93 



fluid v;ith the saiiie a and 4r . There cannot be much 



error involved in aasiinin^- that the amount of energy radiated 



during the contracted stage 1b equal to the total change In the 



right of (1) during this stage. 



The richt of (1) v;ill be evaluated by inserting 



the value of ^ which v/ould obtain if there were no 

 at 



dissipation. V/e shall consider three extreme cases: 



(1) Snail vibrations about the equilibrium radius e^^. 

 This case provides a check on the starting 

 formula (1), which should yield the saii-io result 

 as the usual acoustical theory for a simple 

 source. 



(ii) Near the maximum radius for vibrations of 

 any amplitude, 



(iii) Near the minimiam radius, for vibrations of 

 large aTiplitude. 



In all three cases we shall assume for simplicity that the 



pressure-volume relation is 



pa = Po=a, or s Pniax ^nin ^2) 



(1) From (1) and (2) the energy dissipated in one 

 cycle is 



- 1£ 

 c 



/||,|l)\^« . isrii./i^Jdir .>« 



which in the limit of very small oscillations is 



/ max 

 where Tg is the period. At the sane time the total energy la 



