Thermal noise limits of microphones

The fundamental limit to sensitivity of acoustic tranducers is material to our understanding of nature, has application to microphone technology, and provides a standard with which to assess the evolution of animal and human hearing. The 1933 estimate of Sivian and White depended on applying a Johnson-Nyquist analogue to the acoustic radiation resistance of a piston in an infinite baffle, although actual microphones are not normally baffled. Their result differs by a factor two in power from that derived by Hunt from equipartition of energy. Olson seems to have been the first to observe fundamental acoustic thermal noise in a microphone and interpreted his result as agreeing with the prediction of Hunt. A critical examination shows that the choice of an appropriate method turns on postulating elementary receptors responsive either to the changes in pressure caused by the acoustic wave or to the corresponding velocity changes in the fluid. When this is done in a physically correct way, concordant estimates are obtained by alternative routes, and it proves possible to correct and reconcile the older calculations. Limits are found both for pressure-sensitive and for velocity-sensitive microphones. If equipartition is taken as the logical premise, the analysis may be interpreted as a direct proof of a Johnson-Nyquist formula, in both Thevenin equivalents, for the thermal noise associated with acoustic radiation resistance. Some matters of the history of the subject are discussed, but not all the puzzles these present have been resolved.