VELOCITY MICROPHONES 195 



The ratio of the pressure at the center of a circular plate for any angle 

 of the incident sound is 



p \/l — sin2 



: r 1 - e^^« f: €„iVV" (kR sin eU 9.42 



, 1 — Vl — sin2 



where /x = — 



sin 6 



€u = 1 when u = 0, 

 €u = 2 when u 9^ 0, 

 6 — angle of the incidence, 

 R = radius of the plate, in centimeters, 

 k = 27r/X, 



X = wavelength, in centimeters, and 

 /„ = Bessel function, of the order u. 

 The pressure at the center on the front and back of a circular plate for 

 normal incidence ^ = 0° or 180°, from equation 9.42, is 



po 



P 



pl80 



P 



VS -AcoskR 9.43 



= 1 9.44 



The pressure frequency characteristic on the front and back of a circular 

 baffle for normal incidence computed from equations 9.43 and 9.44 is shown 

 in Fig. 9.14. It will be seen that the pressure at the front rises to a value 

 of three times that in free space at R/\ = .5, then falls back to the same 

 as the free space pressure at R/X = 1, and repeats for R/\ = 1.5 and 

 R/\ — 2, etc. The pressure at the back is the same as the free space pres- 

 sure for all frequencies. The measured pressure at the center on the front 

 and back of a circular baffle is shown in Fig. 9.15. In order to reduce 

 errors in measurement to a minimum, baffles of different diameters were 

 used. In addition, several different pressure measuring arrangements 

 were used. The results shown in Fig. 9.15 represent an average of these 

 determinations. It will be seen that theory and experiment are in fairly 

 good agreement. Some of the deviation may be attributed to finite size 

 of the pressure measuring system. 



The phase at the front and back of a circular baffle computed from equa- 

 tion 9.42 is shown in Fig. 9.16. A point in the plane wave corresponding 

 to the plane of the baffle is the reference plane for the phase. It will be 



