-21- 267 



result Is 



(2.27) P = A /I p^,2 ^ lpg,2 ^ p(^A ^ 



where p(A) Is the pressure of the gas Inside the bubble 



when Its radius is A. 



The principle of stabilization asserts that the most 



important term in the expression (2. 27) is the gas pressure 



term p(A). To obtain the maximum possible effect, one 



should maximize p(A) even at the expense of complete elinina- 



12 1 ? 

 tion of the dynamic terms ■$ pA' + -^ pB« • This is not 



obvious and requires a mathematical proof. 



Rettirning now to the expression (2.26) for P, we 

 wish to determine the time when the pressure pulse reaches 

 a peak value. It is to be expected that the peak pressure 

 occurs when the bubble is of minimum size. Althourh this 

 is not obvious from the expression (2.18) for (a a) , it 

 is a simple consequence of the equation (2.19). By differ- 

 entiating (2.19) with respect to a and by using (2.17), we 

 have 



-2 2 



d /o2!>*_ 1 15 s ^11 k _ '2 93 ,21 k 



g^(aa)---i|5-^ ^6*35 ;T57? " "^ ' ^W "^ 715/5 * 



ji 2' * 

 This shows that ^(a a) Is negative and therefore attains 



its maximum at the smallest possible value of a. Hence 



the peak pressure occurs at the time of the minimum size of 



the bubble . 



The value of the peak pressure P can now be obtained 



by substituting (2.23) in (2.26); the resulting expression 



is 



P L 



(2.28) ^ = ^ • —373 • ^^^^(4 - 3u) . 



