COLLECTION OF SOUND 305 



where Eq = power output of the sound source, in ergs per second, and 

 c — velocity of sound, in centimeters. 

 To simpUfy the discussion, assume that the effective response angle of 

 the microphone is the solid angle 12 radians. The direction and phase of 

 the reflected sound are assumed to be random. Therefore, the reflected 

 sounds available for actuating the directional microphone are the pencils 

 of sound within the angle Q,. The response of the directional microphone 

 to generally reflected sound will be S^/47r, that of a nondirectional micro- 

 phone. The generally reflected sound to which the directional microphone 

 is responsive is, therefore, given by 



En = ^[\-e^^sno,eii-am/4v^^^ _ ^) 12.16 



where a = absorption per unit area, absorption coefficient, 



S = area of absorbing material, in square centimeters, 

 F = volume of room, in cubic centimeters, and 

 / = time, in seconds. 



The ratio of the generally reflected sound to the direct sound is a measure 



of the recorded reverberation. 



Er _ 4D^12 [1 - ^(cS[los,a-a)U)/4V^ ^1 _ ^^ 



Ed ciS 



If the sound continues until the conditions are steady, equation 12.17 

 becomes 



Et> 4D2 



-^ = —.^{\-a) 12.18 



From equations 12.17 and 12.18, it will be seen that the received rever- 

 beration can be reduced by decreasing the distance D, by increasing the 

 absorption aS, or by decreasing ^. 



For a given room employing a directional microphone, the receiving dis- 

 tance can be increased v47r/^ times that in the nondirectional system 

 with the same collected reverberation in both cases. 



The absorption characteristic of a studio is shown in Fig. 12.14. The 

 direct sound picked up by a nondirectional microphone and two direc- 

 tional microphones is the same because the distance between the sound 

 source and the microphones is assumed to be the same for all three cases 

 (Figs. 12.145, 12.14C and 12.14D). The generally reflected sound picked 

 up by a nondirectional microphone is shown in Fig. 12.145. The generally 



