r(h*f)-Rf 



t 



Figure 9. Sketch illustrating the method of calculating the sound pressure radiated by a collapsing 

 vapor cavity according to theory of Gilmore. 



the diagram, the value of (c + u) at the corresponding radial coordinate and instant 

 of time. Outside the immediate vicinity of the cavity, the theory is nearly exact: the 



value of the propagated quantity gives the value of r& and hence, at large values of 



the radial coordinate r, the acoustic pressure p s (since p s = pfy) . In order to construct 

 the outgoing paths, it is necessary to determine the value of (c -f- u) at each radial 

 coordinate and instant of time, information itself partly dependent upon the result of 

 the calculation, so that it is necessary to employ either iterative methods or an adequate 

 analytic approximation to the required velocity field. The calculation is further compli- 

 cated by the development of a shock, whose path of propagation must be computed 

 by separate considerations. The development of the shock also is indicated qualitatively 

 in the diagram, which shows how larger values of the propagated quantity "overtake" 

 smaller values which "left" the wall of the cavity at an earlier instant. The entire 

 diagram is only crudely qualitative; it is impossible to detail the actual situation in 

 undistorted form suitable for ready visualization. 



255 



