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Full text of "Scientific Papers - Vi"

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[Advisory Committee for Aeronautics, T. 618, 1915.]
THE action of a cone in collecting sound coming in the direction ol axis may be investigated theoretically. If the diameter of the mout small compared with the wave-length (A.) of the sound, the cone may op as a resonator, and the effect will vary greatly with the precise relation bet A, and the length of the cone. On the other hand, the effect will depend little upon the direction of the sound. It is probably more useful to con the opposite extreme, where the diameter of the mouth is a large, or at i*ate a moderate, multiple of X, when the effect may be expected to fall off rapidity as the obliquity of the sound increases.
A simple way of regarding the matter is to suppose the sound, inc: axially, to be a pulse, e.g. a condensation confined to a narrow stratum bou by parallel planes.    If the angle of the cone be small, the pulse may be posed to enter without much modification and afterwards to be propa^ along.    As the area diminishes, the condensation within the pulse mui supposed to increase.    Finally the pulse would be reflected, and after e gence from the mouth would retrace its course.    But the argument ii satisfactory, seeing that the condition for a progressive wave, i.e. of a propagated without reflection, is different in a cylindrical and in a conical The usual condition in a cylindrical tube, or in plane waves where there tube, viz. M = as, where u is the particle velocity, a that of sound, and < condensation, is replaced in spherical waves by
a f    . u  as - \srdr,
r2 J        '
showing that a pulse of condensation alone cannot be propagated wil undergoing some reflection. If there is 'to be no reflection at all, the int taken over the thickness of the pulse must vanish, and this it cannot do u fche pulse include also a rarefaction.a/3r, and