66 BELL SYSTEM TECHNICAL JOURNAL 



In this expression, 7 is the adiabatic constant of air, po the atmos- 

 pheric pressure, ai the area of the fictitious diaphragm, and Vi the 

 volume of air in the film. This diaphragm is loaded externally by 

 the air chamber, when the transmitter diaphragm is prevented from 

 moving, by a stiffness reactance of 



JW JWV 



in which v is the volume of the air chamber. Similarly, the load of 

 the air chamber on the transmitter diaphragm, whose area is 02, is 



jw jwv 



The air chamber also acts as a mutual impedance between the 

 thermal unit and the transmitter diaphragm equal to 



,w Sii ypodiai 

 M12 = -T— = — : 



JW JWV 



If, further, the intrinsic impedance of the transmitter diaphragm, 

 which may be any function of frequency, be denoted by Z2, the 

 equations of motion of the system may be written 



F = {Zx^ M[)k, - M[2X2, 

 = - M'nk, + (Z2 + M'2)x.,. 



In these equations, F is the force acting on the thermal receiver 

 "diaphragm" due to alternating current, Xi the velocity of its motion 

 and Xi, the velocity of motion of the condenser transmitter diaphragm. 

 A rough calculation shows that Vi is very small compared with v, 

 so that Si may be neglected compared to Si and that the reaction 

 yiyiXi may be neglected. The analysis of the condenser trans- 

 mitter shows Z2 to be very large compared to M'^. These equations 

 may then be rewritten 



F = ZiXi, 



Mi2Xi=Z2k2. (1) 



The equations of motion, when the receiver is inserted in the ear, 

 may be derived in a similar way. In this case, although the volume 

 of air between the receiver and ear drum is the same as before, the 



