HIGHLY DIRECTIONAL MICROPHONES 



215 



acoustic resistance in the form of a long damped pipe, is used for trans- 

 forming the acoustical vibrations into the corresponding electrical vari- 

 ations. 



MAGNET 



LINE 

 AXIS 



Fig. 9.32. Line Microphone. Useful directivity on the Hne axis. This microphone consists 

 of a large number of small pipes arranged in a line with the distance from the opening of each 

 pipe to the common junction decreasing in equal steps. The system is terminated in a 

 ribbon element and an acoustic resistance. 



The contribution, in dynes per square centimeter, by any element n at 

 the common junction of the microphone may be expressed as 



D o ( s. ^« ~ ^« cos d\ 



pn = Bn COS lirUt I 



+ jBn sin 2x(// — 



^{j 



^71 ^71 COS 



') 



^ _ D 2Trjft2Tri{Xn-Xn COS 6)/\ 



9.64 

 9.65 



where / = frequency, in cycles per second, 

 / = time, in seconds, 

 Xn = distance of the element n from the center of the line, in 



centimeters, 

 X = wavelength, in centimeters, 



6 = angle between axis of the line and the incident sound, and 

 Bn = amplitude of the pressure due to element «, in dynes per 

 square centimeter. 



In the case of a uniform line, with the strength a constant, the resultant 

 when all the vectors are in phase is BJ, where / is the length of the line. 

 The ratio Rg, of the response for the angle 6 to the response for 6 = is 



1 I /•^/2 

 Bnl \J-l/2 



9.66 



