VELOCITY MICROPHONES 191 



The difference in pressure between the two ends of the cyUnder is 



^P = pi — P^ = ^pm cos {kct) sin ( —— cos 6 1 9.32 



The driving force, in dynes, available for driving the cylinder along the 

 X axis is 



— cos d 1 9.33 



where S = area of the end of the cyHnder, in square centimeters. 

 If I^x is small compared to the wavelength the driving force is 



jM — S pm^x cos d cos kct 9.34 



c 



A comparison of equations 9.29 and 9.34 shows that for a wave of con- 

 stant sound pressure the driving force is proportional to the frequency. 



The velocity of the mechanical system for A^ small compared to the 

 wavelength is 



JM Spm Spm 



X = - — = - — Aa; cos d cos kct = —^— A>v cos 6 sm kct 9.35 

 jwm jcm cm 



where m = mass of the cylinder, in grams, and 



CO = 2-71/,/ = frequency, in cycles per second. 



This quantity is independent of the frequency and as a consequence the 

 ratio of the generated voltage to the pressure in the sound wave will be 

 independent of the frequency. 



The velocity of the mechanical system for any value of Hx is 



. (k^x \ 



5m 1 -— — cos Q 1 



\ 2 / 



X = sm [kct) sm ( -— - cos 6 I 9.36 



emu 



. 2^^™ . ^, ^ . /kD \ 

 X = — ^— sm {kct) sm ( -— cos ^ J 9.37 



cmw \ 2 / 



where D = distance between the two ends of the cylinder. 

 The voltage output, in abvolts, of the conductor is 



e = Blx 9.38 



