UNIDIRECTIONAL MICROPHONES 207 



directional, the ratio of energy response to generally reflected sound is one- 

 third that of a nondirectional microphone. It is interesting to investigate 

 the efficiency of response to random sound of other ratios of sensitivity of 

 the bidirectional to the nondirectional unit. 



The output of a microphone consisting of a bidirectional and non- 

 directional unit is given by 



euD = Rx+ Rocosd 9.55 



where Ri = voltage output of the nondirectional microphone, and 



R2 = voltage output of the bidirectional unit for 6 = 0. 

 The efficiency of energy response of the unidirectional microphone as com- 

 pared to a nondirectional microphone for sounds originating in random 

 directions, all directions being equally probable, is 



2t j (Rx + R2 cos 0)2 sin 6 dd 

 ^'^^^"^^^ = ~^ 4x(/?. + R^f 



^ 1 {R, -I- R,y - {R, - R^y 



6 {Ri + R2yR2 



For the standard velocity microphone Ri = 0, R2 = 1 and the ratio is 

 |. For the cardioid unidirectional Ri = I and R2 = I and the ratio is 

 ^. However, for other values the ratio is different. For example, between 

 R1/R2 = to R1/R2 = 1 the efficiency is less than \ and becomes .25 for 

 R1/R2 = .33. The efficiency for various values of the ratio R1/R2 is 

 shown in Fig. 9.27. The data in Fig. 9.27 shows that it is not so important 

 that the two microphones be of the same sensitivity. It is important, 

 however, that the ratio R1/R2 be equal to 1 or less than 1. 



The same results are shown in Fig. 9.28 by means of polar diagrams. 

 This figure shows that the energy response of the bidirectional microphone 

 and the cardioid unidirectional is the same. However, for < R1/R2 < 1 

 the response to random sounds is less in the case of either of these two 

 microphones. 



C. Efficiency of Energy Response to Random Sounds of a Unidirectional 

 Microphone as a Function of the Phase Angle between the two Units ^^ — The 

 preceding discussions have assumed that the phase angle between the 

 outputs of the two units did not change with frequency. There are two 



29 Olson, H. F., Broadcast News, No. 30, p. 3, May, 1939. 



