NSWC/WOL TR 76-155 



size; and if A is smaller than A ,. the new oscillation begins at 

 c n+1 



n 



minimum size. Or, restated we have 



If A > A .. , then AMAX .- = A (B3) 



c n+1 » n+1 c 



n n 



If A < A .. . then AMIN ,. . (B4) 



c n+1 > n+1 = A 



n c 



n 



Equilibrium Bubble Radius . At any time during the motion 

 the internal gas pressure p is related to the bubble radius by 



P(A) = pi^l) (B5) 



Setting P(A) equal to p in (B5) yields the equilibrium bubble 

 radius , 



-/3Y 



/Pi\ X 



A = A. I — 



(B6) 



where y is the adiabatic exponent for air (= 1.40) and the subscript 

 "i" refers to the initial ambient "at rest" state. 



Equilibrium Bubble Period . The equilibrium bubble period 



T (for vanishingly small oscillations about the equilibrium radius) 



n . 5 



was given by Kennard. 



T = 2ttA /p/3Vp (B7) 



n n ' r n 



3 

 where p is the water density = 1.940 slugs/ft . 



B-2 



