
4.5 
Koy 
Key 
4.3 
4.2 
4.1 
4.1 
4.0 
3-9 
3.8 
3-8 
3.7 
3.6 
3.5 
3-5 
3.4 
3-3 
322 
3.2 
3.1 
3.0 
2.9 
2.9 
2.8 
2.7 
2.6 
2.6 
POPS 
2-4 
2-3 
2.3 
Dae 
2.1 
2.0 
2.0 


) 
1.6 
1.8 
1.7 
1.6 
1.6 


3-6} 4.3 
365 | 4.3 
3e5| 4e2 
3-4 | 4.1 
4.1 
4.0 
4.0 
3.9 
OW We sinks} 
Sel | sa8 
3.7 
3.6 
3.6 
3605 
3.4 
3.4 
3.3 
3.3 
3.2 
3.1 
3. 
3.0 
2.9 
2.9 
2.8 
2.7 
PT 
2.6 
2.0} 2.4 
1.9 | 2.4 
Ta? | 2635 
1.8 | 2.2 
1.8 | 2.2 
TaZionh 
1.7 | 2.0 
1.6 | 2.0 
1.6 | 1 
1.5 
1.4 
1.4 
3 
1.3 


3.3 
323 
3.2 
322 
3.0 
3.0 
2-9 
PP) 
2.8 
2-8 
2.7 
2.7 
2.6 
2.6 
2.5 
2.5 
2-4 
2-3 
2.3 
262 
2-2 


2.1 
2.1 
2 


2.8 
2.7 
2.7 
Ziel 
2.6 
2.6 
2.5 
2.5 
2.5 
2-4 
2.4 
263 
2.3 
2.2 
2-2 
2.2 
2. 
2.1 
2.0 
2.0 
2.0 
1.9 
1.9 
8 
1.8 
7 
1.7 
lot 
1.6 
6 
1.5 
5 
1.5 
1.4 
1.4 
1.3 
1.3 
1.2 
1.2 
1.2 
] 
] 
1.0 
1.0 


1.9 
1.9 
1.9 
1.8 
1.8 
1.8 
1.8 
1.7 
1.7 
1.7 
1.6 
1.6 

6 
1.5 
1.5 
1.5 
1.4 
1.4 
1.4 
1.4 
1.3 
1.3 
1.3 
1.2 
1.2 
1.2 

1 
1.0 
1.0 
1.0 


2.0 
2.0 
0.9 
0.9 
0.9 
0.8 
0.8 
0.8 
0.7 
0.7 


1.3 | 2.0 


1.2 
1.2 
1.2 
1.2 
1.2 
1.2 
1.0 
1.0 
1.0 

0) 
1.0 


0.9 
0.9 
0.9 
0.9 
0.9 
0.8 
0.8 
0.8 
0.8 
0.8 
0.7 
0.7 
0.7 
0.7 
0.6 
0-6 
0.6 
0.6 
0.6 
0.5 
0.5 
0.5 
0.5 
0.5 
0.4 


1.1 
1.1 
1.1 


0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.4 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.3 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 


Ole 
-0.2 
0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
=Olee 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.2 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
=O 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
= iva 
=Orea 
-0.1 
-0.1 


-1.0 
-1.0 
-0.9 
-0.9 
-0.9 
-0.9 
-0.9 
-0.9 
-0.9 
-0.8 
-0.8 
= Olt 
-0.7 
-0.7 
-0.7 
-0.7 
-0.7 
-0.7 
-0.6 
-0.6 
-0.6 
-0.6 
-0.6 
-0.6 
-0.5 
-0.5 
-0.5 
=O'5 
-0.5 
=Oiss 
-0.4 
-0.4 
-O0.4 
-0.4 
-O.4 
-O.4 
-0.4 
-0.3 


=lWert 
Weill 
-1.7 
-1.6 
—166 
-1.6 
=ie5 
=—1.5 
-1.5 
-1.4 
=1.3 
=11.3 
= lies 
=Ne2 
-1.2 
Were 
=le2 
=iienl 
Ee 
=ilet 
=61 
-1.0 
-1.0 
-1.0 
-1.0 
-0.9 
-0.9 
-0.9 
-0.8 
-0.8 
-0.8 
=Oleit 
=Olsir, 
=O\.7 
=O 
-0.6 
-0.6 
-0.6 


