422 BELL SYSTEM TECHNICAL JOURNAL 



similar problem can be found in I. B. Crandall's "Theory of Vibrating 

 System and Sound" and therefore will not be considered here.* 



In order to evaluate the constants of the narrow tube used to increase 

 the low-end response we must investigate the discriminant kr. If \kr\ 

 lies between the limits + 1 and + 10 then the mechanical impedance 

 for a tube of length / and area At ^^ given by 



^ _ nk^Arl * 



1 _ 1 llitl 

 kr Jo {kr) _ 



where k = a / , « = a / — . ^ the radius of tube and p is the density 



of air. Ji (kr) and Jo {kr) are Bessel's functions of first and zero order 

 respectively with complex argument. Substituting for the values of k 

 and expressing Jo and Ji in terms of ber and bei functions we have ^ 



Z = ^ 



If values of this impedance are plotted it will be found that the re- 

 sistance and mass components vary again with frequency. It is there- 

 fore necessary to use a new value for rr and nir for each frequency when 

 the response of the network is calculated. 



APPENDIX B 



The "pressure calibration" of the miniature condenser microphone is 

 measured on the thermophone, but the field calibration must also be 

 determined very carefully. The field correction to be applied to this 

 thermophone calibration is made up of two factors, (1) the diffraction 

 effect of the microphone and (2) the resonance of the small cavity in 

 front of the diaphragm. The latter has been calculated carefully and 

 checked experimentally (Fig. 11). 



The condenser microphone itself was used to determine its own 

 diffraction effect. This is possible because of the verified theoretical 

 law giving the diffraction effect to be a function of the product of the 

 diameter and frequency. For example, the diffraction effect that 

 occurs at 2,000 cycles for a 6-inch disc will occur for a 1-inch disc at 

 12,000 cycles. Since the diffraction effect of the small condenser 

 microphone is essentially that of a cylinder of the same diameter, it was 

 only necessary to measure the effect of a large cylinder in a frequency 

 * Reference 8, p. 237. 



