TELEPHONE DIAPHRAGMS. 



477 



whence 



-MJy 



Xr)--r-dr 



gm (54) 



On the assumption that the vibrations are simply harmonic, or sinu- 

 soidal vibrations, we have the well known condition 



whence 



m 



_ 27iy p 



r-dr 



numeric (55) 



gm (56) 



If the integral in the above expression cannot be computed, after the 

 x„ r curve or amplitude curve has been drawn, we may approximate 

 to the value of the integral by a process of quadrature. Let Figure 32 



Fig. 32. — Illustrating Method of Diaphragm Equivalent Mass 

 Determination from Exploration Data. 



represent the amplitude curve, assumed to be known. Let a be di- 

 vided into a series of n elements, corresponding to successive annuli of 

 equal surface area. Let .rV be the mean value of the amplitude in 

 any single annulus. 



mxo'^ 

 or 



IM 

 2 n 



{x\y + (.i-'^)- + W.r- + + (.r'„)'^ ergs (57) 



M Z {^'rf 



•To^ 



gm (56) 



