152 BELL SYSTEM TECHNICAL JOURNAL 



If we substitute r for —y, this expression gives the instantaneous 

 pressure on the diaphragm at the radial distance r from the center. 

 The instantaneous power delivered by the diaphragm is then 



W = - j^ ^0 cos ka - It r (^-^2) cos kict + r - R) • rdr 

 ^ ^ ^if\_A cos kct + B sin kct~\ cos kct, 



where 



5-|l+i4)-in*i?-;^ 



The effective force on the diaphragm is then 



F = r ;— = ^T-r- A cos kct + B sm kctl 



lo cos kct r^fk^ 



The effective resistance is therefore 



ro'^k^ 

 and the effective reactance 



4t pc A B 



ro'k' 



Expressions for the resistance and reactance for other modes of 

 motion of the diaphragm may be obtained in a similar manner. 



Appendix B 

 The motional resistance, Rm, of a moving coil receiver is eciual to 



BH'ir + /) « , 



- ohms, 



(r + r')- + ( mo) h x ) 



where B is the average flux density, 



/, the length of wire in the receiving coil, 



r + jx, the mechanical impedance imposed on the diaphragm 

 by the horn through the coupling air chamber, 



' Keiinellcy luul Pierce, loc. cit. 



