VIBRATING TELEPHONE DIAPHRAGMS. 453 



F-f2 



OCa = = Xyn — X2, kill 68 Z , (24) 



where Xa is the max. cycHc velocity of the diaphragm in the presence 

 of absorption. The C.V.M.F. f., is proportional to the velocity Xa, 

 to the mechanical resistance r^ of the dependent system, and to the 

 relative phase of Xn and n, as defined by the complex ratio ro/^To. 

 That is, 



/2 = XaT'i ( — ) = Xa — , max cy. dynes Z . (25) 

 \ 22 / Z2 



The secondary C.V.M.F. /. will therefore be out of phase with the 

 velocity Xa of the diaphragm, except at the frequency «y„ of second- 

 ary resonance, when s-, = ro ; and 



/02 = Xar2, max cy. dynes Z. (26) 

 Substituting (25) in (24), we obtain 



Xa = , max cy. kines Z , (27) 



whence 



F F 



Xa = "0 = — , — , max cy. kmes Z . (28) 



r2" Z + Za 



z + — 



S2 



The effect, therefore, of the dependent system having a secondary 

 resonant frequency is to add a new absorption impedance 



Za = ?'2"/22 



to the primary impedance s. 



Solving (24) for .r„ the absorption or secondary velocity we obtain 



( F\ Za . ( Za \ 



X2 = 17) '^^~T — = Xm I ~7~ I , max cy. kmes Z . (29) 



\ Z J Z -\- Za \Z -\- Za J 



From an examination of (28), it is evident if the primary and 

 secondary frequencies are tuned to coincide, i. e., if «Q,r=:«p, then 

 at this frequency, Zo='r^ and z^r, so that 



F 



Xa = — , . max cy. kines Z . (^o) 



r -\- r2 



In this case, the velocity, in the presence of distortion, is in phase 



