190 



PERIOD OP OSCILLATION 



A sphere of gas in water under hydrostatic pressure p , not subject 

 to the action of gravity, Is capable of oscillating radially with preserva- 

 tion of its spherical form. Let the gas be assumed to follow the adiabatlc 

 law, pV^ = constant, an assumption that appears to hold well in practical 

 cases. Then, for a small amplitude of oscillation, the period is given by 

 Equation [3^] or 



^o = 2^«ol^ [T 



where Rq is the radius of the sphere when in equilibrium under hydrostatic 

 pressure p^ (atmospheric pressure included), p is the density of water, and y 

 is the ratio of the specific heat of the gas under constant pressure to its 

 specific heat under constant volume. For air, y *= 1 .4 and the formula can be 

 written 



where p^ is the pressure in atmospheres,* and R^ is in inches. For the gas 

 globe from an exploded charge, y = 1.5 more nearly, and 



^0 = i^ P^ -^-'^ [2b] 



In sea water T^ would be 1.3 per cent greater at the same R^ and p^. 



The Value of Rq for gas globes from charges exploded under water is 

 uncertain. Perhaps /Jq = R^^^/2.S is not far from the truth, where i? max is 

 the maximum radius. A fair estimate for tetryl is 



Rm^ = 49(— )» Inches 



where Wis the weight of the charge in pounds and p^ is the hydrostatic pres- 

 sure in atmospheres; the value for TNT should not be greatly different. With 

 this value of /?o. Equation [2b] becomes 



i 

 r, = 0.15-^ [2c] 



With increasing amplitude the period Increases; it may be written 



T = kTf, [3] 



where fc is a dimenslonless factor. In Figure 1 the factor k or T/T^ is plot- 

 ted against R^„/Rq. In the same figure there is shown, for convenience, the 



The period under one atmosphere is thus Rj/l29 second. 



