Velocity of Sound

Shell-Waves. Onde de choc.—When a bullet or a shell, travelling with a velocity greater than that of sound, passes an observer it makes a sound like the crack of an explosion—described by the French as "onde de choc." Tee tips of the propeller of an aero plane often exceed the velocity of sound and emit sounds of this nature as they revolve. In the case of a low speed bullet, the air at the nose is compressed, the compression being trans mitted in all directions with the velocity of sound (approx imately 33om/sec. in air). If however, the speed of the bullet is greater than the velocity of sound the condensation of the air at the nose can be transmitted laterally but not forwards. Photo graphs taken of bullets while in flight show this clearly and reveal the existence of two wave-fronts, one at the head and the other at the base of the projectile. The former can be simply explained on Huyghens' principle of secondary wavelets. If the velocity of sound at the nose of the bullet were normal, the wave-front would be a cone of semi-angle V (c normal velocity of sound and V velocity of projectile). But the velocity of sound increases with increased amplitude of condensation, consequently the wave-front is a blunted cone, as actually recorded in the Plate see Fig. 2. From observations of the changing direction of the "onde de choc" it is possible to trace the bullet or shell to its source. (See Mallock, Proc. Roy. Soc., p. 115, 1908.) This method was used in the war to locate enemy guns.

Velocity of High Frequency Sounds.

Using a quartz piezoelectric oscillator (see p. 12) as a source of high frequency vibrations, G. W. Pierce (Proc. Amer. Acad., vol. 6o, Oct. 1925) determined with considerable accuracy the velocity of sound in air and carbon dioxide by the stationary-wave method. He found that the velocity of sound in air at o°C has the values and 331.64 metres/sec. at frequencies i,000, 5o,000 and 1.5 X p.p.s. respectively. The effect of humidity was negligible, at 8o% humidity differing by less than 0.02% from the velocity in dry air. In the velocity at o° C was found to be 258.82 m/sec. at a frequency of 42,000 cycles/sec. increasing to 260.15 m/sec. at 200,000 cycles/sec. This gas becomes opaque to sound-waves at still higher frequencies. Boyle and Taylor (Proc. Roy. Soc., Canada, 1925) observed a diminution of velocity of high frequency sounds in water at C from 1.51 X cms./sec. to 1-42 cms./sec. at frequencies 43,00o and 598,000 cycles/sec. respectively. The measurements were made in a small tank. The velocity in a viscous oil was found to be the same at 570,000 cycles/sec. as at low frequencies. Lang (Roy. Soc., Canada, 1922) found no change in the velocity of sound in steel bars at any frequency up to 50,000 cycles/sec. Reference has already been made (p. 22) to the piezoelectric measurements of Hubbard and Loomis on the velocity of sounds of frequency 3 X in various liquids contained in tubes.

Change of Medium. Reflection and Transmission.

As in the case of light, when a wave of sound meets the surface of separation of two different media it is partially reflected, and a wave travels back (in the negative direction) through the "in cident" medium, with the same velocity as it approached the bounding surface. The laws of reflection are the same as applied to light waves—angles of incidence and reflection being equal and in the same plane. With sound-waves however, we have often to deal with wave-lengths which are comparable with the dimensions of reflecting objects; the phenomena must then eventually be regarded primarily as diffraction. In the cases which we are now considering the wave-length may be regarded as small, or the reflector large, the ordinary optical laws being applicable.

Reflection of Plane-Waves at the Boundary of Two Extended Media.—It is shown in text-books of sound (Rayleigh, vol.

p. 8r) that the relative amplitudes r and a of the reflected and incident waves are given by p2/p1 — cot' Odcot • 01 = (25) a p2/ pi + cot where and are the respective densities of the first (incident) and second (transmitting) media and and are the angles of incidence and refraction. The law of sines of optical refraction holds in this case also, and we have where and are the velocities in the first and second media. Consequently (25) may be written of the medium (I) and the plate (2). Boyle and Rawlinson (Proc. Roy. Soc., Canada, 1928) have deduced a more general expression for any angle of incidence, and have determined the "critical angle" at which total reflection occurs. It will be seen that the reflected-amplitude r fluctuates between zero and a maximum as the thickness of the plate varies. In the case where the reflected amplitude is zero when lz=o or a multiple of X/2, and reaches its maximum value when 1 is a multiple of X/4. A quarter wave-plate consequently reflects a maximum and trans mits a minimum of the incident sound-energy.

These relationships for the reflection of plane-waves from flat plates have been verified by Boyle and Taylor and Boyle and Lehmann in the case of high frequency sound-waves passing through water in which the plate was submerged. Equations (26) (27) and (28) indicate that solid media in air are prac tically perfect reflectors, whereas in water they are relatively good transmitters of sound. An air film in water or in a solid mass constitutes a perfect reflector, with a reversal of phase at reflection. The practical application of such deductions is dealt with by H. Brillie (Le Genie Civil, Aug. and Sept. 1919) in rela tion to the problem of sound-reception under water.