120 



APPENDIX 7 EFFECT OF THE I N ERT IA OF TH3 GAS 

 ON THE PRESSURE PULSE 



It seems unlikely that OBclllatlons of the gas In 

 the bubble, I.e., non-uniformity of the pressure in the 

 bubble due to the inertia of the gas, can cause any 

 appreciable wiggles in the pressure pulse emitted during 

 the contracted stages. The reasons are as follows: 



(l) The pressure gradient at the outer edge of the 



gap ahpre Is 



/!£) = ^^^ d\ (1) 



\9v]^ =a ^ ^ dt^ 



where (*>g is the density of the gas. The 

 equation of motion ^f the gas can apparently 



be satisfied by a velocity distribution 

 approximating a uniform contraction or ex- 

 pansion combined with a pressure distribution 

 which is roughly parabolic In r with the slope 

 (1) at the boundary. For such a distribution 

 It is easy to calculate the fractional deviation 

 of p (a) from the pressure p which the gas 

 would have under static conditions at the same 

 volume? the result is 



p(a) :::; p 1 



dt~J 



At the mlnlmxun radius, for example. 



5T? ~^ 



(2) 



2 



a i-| — P^gl (eq. (19), Appendix 2) 



dt ^ 



