354 



The second term can be neglected compared to the first. 

 Using (3.1) we find that 



P - (A^a')' ^ (a'^b')' cos 9 .... 

 P"""^~ ^ • 



For moderate distances from the bubble only the first 

 tenn is important, so that 



(3.26) P "^ R~ * 



2 • • 

 The value of (a a) can be found by multiplying 



(3.15) by a and then differentiating. This gives 



o.p,, 4.2* 3" 



2a a(a a) (1 + aL^j-i^) + a a aJjf-^ + 4a a 



+ k(4 - 3r)a^"^'^4 - 3s^a"^d = a. 



Since the peak pressure will be found at the time of min- 



. 2 • • 



Imum size, we may put a = and solve for (a a) . The 



result is 



1 ^ 3if _ k(4 - 3y) a^-3Y 



, 2 • X • 2a^ 2a^ ^ 



(a a) = =^ =^S 



1 + aL^-, 



(3.27) p 



9i + 3k(r - 1) rl-3Y 

 + n a 



4a 



1 + 



Qltf-^ 



if we make use of equation (3.23). Using the notation of 

 (3.24) equation (3.27) becomes 



a 

 (3.28) 



•v. _ 1 r36 , 3(Y - 1) ul-Yn 



3-) - r^L-!5r: + — ^ — 5 ^ J 



3(y - 1) r fe , „l-rT 

 3^V3 ^2/3 ^ (Y - l)u ^ ^ ^ • 



