illustrating not only the radial motion of the cavity but also the resulting sound pres- 

 sure. The abscissa represents time. The curve labelled "External Pressure" indicates 

 a temporal variation in environmental pressure typical of that encountered by a 

 cavity under conditions like those being considered. The radius of the cavity is shown 

 by the heavy solid curve. The constant P is the value of the pressure difference, 

 (p e — P), at the final instant of collapse, t . A characteristic radius, R lt may be 

 defined so that, in the final stages of collapse, the total energy, kinetic and potential, is 

 4 



The sound pressure, shown by the light solid line, oscillates once and, at the 

 end of the collapse, rises in an extremely high narrow "spike." The details of this 

 high narrow pulse (which determine the high-frequency portion of the sound spectrum) 

 are not given correctly by the acoustic theory. While most of the energy radiated as 

 sound is associated with the pulse at the end of the collapse, the sound associated with 

 the earlier part of the motion is by no means negligible. 



The broken lines indicate the solution for the special case, considered by 



Figure 5. Radial motion and sound pressure for a vapor cavity which rebounds after growing and 



collapsing. 



250 



