- 3 - 



41 



the high pressure developed gives rise to an acoustic impulse 

 which can be heard at a aistance. These features of the 

 phenomenon will be discussed in detail in Sections 3 and L of the 

 text, the former dealing with the spherically symmetrical pulsa- 

 tions of a bubble in an incompressible fluid, the latter with the 

 effect of the finite compressibility of the water, which gives 

 rise to acoustic radiation. Mathematical details are given in 

 Appendix 1 and in Appendices 2 and 3, respectively. 



In actual experiments with explosion bubbles there are 

 always asymmetrical influences which prevent the motion of the 

 water from conforming exactly with the spherically symmetrical 

 theory just mentioned. The most interesting features of the pulsa- 

 tion phenomenon are, in fact, those which are associated with 

 asymmetries in the motion, and many of the papers contained in this 

 Volume are devoted to these features. If the only asymmetrical 

 influence is the pressure gradient due to gravity, the bubble will 

 rise; it turns out that the velocity of rise increases enormously 

 during tne contracted stages, and that appreciable departures 

 from spherical shape may also occur in these stages. An additional 

 "migration effect" can be caused by proximity of the bubble to a 

 rigid body or to a free surface: roughly described, a rigid sur- 

 face attracts a pulsating bubble while a free surface repels it; 

 these effects may sometimes be more intense than that due to 

 gravity. The importance of both kinds of asymmetry in the motion 

 is obvious, since the position and characteristics of the bubble 

 at the time of its minimum volume will greatly influence the 



