325 



where the integration extends over the entire r^ - plane, and JA is a 



vector element of area pointing in the negative z-direction. Henceforth 



our attention will be devoted exclusively to the case of r* on the v^ ^ - 



plane. 



In the case of interest we wish to consider the actual "^ , P » 



and u in the water in relation to the corresponding free-field quantities^ 

 "^tf » F* » 3"^ "-0 that WDuld exist if the diffracting obstacle were ab- 

 sent. Let us apply Eq, (3) to the perturbation3 "^-^ and "u-u.^ of the 

 free-field quantities "^^ and 1?^ arising from the diffracting obstacle. 

 Differentiating this result with respect to time, we obtain 



Suppose the obstacle-'^ extends over an area A^ in the r,*^ -plane. 

 Let the remainder of the r^ ^ -plane be denoted by Aj . In the area A^ let 

 us use the relation P-^«> •■ - V p- . £q. (5) then goes into the form 



P'fo- iTxr^^ i^-i="r'[v>,(r;^';] . ,-Ia' 



Ao 





(6) 



* Here, we use the term "obstacle" in a somewhat generalized sense. It 

 is meant to include all parts of a plane underwater structure offering 

 resistance to the underwater e xplosion wave (e.g., plate and baffle). 



16 



