21 



35 



- 



9V 



an emission of negative pressure caused 

 by acceleration of the face of the tar- 

 get. Positive pressure is emitted, how- 

 ever, by any element at which z is nega- 

 tive. The release or emission effect is 

 propagated from one point to another in 

 the fluid at the speed of sound. 



The surface on which the pres- 

 sure is calculated has been supposed to 

 be the surface of a solid body. Nothing 

 would be altered, however, if the sur- 

 face were, wholly or in part, merely a 

 geometrical plane drawn in the fluid; in 

 Equation [13] z will then be merely the 

 displacement of the fluid itself perpen- 

 dicular to the surface. This extension 

 of the interpretation will be useful 

 later. 



The theory of the relief pressure as described here constitutes the 

 mathematical theory, for a plane surface, of the process of diffraction or 

 equalization of pressure which was described in general terms on page 7- 



dS 



p 



Figure lU - Diagram Illustrating 



the Theory of the Incidence of a 



Wave of Pressure upon a Nearly 



Plane Moving Surface 



The pressure p^ due to incident waves causes 

 a net pressure p on the surface; » denotes 

 the distance of an element of area dS from a 

 point Q on the surface, at which the displace- 

 ment of the surface is 2 . 



MOTION OF AN INITIALLY PLANE PLATE OR DIAPHRAGM 

 OF UNLIMITED LATERAL EXTENT 



So long as the plate or diaphragm remains approximately plane, its 



equation of motion can now be written in the form 





= Pw + <t> 



[lU] 



where m is its mass per unit area, z is its displacement at any point perpen- 

 dicular to the plane occupied initially by its face, p„ is the total incre- 

 ment of pressure caused, directly or indirectly, by Incident waves, and 



4> = Po- Pd+ P. 



:i5] 



where p^ is the total hydrostatic pressure, p^ is the pressure on the back of 

 the plate and p^ is the net force per unit area in the direction of z due to 

 stresses in the plate. Motion parallel to the initial plane is assumed to be 

 negligible so far as inertial effects are concerned. Here m, 2, p, and <p may 

 all vary over the plate. Inserting the value of p„ = p - p^ from Equation 

 [13] 



