NA TURE 



117 



THURSDAY, DECEMBER 12, 1S7S 



LORD RAYLEIGH'S " THEORY OF SOUND'' 

 The Theory of Sound. By J. W. Strutt, Baron Rayleigh, 

 F.R.S. Vol.11. (London: Macmillan and Co., 1878.)' 



THE second part of Lord Rayleigh's highly instructive 

 work on acoustics contains the mechanics of oscil- 

 latory motions in liquids and gases. Atmospheric air is 

 that medium by which by far the greater number of 

 sound-waves are conveyed to our ear, since ;t is only 

 exceptional that this happens through solid bodies which 

 are in contact with our teeth or with the bones of the 

 skull. But it is just for this reason that all circumstances 

 are of considerable importance, which influence the 

 transmission of sound-waves in the air, i.e., change either 

 their velocity, their direction, or their intensity. This 

 part of the theory has been worked out very minutely 

 and completely by the author. We find here the com- 

 pilation and demonstration of a large number of facts 

 which, in other works on acoustics, are hardly mentioned. 

 The author, after having first developed (in Chap. XL) 

 the general laws of the motion of liquids as expressed in 

 hydrodynamical equations, and then explained the dif- 

 ference between rotational and irrotational motion of 

 fluids, passes on to the simplification of the equations, 

 which is determined by the circumstance that with sound, 

 as a rule, we have to do with oscillations of extremely 

 small amplitude. First, the motion of plane waves is 

 investigated, and it is shown that with waves which move 

 only in one direction half their equivalent of work con- 

 sists in the vis viva of motion, and the other half in the 

 potential energy of the compression and dilatation of the 

 medium. Then follows the explanation of the influence 

 "Which the change of temperature, taking place with com- 

 pression or dilatation of gases, exercises upon the velocity 

 of transmission of sound. It is shown, in the manner first 

 employed by Prof. Stokes, that if a perceptible quantity 

 of heat could be exchanged between the compressed and 

 dilated layers of the waves during the lapse of one oscil- 

 lation, the intensity of the sound-waves would very 

 quickly decrease in their transmision and they would die 

 away. 



The subjects treated of up to this point are generally 

 known among physicists ; less known are a series of 

 other results of the theory. The author next gives a 

 comparatively very elegant and easily intelligible demon- 

 stration of the results at which Poisson and Riemann 

 arrived, when investigating the propagation of sound- 

 waves for which the velocities of oscillation are no longer 

 infinitesimal when compared to the velocity of transmis- 



I sion. It appears that the different layers of the wave 

 transmit their phases with different velocities, viz., with 



I that velocity which represents the sum of the ordinary 

 relocity of transmission of the smallest waves and of the 

 oscillation relocity of the particles of air oscillating in the 

 same direction. The compressed layers of the wave, 

 therefore, are propagated quicker than the dilated ones,' 

 thus they must gradually change the shape of the wave, 

 --nd finally overtake the preceding dilated layers. What 

 ould happen in that case, whether perhaps a breaking of 



For Vol. I. see Xaturb, vol. xvii. p. 237. 



Vol XIX.— No. 476 



the waves of air would take place, is not yet clear, since 

 the hydro-dynamical equations apply only to velocities 

 changing continuously. 



These circumstances have not always been considered 

 in experimental researches concerning the velocity of 

 sound. A precise answer to the question regarding the 

 magnitude of this velocity can only be given, if we 

 confine ourselves to oscillations of extreme smallness. 



The author has also investigated under what condi- 

 tions a sound-wave of finite amplitude can move forward 

 \Yithout changing its form. It appears that this could 

 happen only under the supposition' of a special law for 

 the compressibility of the medium, which does not 

 correspond with the law applying to gases. 



The propagation of sound in the atmosphere is sub- 

 jected to yet other perturbations, which partly arise from 

 the different temperatures and moistures of the super- 

 posed strata, and partly from the different force of winds. 

 At the surface of water or extensive masses of solid 

 substance, the sound-waves of the air are totally reflected 

 even under very small angles of incidence ; under perpen- 

 dicular incidence their reflection, although not total in 

 the strict sense of the word, is nearly as complete. For 

 that part of the sound which enters the new medium, the 

 same law of refraction holds good which applies to waves 

 of light. But also from a surface of hydrogen one-third, 

 of the sound coming through air at a vertical incidence is 

 reflected, and the angle of incidence for total reflection 

 is not larger than i$\ degrees. 



The problem to determine theoretically how the pro- 

 pagation of sound in the atmosphere is changed by the 

 different temperatures of its strata cannot yet be solved 

 completely. However, it can be ascertained in what 

 direction the most powerful effect must travel. On account 

 of the great dimensions of the strata of the atmosphere, 

 compared to which the wave-length of the large majority 

 of audible tones disappears entirely, the conditions of the 

 propagation of sound are similar to those of light. We 

 may imagine the sound-waves dissolved, as it were, into 

 rays of sound, and then look upon each separate ray as 

 being almost completely independent of the motion of its 

 neighbouring rays. This is no longer admissible if 

 obstacles are in the way of the travelling sound, the 

 dimensions of which exceed the sound wave-lengths only 

 in moderate proportions, as is the case in our houses 

 and rooms, with the transmission of sound through 

 windows and doors. Then, as in the case of light under 

 similar circumstances, diffraction takes place. The great 

 difference in the propagation of sound and light, as it 

 becomes] evident in ordinary experience, has its cause in 

 the verj- different magnitude of wave-lengths. The 

 greater the wave-length the greater the diffraction on the 

 passage through the same aperture. These circumstances, 

 which are forgotten so frequently, the author considers 

 in Chapter XIV. WTien sound is propagated in the 

 unbounded space of the atmosphere the conditions of 

 the problem are such, that they allow of its decom- 

 position into rays of sound. If a source of sound 

 is near the ground then its sound rays are all bent 

 into an upward direction, as Prof. Osborne Reynolds 

 first pointed out, and those which travel in a direction 

 parallel to the ground are mostly annihilated through 

 friction or other obstacles. The sound proceeding from. 



