UNIDIRECTIONAL MICROPHONES 209 



rate unit is Sq volts. The output of the combination is 



e = eo\/ (cos d + cos </))2 + (sin 0)2 9.57 



The efficiency of the energy response of the above system to that of a 

 nondirectional microphone is 



l-n-eo I [(cos2 ^ + 2 cos cos + cos^ 0) + sin^ <^] sin 6 dd 

 ^^^'^"^^y^ ' ^[^^ 9.58 



2W / [cos2 + 2 cos 9 cos (^ + 1] sin ^(9 

 Efficiency = '- ^, =3 9.59 



The efficiency is the same as in the case of no phase angle shift. 

 If the units are separated by a finite distance d, then there will be a 

 phase difference between the units which is 



= - 360 cos 9.60 



X 



where d = distance between the units, in centimeters, 

 X = wavelength, in centimeters, and 



d = angle between the direction of the incident sound and the 

 normal to the ribbon. 

 Note that this separation is in line with the units. Substituting 

 = {d/\) 360 cos 6 = K cos 6 in equation 9.57 the output is 



^ = ^oV[cos d + cos (K cos d)Y + [sin {K cos d)f 9.61 



The efficiency of the energy response of the above system to a non- 

 directional system is given by 



2x^0- / {[cos0 + cos (^cos^)P + [sin (^cos^)P} sin Odd 



Efficiency = — — ; = - 



^ 16 W 3 



9.62 



That is, the efficiency is independent of the separation between the units. 

 Of course, for very large distances the separation disturbs the response for 

 9 = 0. However, in the conventional microphone this does not occur. 

 Therefore, the effect of finite size has no effect on the efficiency of energy 

 response to random sounds- 



