Characterization of condenser microphones under different environmental conditions for accurate speed of sound measurements with acoustic resonators

Condenser microphones are more commonly used and have been extensively modeled and characterized in air at ambient temperature and static pressure. However, several applications of interest for metrology and physical acoustics require to use these transducers in significantly different environmental conditions. Particularly, the extremely accurate determination of the speed of sound in monoatomic gases, which is pursued for a determination of the Boltzmann constant $k$ by an acoustic method, entails the use of condenser microphones mounted within a spherical cavity, over a wide range of static pressures, at the temperature of the triple point of water (273.16 K). To further increase the accuracy achievable in this application, the microphone frequency response and its acoustic input impedance need to be precisely determined over the same static pressure and temperature range. Few previous works examined the influence of static pressure, temperature, and gas composition on the microphone’s sensitivity. In this work, the results of relative calibrations of 1/4 in. condenser microphones obtained using an electrostatic actuator technique are presented. The calibrations are performed in pure helium and argon gas at temperatures near 273 K and in the pressure range between 10 and 600 kPa. These experimental results are compared with the predictions of a realistic model available in the literature, finding a remarkable good agreement. The model provides an estimate of the acoustic impedance of 1/4 in. condenser microphones as a function of frequency and static pressure and is used to calculate the corresponding frequency perturbations induced on the normal modes of a spherical cavity when this is filled with helium or argon gas.