216 



^ TT ^ 3 ^" " r 





\Ro' y - 1 Vi? / 



In which R^ ^ Indicates that R^ may be Inserted in both places, or /Zg may be 

 employed Instead of R^. For y = 4/3, 



/ = i^ 



-^.^{[t4(^r]HV5(0-'f-i'^- '->> 



As H varies from i2, to J?2» -^ ^s given by Equation [44] or [44a] 

 rises to a maximum and returns to zero. Its maximum value represents the 

 contribution of positive pressures and may be denoted by /+; this value oc- 

 curs when p - Pg = dl/dt = 0. If the Bernouilli term pv^Z may be neglected, 

 Equation [39a] gives 



and elimination of R between this equation and Equation [44a] with /?j 3 = ^i 

 gives, for y = 4/3, 



RADIATION OF ENERGY 



As stated on page 9 the pressure field at a distance from the gas 

 sphere Is essentially an acoustic field and involves the usual radiation of 

 energy to infinity. The intensity of a sound wave, or the energy conveyed 

 across unit area per second, is (p - p^)^/pc\ the amount conveyed P'3r second 

 across a large sphere of radius r concentric with the bubble is, therefore. 



4 TT r ^ 



pc 



.2 (P - Po) 



pc 

 since p is uniform over such a sphere, and the total energy emitted will be 



J P c 



In this integration the lag in time caused by the finite rate of propagation 

 of sound waves can be ignored. 



