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APPENDIX 2 PULSATIONS OF A BUBBLE IN A FLUID 

 OF FINITE COMPRESSIBILITY 



In this discussion v/e shall start from the 

 equation of motion of a viscous fluid, although it will 

 turn out that the effect of viscosity on the pulsation 

 of a spherically syinmetrical bubble is negligible. The 

 Stokes-Navier equation is 



Jll^-v-Vv^- _Z^ ^^.v - 4. yV . - V2_ (1) 



at 3(= e p 



v/here the sytnbols have the meanings explained on the 

 notation sheet. For spherically symr.ietrical motion we 

 have for the radial components of trie various terros 



2>r ^ ' 



d r 



1 3 , Z s 



^ V . _2_ 5 v 2v 



or r 3r r 



Let us integrate this equation on r, at a given instant of 

 time, from the surface of the bubble to infinity. The order 

 of magnitude of the effect of the viscosity tei^ is not 

 likely to be much Influenced by assuming that ?? is 

 constant for all stages of compression; this simplifying 

 assumption will therefore be made, since this term v/111 



