Response of a Vibrating Plate in a Fluid 



(see M + F, Vol. i, Page 823) 



ire 



Vm^ 



- 1 *J-(X) 



R^= (y -y')2+z^ 



The contour of integration for the above integral is shown below. 



? -Plane 



Define 



I(u) = rdee'^-Hi"(R#T7 



By considering the asymptotic form of the Hankel function, the above 

 integral is seen to be convergent in the upper half-plane for values 

 of u and R such that 



u > R 



that is, the region inside the Mach cone. 



The contour nmay be defornned to be a contour along the branch 

 cut as shown below. 



{ - plane 







Thus 



511 



