121 



so the second term In the brackets Is essentially 

 Prr t which Is negligible at all times after the 



Initial stages of the explosion. Thus a motion is 

 possible for which gas inertia is negligible, al* 

 though it may not be the motion which actually occurs. 

 (11) We might suppose the gas to oscillate in one of its 

 normal modes, with an amplitude that Increases as 



the radius gets smaller* Now the lowest normal 



29 

 mode of a sphere of gas has the period (for small 



amplitudes) l«40a/c , where c is the velocity 

 g g 



of sound in the gas. Near the minimum radius 



the gas is hot, so t?aat c is high, and the 



S 



period of the gas oscillation la rather small even 



on the scale of the a vs. t curve at this stage. 

 We may, therefore, expect the efficiency of the 

 water in exciting such an oscillation to be smallo 

 (lilj If the amplitude of such a normal mode of vibration 

 is CO Increase greatly as the bubble contracts^ the 

 normal mode cannot lose much of its energy to the 

 water in a period. But if little energy is lost in 

 this wa^ the effect of the gas oscillations on the 

 sound I'ecelved at a distance in the water will be 

 small e 



29 



Lord Raylelgh, Theory ^ Soimd, #331. 



