148 Lecture 9 
Fig. 9.11. Relation between pressure curve and optical diffraction pattern, 
index of refraction in the sound field also follows a saw-tooth curve. The phase 
surface of the light wave entering the sound beam is plane; but, after penetrating 
the sound beam, the phase surface becomes sinusoidal if the amplitudes are 
small. But at high amplitudes, the phase surface of the light wave will also be 
saw-toothed in shape. This is similar to the diffraction of light by a specially 
made amplitude grating ("Echelette" grating), which is dissymmetric and 
diffracts more light into certain orders. The envelope of the spectral distribution 
of the different orders of diffraction resembles the phase surface of the light 
beam which, in turn, reflects the shape of the sound pressure wave. 
Figure 9.11 was taken from the paper of I.G. Mikhailov and V. A. Shutilov 
[14]. It displays the theoretical intensity distribution in the diffraction spectra 
for four different sound pressure patterns or optical index-of-diffraction pat - 
terns respectively. Dissymmetric sound pressure curves produce dissymmetric 
spectra and, furthermore, a distinct preference for certain orders in the spec- 
trum is observed, and it is also possible from the shape of the spectrum to 
deduce the shape of the sound wave. 
It should be mentioned in this connection that by using A /2-plate filters 
certain harmonics may be filtered out and indicated separately (Mikhailov and 
Shutilov [15]). 
9.3.3. Generation of Shock Waves by Collapsing Cavities 
This paragraph will treat the question of how a collapsing cavity filled with 
more or less gas generates a shock wave. Starting with Rayleigh's theory, 
W. Guth [16] gave a simple explanation ofthis process. A segment of a cavitation 
bubble is shown in Fig. 9.12, where the pressure inside the bubble is py, the out- 
side atmospheric pressure is pa, and the initial radius is Ry. The flow velocities 
in the water streaming into the cavity are indicated in Fig. 9.12 at an arbitrary 
moment. The distribution of flow velocities as a function of the distance from 
