114 BELL SYSTEM TECHNICAL JOURNAL 



1 



R' = R- 



J _ ^ . g ''^i gh 



when 



V5i' log, 2 



6' A + g S (//+g)2 



Si = area of perforation, 5 = total area. 



II 



An upper limit on the above correction is given by: 



1 



R' = R' 



-f 



The R' actually used was the mean of the above two values. The 

 value of R obtained with the screen electrode is shifted up or down to 

 make it coincide with R' given by the perforated electrode, at 100 c.p.s. 



Appendix V 



For frequencies below about 5,000 c.p.s. the difference between the 

 pressure and normal field calibrations is mainly due to two effects: (1) 

 reflection from the transmitter face and from the diaphragm; (2) air 

 resonance caused by the recess in front of the diaphragm. 



Consider Fig. \A. Assume that in the circular aperture PQ, the 

 air particles are all moving in phase and parallel to AP. Then we may 

 treat PQ as a rigid massless piston in the wall RS. If RSjX is large 

 enough, the pressure on PQ held motionless will be double that of the 

 field pressure. The motional impedance of PQ imposed by the air 

 above P(3 is given by Rayleigh (Sound, vol. II, §302). Per unit area it is 



where 



Z] = pC{a + ib), 



a = l-^^: b=-^K,(2kR): k = 'f: 2R = PQ. 



Let Rp/Rp represent the ratio of " field " to " pressure " calibration. 

 Using the expression for plane wave propagation in a tube (e.g. 

 Crandall, Theory of Vibrating Systems and Sound, p. 99) we have at 

 once: 



Rf _ . 1 



„ — Z • ■ -7-. , 



^ [cos kl + i(a + ib) ■ sin kQ + ^Lia + ib) cos kl + i sin ^/] 



where Za is the equivalent impedance per unit area of the transmitter 

 diaphragm, and / = AP. On substituting numerical values, Rp/Rp is 



