218 



MICROPHONES 



delay. In the case of a delay path comparable to the wavelength, loss in 

 sensitivity occurs. 



3. Line Microphone: Useful Directivity on the Line Axis. Two Lines 

 and a Pressure Gradient Element. — This microphone consists of two lines 

 of the type shown in Fig. 9.34 arranged so that the ribbon element measures 

 the difference in pressure generated in the two Hnes (Fig. 9.36). The 



Fig. 9.36. Line Microphone. Useful directivity on the line axis. This microphone consists 

 of two lines of the type shown in Fig. 9.34 displaced by a distance D along the axis. In the 

 line nearest the ribbon element a bend is inserted which introduces a path length D. The 

 ribbon element measures the difference in pressure in the two lines. 



centers of the two lines are displaced by a distance D. In the line nearest 

 the element, a bend of length D is inserted between the junction and the 

 ribbon element. 



To show the action of the pressure gradient system, assume that the 

 length of all the small pipes is the same and the openings between the two 

 sets are separated by a distance D. Under these conditions the line systems 

 are nondirectional. 



The difference between the forces on the two sides of the ribbon, assum- 

 ing the mass reactance of the ribbon is large compared to the resistance of 

 the damped pipes, may be expressed as 



rD cos Q^ 



Jm = A cos (27r/>) sin 



/ ttD cos Q \ 



9.71 



where A = constant, including the pressure of the impinging sound wave 

 and dimensions of the microphone. 



If D is small compared to the wavelength, equation 9.71 becomes 



ttD 

 Jm = A — cos (27r/>) cos Q 



A 



9.72 



Equation 9.72 shows that the force available for driving the ribbon is 

 proportional to the frequency and the cosine of the angle Q, 



