226 



38 



Pe 



c ^ 



I 2 2\2 , D 



0) Pj sin( w( 4- y) 



where y Is a phase angle of no present importance.- The coefficient of 

 sin (wt + y) represents p^, the amplitude of p^ ; in this coefficient the term 

 i^d^wVc' can again be dropped in comparison with unity. With the value of pj 

 thus obtained. Equation [72] becomes 



Q = 



2 TV Rq 

 pc 



(J p, 



(< 



R. 



:73] 



It is more useful, however, to express Q in terms of the intensity 

 of the incident waves, or the energy transported by them across unit area per 

 second, which is, in analogy with Equation ['{^], 



I =^1^ 

 2pc 



In terms of A" as defined in Equation [64], 



a = Ai 



[74] 



A = 



(^0 \ 



7TR„ 



:75] 



Thus the bubble scatters as much energy as falls on an area A placed perpen- 

 dicularly to the direction of propagation of the incident waves. 