0.0 
0.5 
1.0 
le 
2.0 
Ze5 
3.0 
365 
4.0 
4.5 
6.5 
7.0 
7.5 
8.0 
8.5 
9.0 
9.5 
10.0 
10.5 
11.0 
11.5 
12.0 
12.5 
13.0 
13.5 
14.0 
14.5 
15.0 
15.5 
16.5 
17.0 
iar 
18.0 
18.5 
19.0 
19.5 
20.0 
20.5 
21.0 
21.5 


32 


4.8 
4.5) 4.8 


4.5 
4.0 
3-8] 4.1 
3.6 


4.1 
3.9 
3.8 
3.6 
3.5 
SoS 


3.7 
3.6 
3-5 
Ses 
3.2 


3.4 
3013 
3.1 
3.0 
2.9 
2.7 
2.6 
2.5 


2.8 
2.7 
2-6 


2.7| 3.1 


Oe KO «725°? 


Doe 
2.1 


2.5 
264 
eteS 


2-4 
A250) 


2.) 
2.0 
1.9 
1.9 
1.8 


1.8 
1.7 
ote 
1.6 
1.5 


1.5 
1.5 
os! 
Was) 


1.2 
1.2 
1.0 


1.1 


1.0 
0.9 
0.8 
0.8 


0.7 
0.7 
0.6 
0.6 


0.4 
0.4 
Oo4 
0.3 


0.2 
(0/72 
0.1 


-0.5/-0.3|-0.1 


-0.4 


24.0 


oan 


Ke 
ue 
ue 


el 
9 
Sif 


8 
6 
3e4 
3.3 


4.0) 4.3 
° 4 
. 5 


3 
3 


5 
3 
3.1 


ee 
nn 


3.0 
2.9 


WOO), a)! 26S) 
Po) Aas 

Wo ta) 46 2.2 
2.) 


1.7 
1.6 
1.5 


1.4 
1.4 
1.3 


0.5| 0.7 
0.5| 0.7 
0.5) 0.7 


0.3 
0.3 
0.3 


0.1 
0.1 
0.1 


-0.1 
-0.1 
=(lenl 


-0.3 
-0.2 
-0.2 
-0.2 
—Oia2 


-0.4 
-O.4 


24.5 
25.0 
25.5 


4.0 
324 
3.2 
3.0 
2.8 
2.6 
2-4 
2.2 
2.0 
1.8 
1.2 
1.0 
0.8 
0.6 
0-5 
0.3 
0.1 
—0.1 
-0.5 
-0.7 
-0.9 
-1.1 
Ves 
S58) 


3.3 
Sle2. 
3.0 
2.8 
2.6 
2-4 
(2572 
2.0 
1.8 
1.7 
1.3 
1.1 
0.9 
0.7 
0.5 
0.3 
0.2 
-0.0 
-0.2 
-0.6 
-0.8 
-1.0 
= 1115 
—1.3 
55 
-1.7|-1.7 


-l 
226) 2e9 
2.7 
29) 
2-4 
2-2 
1.8 
1.7 
1.5 
1.3 
1.0 
0.8 
O.4 
0.3 
0.1 
-0.1 
-0.3 
-0.6 
-0.8 
=e0 
S52 
=e 
= 41.555) 
Silote 


3.0 
2.8 
2.5 
2.3 
2-2 
2.0 
1.7 
1.5 
1.3 
1.2 
0.8 
0.7 
0.3 
0.2 
-0.2 
-0.3 
-0.6 
-0.8 
-1.0 
ihe 
ie 
sss 
Soe 


2.7 
2-23] 2.6 
2-3 
2.1 
1.9 
1.8 
5 
1.3 
1.2 
1.0 
0.9 


222 
760) 


2.9 
2.4 
0.7 
0.6 
0.3 
0.1 
=0.2 
-0.4 
-0.7 
-0.8 
-1.0 
Sou 
Nise} 
-1.4 
Saw 


2-6 
205 
1.9 
1.8 
1.6 
1.5 
1.3 
1.2 
1.0 
0.9 
0.8 
0.6 
0.5 
0.3 
0.2 
0.0 
-0.2 
-0.4 
-0.7 
-0.8 
-1.0 
—iliett 
Nis. 
—1.4 


2.4 
2-2 
2.1 
2.0 
1.8 
1.7 
1.6 
1.4 
1.3 
Were. 
1.0 
0.9 
0.8 
0.6 
0.5 
0.4 
0.3 
0.1 
-0.0 
—Olef 
-0.8 
-0.9 
tou 
aia 
= eS) 
Sas aes 


