PRESSURE MICROPHONES 179 



The solution of equation 9.8 is 



/ = — . sin (co/ + 0]) 



CboV (1/Cijoco)2 + r£2 



sin (ico/ + 01 — 02j 



CWV[(l/C£oco)2 + 4r£2][(l/C£oa;)2 + Ve^] 

 + terms of higher order 9.9 



where 0i = tan""^ l/CBo<^r£ and 02 = tan"^ l/2CBowrB. 



For small diaphragm amplitudes, the generated voltage, in statvolts, is 



,/ = r^i = J^ sin (co/ + 0i) 9.10 



Equation 9.10 shows that the condenser microphone * may be considered 

 as a generator with an internal open circuit voltage of 





e = eoi — — ] sin (co/ + 0i), in statvolts, 9.11 



\Ceo/ 



and an internal impedance of l/C^oco, in statohms. 



Equation 9.11 shows that the voltage is proportional to the amplitude. 

 Therefore, to obtain a microphone in which the sensitivity is independent 

 of the frequency the amplitude for a constant applied pressure must be 

 independent of the frequency. In the range below the resonance fre- 

 quency the amplitude of a stretched membrane for a constant applied force 

 is independent of the frequency. See Sec. 3.4. The addition of the back 

 plate with very close spacing introduces mechanical resistance ^-^ due to 

 the viscosity loss in the narrow slit. See Sec. 5.4. This mechanical re- 

 sistance reduces the amplitude at the resonance frequency. The back 

 plate also introduces stiffness due to the entrapped air. This stiffness can 

 be reduced without reducing the mechanical resistance by cutting grooves 

 in the back of the plate. If the damping is made sufficiently large the 

 amplitude at the fundamental resonance frequency of the diaphragm can 

 be made to correspond to that of the remainder of the range. 



^Wente, E. C, Phys. Rev., Vol. 10, No. 5, p. 498, 1922. 

 ' Crandall, I. B., Phys. Rev., Vol. 11, No. 6,^p. 449, 1918. 



^ Crandall, " Vibrating Systems and Sound," p. 28, D. Van Nostrand Co., New 

 York. 



