Figure 7 5. Splash, cavities, and bubbles accompanying entry of aluminum sphere. The sphere, 

 3.9 inches in diameter, struck the surface with a velocity of 29 ft/sec. 



so that the dependence of the sound pressure upon p, c, U, L, r, 6, and t, can be 

 expressed in the form 



P U 3 L cos 6 I U \ 



p s (r,6,t) = Z[ -(t- r/c) (19) 



re \L J 



It will be recognized that gravity and also various properties of the liquid and 

 gaseous media will to some extent influence the course of the disturbance. Fig. 15 

 shows some further details of the complicated sequence of events accompanying the 

 vertical entry of a solid sphere. Besides the primary flow implicit in the displacement 

 of the water by the entering object, we can discern a number of more-or-less distinct 

 features such as the spray, the entrance cavity, the cavity formed by the air trapped 

 below the surface after closure of the entrance cavity, and the smaller air bubbles. 

 The manner in which the last two phenomena radiate sound has been discussed in 

 Sect. 2. But even without adverting to details, we recognize various physical 

 parameters not considered in the derivation of [19] as relevant: the acceleration of 

 gravity, g; surface tension, T; the viscosity of the liquid, p.; and the pressure , P , 

 adiabatic compressibility modulus, yP , and thermal diffusivity, D', of the overlying 

 atmosphere. Their influence may be indicated, in a formal way, simple by the inclusion 

 of the appropriate dimensionless parameters as additional arguments in the func- 

 tion Z in Eq. (19), the essential results being unaffected:* 



P U S L cos 9 /U U 2 P UL P U 2 L plP UL 



Vs = Z[-(t- r/c), — , , , - - , 7, — ! (20) 



re \ L gL n T P D' 



* Sounds associated with mechanical vibrations of the entering object are outside the 

 scope of the present discussion. They may be very significant, however. 



261 



