Experimental Study of Wave Transmission.—Many of the "opti cal" characteristics of sound which we have mentioned may be studied on a laboratory scale by the following methods: (a) Spark Photography. The progress of a sound pulse may be ob served either by the "Schlieren Method" (due to Topler 1867) or the "Shadow Method" (due to 188o). In the latter case, the sound pulse is produced by an electric spark (the sound spark), followed by a second spark (the light spark, be tween magnesium electrodes) at a known short interval of time. The highly compressed region forming the envelope of the sound pulse casts a shadow, when illuminated by the light spark, on a screen or a photographic plate. A succession of photographs at varying time-intervals after production of the sound-spark in dicates the progress of the sound-pulse. The various phenomena of reflection, refraction and diffraction have been demon strated in this way (see for example, Foley and Souder, Phys. Rev., 35. 373. 1912). Photographs of this nature are shown in the Plate, figs. Ia to f. (b) Ripple Photography. Results of a simi lar character may be obtained more easily by means of the ripple tank. This method is based on the fact that impulsive ripples on the surface of a liquid, e.g., water or mercury in a small tank, bear a striking resemblance to impulsive sound waves. The ripples are reflected, refracted and diffracted from objects placed in the liquid, as shown in the Plate, Fig. 12. The method was first used by Vincent (Phil. Mag., 43. 17. 1897) to demonstrate interference phenomena, but more recently it has received a wider application in the study of complex reflections occurring in models of buildings (see Article on ACOUSTICS OF BUILDINGS; and Davis, Proc. Phys. Soc., 38. 234. 1926). (c) Bullet photography. The "bow" wave from a high speed bullet. (see Plate I., fig. 2) has been utilised to demonstrate the reflec tion and diffraction of a sound-pulse. Thus in C. V. Boys photo graphs of a bullet in flight (Nature, 47. 1893) the pulse is seen to be reflected according to optical laws. Cranz (Hand buch der Physik, Vol. VIII, Geiger and Scheele) has photo graphed the track of a bullet passing between two parallel plates, and the multiple reflections of the bow-waves are beautifully shown. The method is not so convenient as the spark and ripple methods, but it possesses certain novel features.
Doppler's Principle.—Moving Sources and Receivers.—The pitch of a sound is liable to be modified when the source and re ceiver are in relative motion. Thus an observer approaching the source with velocity v will encounter more sound-waves per second than if he had remained at rest, the number of sound waves per second (the pitch of the note) being increased in the ratio (c+v)/c where c is the normal velocity of sound in the medium. Similarly when the observer is at rest and the source moving, the change of pitch will be in the ratio c/c±v accord ing as the source is approaching or receding. The whistle of a locomotive is raised in pitch as it approaches, and falls in pitch as it recedes from an observer. The principle of change of pitch by relative motion is due to Doppler, who first enunciated it in connection with the change of colour of certain stars moving in the line of sight of an observer. If the medium is also in motion (e.g., wind) with velocity w in the direction of the sound wave, the observed pitch N' relative to the actual pitch N will be Ni/N= (c± w± v) (c±w). When v= o, Ni = N irrespective of the velocity of the medium. The latter velocity w only affects the ratio N'/N slightly when the source and observer are in relative motion also. The Doppler effect can be produced in the
laboratory by the simple expedient of rotating a maintained source of sound at the end of a bar or cord. Preferably the source should be maintained in vibration by virtue of the rotation. The observer in the plane of rotation hears a note which rises and falls in pitch once per revolution. The observed pitch of the sound from an aeroplane may vary by 20% according to the speed and direction of flight.
Attenuation of Sound-Waves. Viscosity and Heat Con duction.—We have hitherto considered plane or spherical waves travelling through various media without loss of energy. Apart from other considerations it will be evident that energy loss must take place wherever there is relative motion between the various particles comprising the medium, such loss being due to ordinary viscous forces which tend to degrade the sound energy into heat. In addition to this viscous loss there must be energy loss due to thermal conduction and radiation consequent on the compres sion and rarefaction of the medium. If the compressions and rarefactions succeed each other with sufficient rapidity the process will be strictly adiabatic, that is, there will be no transfer of heat between compressed and rarefied regions or to the parts of the medium unaffected by the sound-wave. Sound-waves of small amplitude in air are propagated under almost perfectly adiabatic conditions. Otherwise, as Stokes proved in 1851, the sound would be rapidly stifled, which is contrary to experience. In the case of sounds of very large-amplitude however (an explo sion impulse, or the sound-wave emerging from a very powerful source), it is conceivable that the large temperature fluctuations in each cycle of pressure may be such as to involve appreciable temperature losses due to conduction and radiation even in a very short time interval. This would result in a more rapid de crease of sound-energy with distance than the inverse square law requires, the effect becoming increasingly serious the lower the frequency and the greater the amplitude of the sound waves. With regard to energy loss due to viscosity, Maxwell pointed out that the factor involved is the "kinematic viscosity coeffi cient" v, which is equal to the ordinary "static" coefficient At divided by the density p. Thus for air v=0.132 and for water v =0.013 at io° C. The amplitude of the progressive wave therefore diminishes exponentially on account of energy loss on the way. In the case of plane-waves we have where 1 is the distance travelled by the wave before the amplitude falls to vie of its initial value. In this expression 1= indicating a rapid increase of attenuation with diminishing wave-length X (i.e., with increase of frequency). Tc include the losses due to heat conduction also Maxwell multiplied v in the above expression by 2.5, the effect being therefore equiv alent to a marked increase (to v') of kinematic viscosity. On the above grounds there is clearly a physical upper limit to the fre quency of vibration which can be transmitted an appreciable distance'. Rayleigh (Vol. I p. 28) concludes that the effects of energy losses of the above nature are to be sought for in the damping of the vibration rather than in the altered velocity of propagation. It should be mentioned that changes of velocity with frequency have actually been observed by Pierce in air and CO, and by Boyle and Taylor in water, although no such change could be detected by Lang in the case of steel bars.