—Oles 
-0.4 


2.0 
1.9 
1.7 
1.6 
1.5 
1.4 
1.1 
1.0 
0.9 
0.8 
0.7 
0.5 
0.4 
0.3 
0.2 
0.1 
-0.1 
-0.3 
-0.4 
= O)ent 
-0.8 
-0.9 
-1.0 
=I" 1 
leet 
-1.4 


1.9 
1.8 
1.7 
1.5 
1.4 
1.3 
1.2 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.3 
0.2 
0.1 
0.0 
-0.1 
-0.3 
-O0-4 
-0.7 
-0.9 
-1.0 
Alkan] 
= 5° 
Nis 


-0.6 


1.6 
1.5 
1.4 
1.3 
1.3 
1.2 
1.1 
0.9 
0.8 
0.7 
0.6 
0.5 
Q.4 
0.3 
0.2 
0.1 
-0.0 
-0.4 
-0.7 
-0.8 
-0.9 
15 (0) 


=o i 
-0.3 
-0.6 
=jholl 
—1.2 


1.4 
1.3 
1.3 
Wer2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
U.0 
=-0.0 
-0.1 
-0.3 
-0.4 
-0.6 
5 7p 
l0)5 Tr 
-0.8 
-0.9 
1.0 
=i 


1.2 
1.1 
1.1 
1.0 
0.9 
0.8 
0.8 
0.7 
0.6 
0.5 
0.5 
O44 
0.3 
0.2 
0.1 
0.0 
-0.1 
-0.1) 
-0.3 
-O.4 
-0.5 
-0.6 
AVE 7f 
=(Olow, 
-0.8 
-0.9 
-1.6 


1.0 
0.9 
0.9 
0.8 
0.8 
0.7 
0.6 
0.6 
0.5 
0.4 
0.4 
0.3 
0.2 
0.0 
-0.0 
-0.1 
-0.1 
-0.3 
=(0}.55) 
-0.5 
-0.5 
-0.6 
-0.7 
-0.7 
-0.8 
-0.8 


0.8 
0.8 
0.7 
0.7 
0.6 
0.5 
0.5 
0.4 
O.4 
0.3 
0.3 
0.2 
0.0 
-0.0 
-0.1 
-0.1 
-0.2 
-O.4 
-0.5 
=O 
-0.6 
-0.6 
-0.7 
=O 


0.6 
0.6 
0.5 
0.5 
0.5 
0.4 
0.3 
0.3 
0.2 
0.2 
0.2 
-0.0 
-0.0 
-0.1 
-0.1 
-0.2 
=O)s2-|—055 
-0.3 
-0.4 
-O.4 
-0.5 
-0.5 
-0.5 
-0.6 


0.4 
0.4 
0.4 
O.4 
0.3 
0.3 
0.2 
0.2 
0.1 
0.1 
0.0 
-0.0 
-0.0 
-0.1 
-0.1 
-0.2 
-0.2 
-0.3 
—( 053) 
=()5 3} 
-0.3 
-0.4 
-0.4 
-0.4 


0.3 
0.2 
0.2 
0.2 
0.1 
0.1 
0.1 
0.1 
0.0 
0.0 
-0.0 
-v0.0 
-0.1 
-0.1 
-0.1 
-0.1 
-0.2 
-0.2 
05 
-0.2 
-0.2 
-0.3 
-0.3 


0.1 
0.1 
0.1 
0.1 
0.0 
0.0 
0.0 
0.0 
0.0 
-0.0 
=07.0 
-0.0 
-0.0 
-0.0 
-0.0 
= (Ost 
=001 
-0.1 
-0.1 
-0.1 
=0.1 
10) | 
-0.1 
-0.1 


-0.1 
=O 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
-0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
0.0 


-0.2 
-0.2 
-0.1 
-0.1 
-0.1 
-0.1 
-0.1 
-0.0 
-0.0 
-0.0 
0.0 
0.0 
0.0 
0.0 
0.1 
el 
0.1 
0.1 
0.1 
0.2 
0.2 
0.2 
0.2 


-0.4 
-0.3 
-0.3 
-0.3 
-0.2 
=0.2 
-0.2 
-0.1 
=1)5 1 
-0.1 
-0.0 
-0.0 
0.0 
0.1 
0.1 
0.1 
0.2 
0.2 
0.2 
0.3 
0.3 
0.3 
0.3 
0.4 
0.4 
0.4 


26.0 
26.5 
27.5 
28.0 
28.5 
29.5 
30.0 
31.0 
31.5 
32.0 
32.5 
33.0 
3325 
34.0 
34.5 
35.0 
35-5 
36.0 
36.5 
37.0 
37-5 
38.0 
38.5 
39.0 
39.5 
40.0 
40.5 
41.0 
41.5 
42.0 


