38 



24 



uniform over the plane beyond the edge, as It 

 would be if a plane baffle were present, hence 

 Equation [l8] can be used In place of Equation 

 [l6]. Here dzf,/dt is now merely the particle ve- 

 locity in the incident wave or p^/pc, so that the 

 term containing this velocity becomes -p^. Thus 

 Equation [l8] becomes, for the motion of any ele- 

 ment of the plate. 



Figure l6 - An Air-Backed 



Diaphragm Forming One 



Side of a Box 



The pressure due to incident waves 

 is p^. The broken lines represent 

 a continuation of the plane of the 

 diaphragm into the water. 



m 



dt' 



dS 



, 4. A P f l±± 1 ^Pi\ S± roil 



plate 



or, if the incident wave varies slowly enough, 

 approximately. 



d'z „ , . P f (dh\ dS 



■22 



plate 



In the special case of axial symmetry, again, a simpler alternative 

 equation is useful. If the plate is a circle of radius a and if everything 

 Is symmetrical about its axis, then similar changes In Equation [109] of the 

 Appendix give, for the motion of the central element only, the approximate 

 equation 



d\ 





:23: 



in which d^z/dt^ on the left and p^it) and </> refer to time t, while p,(t- a/c) 

 is the value of p^ at time ( - a/c, r denotes distance from the center of the 

 plate, and dS has been replaced by 2nrdr. 



Thus the dlffractlve release of pressure around the edge of the 

 plate has the effect of diminishing or even eliminating the doubling of the 

 incident pressure that results from reflection. 



If the plate is mounted in a supporting ring with a plane face, 

 this ring can be treated in the equations as if it formed part of the plate. 



MOTION OP THE FREE SURFACE OF A LIQUID 



Equation [l6] can be applied also to the motion of the free surface 

 of a liquid. This can be done by setting m = 0, replacing <(> by p^ - p, where 

 Pj is the hydrostatic pressure at the level of the surface and p is the ex- 

 ternal pressure on the surface Itself, and interpreting z as the displacement 

 of the surface. Atmospheric pressure is included here in p^ , which may dif- 

 fer from p because of an accelerating pressure-gradient in the liquid. 



