SPHERICAL WAVES 11 



The rate of growth of mass in the shell is 



. o dp' 



47rr2--Ar 1.32 



dt 



The difference in flux must be equal to the rate of growth of mass, expres- 

 sions 1.31 and 1.32, 



K^-S- 



dp' d 



^+^|PV^|=0 1.33 



Using equations 1.6, 1.9 and 1.13 equation 1.33 may be written, 



(-?)- 



r^^ -f^-lr^T^) =0 1.34 



Equation 1.34 may be written 



— - — c^ 



a/2 a^-2 



= 1.35 



which is the same as equation 1.28. The solution of equation 1.35 for 

 diverging waves is 



r 

 From equations 1.19 and 1.36 the condensation is given by 



,= _l^ = _iM,*«-. 1.37 



c^ at cr 



A. Pressure in a Spherical Wave. — The pressure from equation 1.21 is 



p = c'ps 1.38 



The pressure then from equations 1.37 and 1.38 is 



r 



Retaining the real part of equation 1.39 the pressure is 



kcA . ^^ 

 p = p sm k{ct — r) 1.40 



