8 KENNELLY AND KUROKAWA. 



Z ), z' is the mechanic impedance of the diaphragm at the same 

 frequency and load (dynes per kine Z or mechanic absohms Z). 

 Then x the rms. vibrational velocity of the diaphragm over either pole 

 of the receiver is 



AI ■ 



a- = — r rms. kmes Z (13) 



z 



If the mechanical impedance z' is reactanceless, as happens at the 

 impressed frequency of apparent resonance, it degrades from a com- 

 plex quantity to the real quantity r", or mechanic resistance. In 

 this case, the phase of the velocity x will be the same as that of the 

 product (AI). Taking the phase of I as standard, or its slope as zero, 

 that of A is — i8°; so that x will then lag /3° behind I in phase. In 

 general, however, with mechanic reactance present, the phase of x 

 will be displaced from that of (AI) by the slope of z'. 

 Again, 



. . 12 electric absohms Z 



2! = — — = — or C.G.C. magnetic (14) 



imits of resistance Z 



This means that in the motional impedance circle of the receiver, at 

 any impressed frequency, the vector motional impedance TJ , as 

 obtained from electrical measurements with a Rayleigh bridge, is 

 equal to the square of the complex force factor A, divided by the total 

 mechanic impedance z' at that frequency. At the frequency of 

 apparent resonance, this becomes 



A^ 

 Zo = —^ electric absohms Z (15) 



since z' degrades at resonance into the total mechanical resistance r" . 

 The slope of the motional impedance Z' will then l)e the same as the 

 slope of A", or —2/3°. Zo is thus the diameter of the motional imped- 

 ance circle, in the ordinary simple case, where the telephone is tested 

 for its motional impedance. 



From (14) it follows that, at any impressed frequency, the total 

 mechanic impedance z' is 



z'='^"=\2Y' dynes per kine Z ,^^. 



7J " or mechanic absohms Z ' 



Consequently, if we divide the complex constant A- by the measured 

 motional impedance Z', we obtain the size and slope of the total 

 mechanic impedance of the diaphragm at this frequency. 



