50 



36 



dt' 



0.25 



0.20 



0.15 



dl 



0.10 



0.05 



Figure 20 - Curves for a. Diaphragm under Uniform Pressure Suddenly Applied 



The diaphragm is constrained to move paraboloidally ; z^ is the deflection of its center, t is the 

 time, and Tj is the diffraction time, equal to the radius of the diaphragm divided by the speed 

 of sound. The curves represent actual values of acceleration and velocity; the lines represent 

 the non-compressive values. The plot is drawn for a particular case, as explained in the text, 

 and is only approximate. 



figure would not be greatly changed if the more correct integrodlfferentlal 

 equation were employed. Instead of the approximate difference-differential 

 equation. 



Impulsive Pressure 



The second special case that is of particular interest is the fol- 

 lowing. After the plate has been at rest for a time exceeding D/c, let it be. 

 given by Impulsive action a velocity z^ = Vq and then left to Itself, with 

 Fj = = 0. In this case it is evident, by Integration of Equation [U8] dur- 

 ing the time of impulsive action, that 



_ dz, _ 2 



"'^'wl""" 



whereas according to the reduction principle the velocity dzjdt will ap- 

 proximate within the diffraction time to the non-compressive value as given 

 by Equation [50b] or 