1500 METERS 
(155.81 kg/cm“) 


TABLE 6. CORRECTION TO SOUND SPEED, V, (1449.1 m/sec). FOR SIMULTANEOUS CHANGES IN 


SALINITY, TEMPERATURE, AND PRESSURE, Vetp - Continued 


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1.9 
1.9 
1.9 
1.8 
1.8 
1.7 
7 

; 

6 

6 

5 

5 

5 
1.4 
1.4 
3 

3 
1.3 
2 
1.2 
orl 
21 
20 
-0 
-0 
9 
0.9 


0.9 
0.8 
0.8 
0.8 
0.8 
0.7 
0.7 
0.7 
0.6 
0.6 
° 0.9 
0.5 0.9 
0.5 0.9 
0.5 . 
Ono 0.8 
. 0.7 
0.4 0.7 
0.4 0.7 
O.4 0.6 


O.4 
0.4 
0.4 
0.4 
O.4 
O.4 
0.3 
0.3 
0.3 
0.3 
0.3 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0.2 
0. 

0. 

0.1 
0.1 
0.1 


-0.3 
-0.3 
-0.3 
-0.3 
0.2 
-0.2 
0.2 
-0.2 
0.2 
-0.2 
0.2 
0.2 
-0.2 
0.2 
0.2 
=Oreit 
-0.1 
=Olsil 
-0.1 
-0.1 


Nite) 
— old) 
-1.0 
-1.0 
9 
-0.7 
-0.6 
-0.6 
-0.6 
-0.5 
0.5 
-0.5 
0. 
-0.5 
-0.4 
-0.4 
-0.4 
-0.3 


—1.7 
Sot 
"lent 
1.6 
-1.6 
6 
-1.6 
5 

5 

5 

5 
-1.4 
4 

4 
—-1.3 
3 
Cie) 
—-1.3 
1 

0 

= 1.0 
-1.0 
1.0 
-0.9 
-0.9 
-0.9 
-0.8 
-0.8 
-0.8 
-0.7 
-0.7 
-0.7 
-0.6 
-0.6 
-0.6 


=i 
1 
1 


0.0 

5 
1.0 

25 
2.0 
2.5 
3.0 
3.5 
4.0 
5.0 
SI) 
6.0 
6.5 
7.0 
7-5 
8.0 
8.5 
9.0 
9.5 

0 
15 
8.0 


1 
1 
13.0 
13.5 
14.0 
14.5 
16.0 
17.0 
1 
18.5 
19. 
19.5 
0. 
20.5 
21.0 
21.5 


34 


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35 


2000 METERS 
(207.41 kg/cm?) 


- Continued 


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‘YaLVM WAS NI GaadS GNNOS AO SA TAVL 
ao0jO 2tyderdouesdO [RAPN “S “N 


“(L661 paqtadey) $19 “aNd “O “H 0} quauratddns e 
se peystiqnd ‘paquesead st urerdsouiou paads punos vy 
‘aanssaad 10 yjdap iayyIe qyIM pesn aq Aeur satqeyz 
Aqaiaym paystiqejse st drysuorjejas yydap-aanssaid y 
7g 8 09ZT 03 EOI PUL “"H61F 93 093 ‘D.6°FE 9345°2- 
wioi1y saduer aansseid pue Ajruiyes ‘ainjeradura3 
I2A0D satqey “19}e4 eas ur punos jo paaeds zo; 


uoyenba s,uos{ImM “q auAeM uo paseq aie salqey 


saouarayay 


*(g¢-das) “s919e3 2 “3 1 

‘dip *2961 ysn3ny ‘uorstarq stshjeuy I1yderd0ues00 
‘UGLVM WHS NI Gaads GNNOS 4O saTaVL 

20130 21ydead0uesz0 TRARN *S ‘“N 


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*(LS61 pewutadey) #19 ‘GMd ‘O “H 0} queuratddns e 
se paystiqnd *pazuasead st urerdourou paads punos y 
‘aanssaid 10 yjdap rayjta yyIM pesn aq Aeur salqez 
Aqaiaym paystiqeisa st diysuorejar yydap-aanssaad y 
8S-dS “HH *{W19/BA O9ZT 0} COT PUL ‘%6 Th 03 009 'D.6"FE 0365°2- 
uiorty saduer aainssaid pue Ajrutpes ‘aanjyeraduraz 
I2A0D salqey, “1a3e" eas ut punos jo paeds oz 


uoyenba s,uos[ImM *‘q audeM uo paseq are salqeL 


*I372M 2S ut peads 
punos jo SaTqel 'e9nn “tr 


peeds ~—punos ~lajem—eas ‘¢ saouetTajay 


SoWsNooy 1azeMrapun *7 *(gS-ds) “s91qe1 2 “301 
‘di ‘7961 ysnd3ny ‘uotstatq stskleuy styderZ0ue3s0Q 
‘UAaLVM VAS NI Ga3ads GNNOS JO SaTAVL 

