47 



3. NON^ COMPRESSIVE THEORy WITH SPHERICAL SYMMSTRg 



Let us consider now the simplest possible model of 

 the motion of the bubble, by assuming the water incompreeslble 

 and the motion spherically symmetrical. This model, simple 

 though It Is, turns out to be capable of giving a fairly 

 satisfactory ac-count of the radlus-tlme curve under most 

 conditions. It Is not surprising that It does so, In view 

 of the following facts; 



(a) The shock wave advances so much faster than the 

 boundary of the bubble that, before an appreciable 

 part of the first pulsation period has elapsed, the 

 motion of the water has become fairly clearly 

 separated Into a shock wave region and a "bubble 

 region", between which the water Is relatively 

 quiescent, as shown In Fig. 1 ( b) .* This empirical 

 fact is accounted for by theoretical calculations 

 on the form of the shock wave.^ 



(b) In the "bubble region" the pressure Is never 

 large enough to change the density of water by more 

 than a few percent. 



(c) With the possible exception of times very close 



to the minimum of the contraction, the pressure in the 



9 

 See the articles by Kirkwood and Brlnkley and by Temperley 



and C-raig in Yolume I of this Compendium. 



*Refer to the end of this article for all referenced figures. 



