84 



wave front. In the Interpretation of the rl^ht side of (3) 

 we should ro:r:e:;iber that, strictly apoalcinn, p is not quite 

 the sa-ie function of ^ in the shock wave front that it is 

 elsewliere, because heat is beinc coJ^Qratod in this region 

 h-j ir'-^eversible processes. In practice we rr.ay Ifpiore this 

 complication, hov/ever, as the extra pressure due to this 

 heating is nQ^llgVole. If this is done, the ri^^it side 

 of (3) will be a knovm function of the pressure at r ss a> 

 I'.or-eover, v;e have 



°-<'-=--^^| ---^§] (*' 



— 'r^a _,' rwa 



v/hore c splHj'^is bho velocity of sound in water. Tlius, 



it Y9 asEuino t iat the pressure is •jnifoiTi throuchout the 



bubble, so that p(a) is a knov/n function correapondinc 



to an adiabatic law, (3) v;ill becc:;ie aii ordinory differential 



r 2jf dr . vVo 

 shall now trj to transform this torm- 



An inspection of (3) shows that the only teins 

 \7h.lch can be responsible for a dissipation of ener£^ are 

 the last two on the left, since all the others are un- 

 changed when the sign of ^ Is changed. The first of 



dr 



these must account for the energy radiated av/ay in the 

 form of sound o / hint on hov; to evaluate this term Is 

 pr.'/vided by considering the special case in v/hich the 

 oriplivudo of the motion Is small enough so that the 

 ordinary acoustical theory can be used. In such a case 

 C> will obey tho wave equation andysijica only outi^oLng 



