UNIDIRECTIONAL MICROPHONES 205 



is the purpose of this section to consider the response of the unidirectional 

 microphone as a function of the frequency and distance from a point 

 source. 



The voltage output of a nondirectional microphone as a function of the 

 distance r is given by 



snd = — sin oit 9.52 



r 



where Ri = sensitivity constant of the microphone, 

 CO = 27r/, 



/ = frequency, in cycles per second, 



r = distance, in centimeters, from a point source of sound, and 

 / = time, in seconds. 

 The voltage output of the bidirectional velocity microphone as a function 

 of the distance and the wavelength X, in centimeters, is 



esD = -^2 { - sin w/ — - — cos co/ ) cos 6 9.53 



\ r 2irr^ / 



where R> = sensitivity constant of the microphone, 



r = distance, in centimeters from a point source of sound, and 

 = angle between the direction of the incident sound and the 

 normal to the ribbon. 

 If the output of the unidirectional microphone as a function of the angle 6 

 is to be a cardioid of revolution for plane waves, then Ri must be made 

 equal to R2. The ratio of the output of the unidirectional microphone as 

 a function of the distance and frequency as compared to a pressure micro- 

 phone is 



y-e-s-o^ 



Response Ratio = j -^-^^ 9.54 



This ratio for 6 = 0, 30°, 60°, 90°, 120°, 150° and 180° for 1, 2 and 5 feet 

 is shown in Fig. 9.26. The same ratio for a conventional velocity micro- 

 phone for 1, 2 and 5 feet is shown in Fig. 9.26. It will be seen that the 

 accentuation in the unidirectional microphone is smaller than in the case 

 of the velocity microphone. 



