187 



Figure 8a - Before the Explosion Figure 8b - After the Explosion 



Figure 8 - Photographs showing a Shock Wave forming in Bubbly Water 



which In turn cause a layer of bubbles to behave as a dispersive absorbing 

 medium. The layer thus reflects an acoustic wave in somewhat the same way 

 and fcr somewhat the same reason as a layer of molecules reflects light. 



The only case yet amenable to full analytical treatment is a weak 

 sinusoidal wave traversing a field containing many bubbles in each cubic wave 

 length. The alteration in the speed of sound caused by the presence of the 

 bubbles is shown to be proportional to the fraction of the whole space occu- 

 pied by the bubbles, and, in a rather intricate way, on the ratio of the fre- 

 quency of the wave to that of the bubbles; see Equation [21], page l8. The 

 symbols used in this development are separately listed on page l8. 



It is found that even a small concentration of bubbles may produce 

 a surprisingly large reflection coefficient, and where the frequency of the 

 wave is near that of the bubbles, not over, say, three times as great, re- 

 flection is nearly total. At much higher wave frequencies the reflection 

 falls away to near zero. 



It is thought that results similar in a qualitative sense will hold 

 in the case of an incident shock wave, except for the unknown results of cav- 

 itation. 



