55 67 



pressure p„. The corresponding static deflection, obtained from Equation 

 [85] with 2F^ replaced by F^ is 



^„='f^ [88] 



From Equations [86] and [87] 



'cm = 2Nz,„ [89] 



where the dynamic response factor or load factor N Is the first maximum value 

 of 



,2 

 11- \ n 



Or, N is the first maximum value for i > of 



—5— — j-fe "* + — sin/it — cos /it) 



-7— — 2 (e"'^ + q sina; — cosx) 

 which is the solution for y = dy/dx = at x = of the type equation 



+ y = «-- [90] 



A plot of N is given in Figure 28; the abscissa represents q from 

 to 1, then ^/q from 9 = 1 to 9 = «>. In the present connection, 



a 2a ^ 2 T. , , 



where r„ = l/a and represents the time constant of the wave, while T, = n/Zfi 

 and represents the swing time or the time required for a maximum deflection 

 when the diaphragm is started moving from its flat position and then left to 

 itself. 



The greatest possible value of z^m for a wave of positive press.ure 

 Is ^Zco', this is attained when the pressure remains sensibly constant during 

 the entire swing time. The factor U arises from a doubling by reflection of 

 the Incident wave, and a second doubling by dynamical overshoot.* 



If no baffle is present, so that even the diffraction time for the 

 entire target is small as compared with the time constant of the wave, the 

 factor 2 is to be omitted from Equations [85] and [86], and Equation [89] 

 becomes 



z,„ = 2Nz„ [92] 



In this case, for a very long wave, only the doubling by dynamical overshoot 

 remains. 



See also Reference (25). 



