CALIBRATION OF MICROPHONES 249 



The determination of the ratio elp is carried out in the same manner as 

 the pistonphone. 



2. Field Response. — The field or free wave response frequency char- 

 acteristic of a microphone is the ratio ejp as a function of the frequency 

 where e is the open circuit voltage generated by the microphone in volts 

 and p is the sound pressure in dynes per square centimeter in a free pro- 

 gressive wave prior to the introduction of the microphone. 



At the present time the Rayleigh s-io-i^'i^ ^-y^^ provides the only satis- 

 factory method for obtaining the field response frequency characteristic of 

 a microphone. Rayleigh observed that when a disk was suspended by a 

 light fiber it would tend to turn at right angles to the impinging sound 

 wave. Koenig ^^ developed the formula for the turning moment of the 

 disk as 



4 

 M= -p^Vsm29 11.4 



3 



where M — turning moment acting upon the disk, in dynes per centimeter, 

 p = density of the fluid, in grams per cubic centimeter, 

 a = radius of the disk, in centimeters, 

 Q = angle between the normal to the disk and the direction of 



propagation of the sound wave, in degrees, and 

 u = particle velocity of the sound wave, root-mean square, in 

 centimeters, per second. 

 When a sound wave falls upon the disk the angular deflection will be 



where S = moment of torsion of the suspension, in dynes per centimeter. 

 The moment of torsion of the suspension is given by 



■ ' ' '^ = ^[4X^ + (logeT)^] 11.6 



where T = periodic time of the suspended disk, in seconds, 

 / = moment of inertia of the disk. 



9 Rayleigh, Phil. Mag., Vol. 14, p. 186, 1882. 

 10 Ballantine, Phys. Rev., Vol. 32, No. 6, p. 988, 1920. 

 " Olson and Goldman, Electronics, p. 106, Sept., 1931. 



12 Sivian, L. J., Bell Syst. Tech. Jour., Vol. 10, No. 1, p. 96, 1931. 



13 Koenig, Ann d., Physik, Vol. 43, p. 43, 1891. 



