HIGHLY DIRECTIONAL MICROPHONES 



219 



Employing mass controlled ribbon of mass m^, the velocity is given by 



A 



X = 



j2Tr/mr\ X 

 A 



■kJT 



— 1 cos (27r//) cos B 



-(^)si„2.. 



— 1 sin 27r// cos 



9.73 



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 above discussion assumes that the lines are nondirectional. The 

 directional characteristics of the individual lines of Fig. 9.36 are given by 

 equation 9.70. The directional characteristics of the microphone, shown 

 in Fig. 9.36, for D small compared to the wavelength are the product of 

 equations 9.70 and 9.73. The directional characteristics may be written as 



• ^ (1 

 sm -(/ 



/ cos + d) 



R, = 



-(/ - Icosd + d) 



cos 9 



9.74 



The directional characteristics of the microphone shown in Fig. 9.36 for 

 various ratios of the length of the line to the wavelength for a delay of 

 one quarter times the length of the line are shown in Fig. 9.37. A measure 



LENGTH ='4A 



Fig. 9.37. The directional characteristics of the microphone shown in Fig. 9.35 for a time 

 delay of one-quarter the length of the line as a function of the ratio of the length of the lines 

 to the wavelength. The polar graph depicts the output, in volts, as a function of the angle, 

 in degrees. 



of the value of a line with progressive delay and a pressure gradient ele- 

 ment for improving the directivity may be obtained by comparing Fig. 9.37 

 with Fig. 9.33. Employing these expedients approximately the same 

 directivity can be obtained with a line of one quarter the length of the 

 simple line shown in Fig. 9.33. 



