55 



a of the bubble. This equation Is similar to that which would 

 be obtained by differentiating Eq. (5) above with respeot to 

 time, but contains several additional terms, of which the most 

 Important 1? one proportional to a^(da/dt ) [dp( a)/dt] / ^ c , 

 where c is the velocity of sound in water. As this expression 

 is intrinsically negative, one might be tempted to interpret it 

 as the Instantaneous rate of loss of energy by acoustic radiation. 

 This is not quite correct, however, although It gives the 

 correct total loss of energy over the whole interval when a is 

 small. For the fact that the term Just written is proportional 

 to the time rate of change of the left of (5) does not imply 

 that It Is proportional, with a suitable constant time lag, 

 to the rate of reception of acoustic energy at a distance. 

 The equations of Appendix 2 are therefore directly 

 applicable only to the calculation of the total energy of a 

 pulse and to the calculation of how the time variation of a 

 is affected by corapresalbllity. It is easy to show from these 

 equations that the effect of the finite compressibility of 

 water on the curve of a against t ^s negligible when a la 

 more than a few times its minimum value; details are given in 

 Appendix ?. l^ear the minimum the effect may theoretically be 



either small or large, depending on the equation of state of 



17 

 the gas In the bubble. Recent experiments have shown that 



17 



A. ^. Arons, J. P. Slifko, and A. Carter, J. Acous. 



Soc. Am. 20, 271 (19A8); A. B. Arons and D. R. Yennie, Rev. 



Mod. Phys. 20, 519 (1943), also Volume I of this Compendium. 



