GENERALIZATION TO ANY TYPE OF DIAPHRAGM MOTION 17 



generalization of the previously used radiation im- be found in a manner analogous to that used above. 

 pedance z,.. When no sources other than the trans- These calculations involve, in general, the solution 

 ducer are present in the medium, the pressure at any of linear integral equations which can be solved in 

 point Rin the medium is, by equations (39) and (10), principle, though practical solutions may be difficult 

 given as to obtain except in simple cases. The reciprocity 



theorem, equation (28), can be proved in this general 

 p(K) = - — I G(R, r') j'„(r') dr'. (-12) case provided that 



4,7 Js 



|A(r)| = |A'(r)| (43) 



The above equations allow the behavior of the trans- 

 ducer to be calculated under any conditions. The anc * 

 various impedances, sensitivities, and efficiencies can z o(r,r') = z (r',r). (44) 



