190 



MICROPHONES 



CONDUCTOR 



Fig. 9.10. Pressure gradient microphone. 



gradient microphone consists of two pressure actuated units, separated by 

 a very small distance, with the electrical outputs connected in opposition. 

 Figure 9.10 schematically depicts the essential elements of a pressure gra- 

 dient microphone. A cylinder 

 of mass 7n is coupled to a con- 

 ductor located in a magnetic 

 field. The cylinder is assumed 

 to be the only portion of the 

 system which will be influ- 

 enced by sound waves. The 

 diameter of the cylinder is 

 assumed to be small compared 

 to the wavelength. Therefore, 

 the average intensity will be the same for all points on the surface of the 

 cylinder. The vibrating system is assumed to be constrained so that the 

 only motion possible is one in a direction parallel to the longitudinal axis 

 of the cylinder. Under these conditions the vibrating system is driven 

 by the difference between the forces on the two ends of the cylinder due 

 to the impinging sound wave. 



Assume a plane sound wave, from equation 1.22, the pressure, in dynes 

 per square centimeter, at ;c = may be written 



p = kcpA sin {kct) ^ 29 



p — pm sin kct 



where c = velocity of sound, in centimeters per second, 

 k = 27r/X, 



X = wavelength, in centimeters, 

 p = density, in grams per cubic centimeter, 

 yf = amplitude of </>, 

 ct) = velocity potential, and 

 pm = maximum sound pressure, in dynes per square centimeter. 

 The pressure at the end of the cylinder xi = — A;c/2 for a direction of 

 propagation 6 is 



(Ax \ 



f/ + — cos 6 J 



9.30 



The pressure at the other end of the cylinder xo = Ax/2 is 



ct — cos d j 



9.31 



