23 37 



the diaphragm to the extent of pc times the velocity of the baffle, or to in- 

 crease the pressure to this extent If the baffle is moving toward the side of 

 incidence. The factor pc is the same as the ratio of the pressure to the 

 particle velocity in a plane wave, or about 70 pounds per square inch for 

 each foot per second of velocity. If the velocity of the baffle is variable, 

 however, the release effect is modified by the presence of the term in 



Other useful forms of the equation are possible. In the case of a 

 circular plate of radius a, for example, with everything symmetrical about 

 the axis of the circle. Equation [l6] as applied to the central element of 

 the plate can be written in the alternative form 



mz =2p, + 0-pc[i,(t- ^)-i,(t- x)] -'"/'"'«-? ^"^ ^"9] 



Here the first three terms refer to quantities at the center and at time t, 

 and in the integral s has been replaced by r, the distance from the center of 

 the plate; also, because of the symmetry, it is possible to write dS = Znrdr. 

 The part of the release integral that contains d^z^/dt^ has been transformed 

 as in Equation [105] of the Appendix. For generality, it has been assumed 

 here that only the part of the baffle lying between r = r^ and r = rj is mov- 

 able, while the remainder is at rest; 'z^{t) is the velocity of the movable 

 part at time t. 



If the entire baffle is movable, the equation becomes 



mi = 2pi+ 4> - pcz^[t - f) -pj "z",. r dr [20] 



FINITE PLATE OR DIAPHRAGM WITH NO BAFFLE 



For a plate or diaphragm forming one side of an air-filled box, an 

 approximate equation of motion may be obtained from the last equation by the 

 following argument. Equation [l6] should hold even if part of the "plate" Is 

 reduced to a mere imaginary plane drawn through the fluid; see Figure l6. 

 Then, in the Integral, at elements dS located on the imaginary plane, d^z/dt^ 

 refers to the acceleration of the fluid. These values of d'^z/d.t^ are not 

 known accurately because the pressure in the fluid is modified in an unknown 

 manner by the presence of the plate. For an approximate result, however, we 

 may resort to the assumption that is commonly employed with success in phe- 

 nomena of optical diffraction. 



Let It be assumed that the disturbance in the fluid beyond the edge 

 of the plate is the same as it would be if the plate were not there. Then, 

 if the Incident wave is plane and falls normally on the plate, d^z/dt^ is 



