326 



Since we are interested only in pressiires near the center of the obstacle, 

 the contribution of the third integral in (6) (involving the difference 

 iC -"^0 in the area A^ outside the obstacle) will be quite small for most 

 cases since this term represents the diffraction of the scattered (not the 

 primary) wave. This is obviously true when the thickness of the pressrire 

 wave is .-nnall compared with the width of the obstacle. Consequently, we 

 shall neglect this term obtaining the result. 



(7) 



^Zi- C if*-r'\-' ^c^:t*;.aT. 



Now let us specialize the above result to the case of an incident 

 plane pressure, wave and a circular plate of radius t?^ clamped to a rigid 

 baffle whose outside radius is R^ , In this case P(,Cr^6)« poC'-^/^e^ ' 

 thua Vp,(r*,^^c -T^pJCtVco ^°^ «^ °^ ^^^ r^^-plane. Also let 'r'-i' 

 = f**, and let t^* = r * ( l!, c*a. <^ *" -V ^T^ cC- 4»*' ). (It should be 

 emphasized that we are limiting "^ and r* to the r 4 -plane.) Finally, 

 let -x denote the displacement of the plate in the z-direction. With these 

 assumptions and definitions, Eq« (?) becomes ( v A R^ ) 



where 

 and 



17 



