Jed Lecture 9 
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Fig. 9.15. Schlieren photograph of the shock wave. 
the center of the spherical cavity is plotted in Fig. 9.13 for several instances 
during the collapse of the bubble where R/Ry = ‘Ag to ‘499. Under favorable cir- 
cumstances, the velocity of the surface of the bubble reaches the velocity of 
sound. The corresponding pressures in the "pressure head wave" at different 
stages of the implosion are plotted in Fig. 9.14. These also determine the pres- 
sure in the radiated shock wave. At the front of the shock wave the pressure 
gradually increases up to very high values; this is confirmed by the Schlieren 
photograph of Fig. 9.15. The shock wave pressure is obviously higher the smaller 
the gas content of the initial cavity. With such collapsing cavities, extremely 
powerful sound waves may be generated. At the time of formation, the cavity 
is almost spherical, but no one has ever succeeded in having the bubble collapse 
with a spherical shape throughout. The shape of the surface is unstable on ac- 
count of the surface tension, and therefore the sphere, at the end phase of the 
collapse, usually disintegrates into a number of smaller bubbles of various sizes 
and closely neighboring centers. Eachofthese bubbles generates individual shock 
waves separated with respect to time and space. An example illustrating this 
effect, shown in Fig. 9.16, is taken trom the work of J. Schmid [7]. In his work, 
the movement of a water-filled vessel is suddenly stopped and the water column 
torn apart by inertial forces at a bubble nucleus in the water, forming a cavity 
why, I 
Fig. 9.16. Implosion of a bubble. 
