Electroacoustics

Electroacoustics studies conversion between electrical signals and sound, together with the measurement and control of that conversion. A microphone produces an electrical response to an acoustic input; a loudspeaker performs the reverse conversion. Their frequency responses, loading and directional behavior matter as much as a single sensitivity number.

For a receiving microphone, one can define the complex frequency response $M_p(f)=V(f)/p(f)$ in volts per pascal, with the electrical termination and acoustic conditions specified. Equal outputs do not imply equal incident sound pressures if the two microphones have different sensitivities. Calibration supplies the link between the electrical recording and an acoustic measurement.

A motivating primary method is microphone reciprocity calibration. In the NIST system reported by Randall P. Wagner and collaborators, three laboratory microphones are measured in pairs using acoustic coupling cavities. One microphone transmits while another receives; known coupling properties and reciprocity relations allow the individual pressure sensitivities to be determined without starting from a separately calibrated reference microphone. Comparing results with different cavity lengths tests the acoustic corrections and associated measurement uncertainty.^[ref]

Microphone reciprocity calibration obtains absolute pressure sensitivities by measuring pairs of reciprocal microphones, rather than starting with a microphone of already known sensitivity. One microphone transmits into a known acoustic coupler while another receives. Reciprocity relates transmitting and receiving behavior, so the electrical transfer measurement constrains the product of their receiving sensitivities.

Schematically, after correcting each pair measurement for its coupling and electrical factors, write $P_{12}=M_1{M}_2$, $P_{13}=M_1{M}_3$ and $P_{23}=M_2{M}_3$. Then $M_1^2=P_{12}{P}_{13}/P_{23}$, with analogous expressions for the others. The actual frequency-dependent calibration includes phase conventions, acoustic losses, diaphragm impedance and cavity geometry.

The NIST apparatus uses three laboratory-standard microphones in opposed ports of cylindrical air-filled couplers. The reported long and short coupler lengths are 9.4 mm and 4.7 mm; a sinusoidal source and electrical measurements determine pair transfer responses while temperature and static pressure are recorded. Comparing results from both couplers checks corrections that would be invisible in a single geometry.^[ref]