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THE PERCEPTION OF SOUND.
[Nature, Vol. en. p. 304, 1918.]
I REGRET that I overlooked Prof. Bayliss's letter in Nature of October 17, n which he made an appeal for my opinion. But, if I rightly understand, ;he question at issue seems to be mainly one of words. Can we properly speak of the propagation of sound through an incompressible fluid? I should mswer, Yes. There may be periodic motion and periodic variation of pressure; the fact that there are no variations of density seems immaterial. Consider plane waves, corresponding with a pure tone, travelling through air. [n every thin layer of air—and thin means thin relatively to the wave-ength—there are periodic motion and periodic compression, approximately miform throughout the layer. But the compression is not essential to the iravelling of the sound. .The substitution of an incompressible fluid of the same density for the gas within the layer would be no hindrance. Although :here is no compression, there remain a periodic pressure and a periodic notion, and these suffice to carry on the sound. ' • •
The case is even simpler if we are prepared to contemplate an incompressible fluid without mass, for then the layer' need riot be thin. The nterposition of such a layer has absolutely no effect, the motion and pressure it the further side being the same as if the thickness of the layer were •educed to eero. To all intents and purposes the sound is propagated through )he layer, though perhaps exception might be taken to the use of the word propagation.
As regards the ear, we have to consider the behaviour of water. From some points of view the difference between air and water is much more one >f density than of compressibility. The velocities of propagation are only as I) or 5 to 1, while the densities are as 800 to 1. Within the cavities of the ear, ivhich are small in comparison with the wave-lengths of musical sounds, the i,vater may certainly be treated as incompressible; but the fact does not seem ;o be of fundamental importance in theories of audition.. If DJ3, B FG be drawn parallel to 0(7, so that OD, OF are equal to 8, the prohibited region is that part of the square lying between these lines. Our inte- p grations are to be extended over the remainder, viz. the triangles FBG, DAE, and every point, "° D or rather every infinitely small region of given •Plg' 3*