PRESSURE MICROPHONES 187 



a in centimeters, from an elementary source is (see Sec. 2.2) 



P = -^ipco«maxe^'"*6-^'^" 9.19 



where dS = area of the source, in square centimeters, 



^max = maximum velocity of dS, in centimeters per second, 



p = density of air, in grams per cubic centimeter, 



w = It/, 



/ = frequency, in cycles per second, 



u = velocity over the surface dS, in centimeters per second, 



t = time, in seconds, 



k = 27r/X, and 



X = wavelength, in centimeters. 

 The pressure at any point on the ribbon due to a velocity ^max^"^' of the 

 ribbon is 



P='f' «...«-' ff-^-*' 9.20 



47r t/./ ai 



where ai = radius vector having the shortest air distance from the point 

 1 to the surface element dS. To compute the total force, the above in- 

 tegration must be performed and then the resulting pressure integrated 

 over the surface of the ribbon. 

 The total force is 



where dS' = surface element at 1. 

 The acoustic impedance is 



ZaA = VaA +JXAA = — JTt 9.22 



The ribbon is spaced from the pole pieces of the magnetic structure to 

 allow freedom of motion. This slit or aperture Tas and Mas gives rise to 

 an impedance (see Sec. 5.4). 



zas ^ rAs + Jo^Mas 9.23 



where Tas = acoustic resistance of the slit, in acoustic ohms, and 

 Mas = inertance of the slit, in grams per (centimeter).^ 

 The back of the ribbon is terminated in an acoustic resistance in the form 

 of a finite pipe damped with tufts of felt. The equivalent circuit of the 