20130 otyderZoue|acO [BARN ‘SN 


peads - punos *| 


“(LS61 peqatadey) #19 “GNd ‘O “H 03 quouratddns e 
se paystiqnd ‘pazueseid st wreidourou pasds punos y 
‘aanssaaid io yjdap rayj3ta yyIM pesn aq Aeur salqe} 
Aqaiaym paystiqejsea st drysuoyelaa y3dap-aanssaad y 
119/34 09ZT 0F €O°T PUL '™%H6"1H OF 093 D.6°FE 0345°2- 
uiozy saduer aainsseid pue Ajrurtes ‘aanjeradura, 
I2A09 salqey “1a3e" eas ut punos jo paads 0; 
uo1enba s,uos[tm *‘q audeM uo paseq aie salqey 


8S-dS ‘tt 


"I372M 2S ut paads 
punos jo saqqey 7a ‘rt 


pads - punos - 193em— ag sa90Uerazay 


SOSNOOY IazeMmzapuy *(gg-dS) *s91qei 2 “8 1 
‘d)} "7961 ysn3ny ‘uorstatq stshTeuy 2tyderZ0ue|0Q 
‘UGLVM VAS NI GaadsS GNNOS 4O SaTAVL 


291330 D1yderd0ue|sz0O [eARN ‘SN 


peeds - punos ‘| 


8S-dS ‘tr 


"13JBM BAS ut paads 
punos Jo salqey :ap3ta *t 


peads - punos - 1a3em—Pag ‘¢ 


SO1sNooy TayemMitapuy 


Nn 


paads - punos *{ 


8S-dS ‘It 


*12}72M Bas ut paadg 
Punos jo SeTqeL +2131) “tr 


peads - punos ~ 1aj3em—P ag “¢ 
SO1}SNOOY I9a}eMIapuy “7 


peads - punos *{ 


‘(LS61 payutaday) $19 “Qnd “O “H 0} quauatddns e 
se peysttqnd ‘pajuasead st weadsoulou paads punos y 
*aanssaad 1x0 yjdap rayita yyIM pasn aq Aeu satqrz 
Aqaiaym paystiqeisa st dtysuoejaa yjdap-aanssaad vy 
* {W192 /34 09ZT OF EO" 1 PUL SLE 93 099 ‘D6 HE 0345°2- 
uio ry saduei aanssaid pue Ajruijes ‘aanjeraduiay 
I9AOD salqey, ‘1azeMm eas ut punos jo paads zo; 


uotjenba s,uos[ImM "q auAeM uo paseq aie salqey 


saouatajay 


‘(gs-ds) satqes 2 “85 1 

‘dib ‘2961 3snsny ‘uotstatq stshjeuy 21ydeas0ue|a0Q 
‘WGLVM WAS NI GaadS GNNOS AO SATAVL 

20730 Dtydeadoue|scO TRARPN “SN 


*(Lo61 paqutadey) $19 “aNd “O “H 0} Juauratddns e 
se peyst[qnd ‘pajuesead st urer30u1ou paads punos yw 
‘aainsseid 10 yjdap reyjIa yIM pesn aq Aeur sa[qe} 
Aqearaym paystiqgeysa st drysuorejer yjdap-ainssaid y 
yar BA 09ZT OF EOL PUL “HTH 03 093 ‘DHE 07.45°2- 
uioi1j saduer aanssaid pue Ajuiyes ‘aainjeraduraz 
I3A09 sajqey, *193e" eas ut punos jo paads 0; 
uotjzenba s,uos[tmM ‘qd aukeM uo paseq aie salqey 


soousTajoy 


*(gg-ds) "setqe 2 “31 T 
‘d)} “7961 ysn3ny ‘uotstatq stshjeuy Ityderso0ueasQ 
‘YGLVM WAS NI Gaads GNNOS 4O Sa TAVL 
a0jO Dtyderd0uP|DDO [RAPN “S ‘N
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