192 MICROPHONES 



where B = flux density in the field in which the conductor moves, in 

 gausses, 

 / = length of the conductor, in centimeters, and 

 X = velocity of the conductor, in centimeters per second. 



The response frequency characteristic of a mass controlled, dynamic 

 pressure gradient microphone computed from equations 9.37 and 9.38 is 

 shown in Fig. 9.11. 



The directional characteristics of a pressure gradient system of the type 

 shown in Fig. 9.10 and computed from equation 9.37 are shown in Fig. 9.12. 

 It will be seen that when the ratio D is greater than X/4 the directional 

 pattern becomes progressively broader as the frequency increases. In the 

 case of the baffle type ribbon microphone, the directional characteristics 

 first become sharper than the cosine pattern and then broader as the dimen- 

 sions become comparable to the wavelength. In other words, the doublet 

 theory is not in accord with the observed results. Of course, deviations 

 would be expected when the dimensions of the baffle become comparable 

 to the wavelength because of variations in both intensity and phase due 

 to changes in the diffraction of sound by the baffle. 



The above considerations have been concerned with a plane wave. 

 From equation 1.40 the pressure component in a spherical wave is 



p = —^— sm k(a - r) 9.39 



r 



Let the distance on the axis of the cylinder between the source and points 

 xi and Xi on the cylinder be r — Ax /I and r + Lx/1 (Fig. 9.10). The 

 difference in pressure between the two ends of the cylinder is 



A/) = kcpA 



1r cos k ict — r) sin I — 1 + 2D sin k {ct — r) cos ( — 1 



9.40 



If D is small compared to r and kD is small compared to unity equation 

 9.40 becomes approximately 



z. ^r. r^^ ^°^ ^^'^^ - r) + sin k{ct - r)"| 

 Ap = kcpAB ^ 9.41 



This equation is similar to equation 1.42 for the particle velocity in a 

 sound wave. Therefore, the voltage output of this microphone corresponds 



