THERMAL NOISE IN MICROPHONES 225 



the sound wave is /mo and the mechanical impedance due to the electrical 

 circuit is Zme- The effect of the electrical circuit upon the vibrating systems 

 of other types of transducers, namely, electromagnetic, condenser and 

 piezoelectric can be obtained from Chapter VI. 



9.11. Thermal Noise in Microphones. — The smallest voltage that can 

 be measured at the terminals of a resistance is limited by the voltage due to 

 thermal agitation ^^'^^ of the electrons. The lower limit of sound intensi- 

 ties which may be measured with a dynamic, ribbon, inductor or magnetic 

 microphone is the intensity at which the signal voltage is just equal to the 

 voltage of thermal agitation. 



The voltage, in volts, of thermal agitation is 



e = V^KT{f, - f,)rE X 10"^ , 9.75 



where K = Boltzmann constant = 1.37 X 10~^^ ergs per degree, 



T — absolute temperature, for 20° Centigrade T = 293, 

 Ji — J\ ^ width of the frequency band, in cycles per second, and 

 Ye = resistance of the element (coil, ribbon or conductor), in 

 ohms. 

 For a microphone having a resistance of 250 ohms and a frequency band 

 of 15,000 cycles the thermal voltage is 2.5 X 10~'^ volts. The voltage de- 

 livered by a sensitive velocity or dynamic microphone at this impedance is 

 3.0 X 10~* volts per dyne per square centimeter. The smallest pressure 

 that can be measured with this microphone is 0.8 X 10~^ dynes per square 

 centimeter. Referring to Fig. 13.1, this is about 20 db above the ear 

 threshold of hearing at the most sensitive region. 



Johnson, J. B., Phys. Rev., Vol. 32, No. 1, p. 97, 1928. 

 Nyquist, H., Phys. Rev., Vol. 32, No. 1, p. 110, 1928. 



