Thermal boundary layer effects on the acoustical impedance of enclosures and consequences for acoustical sensing devices

Abstract

Expressions are derived for the acoustical impedance of a rectangular enclosure and of a finite annular cylindrical enclosure. The derivation is valid throughout the frequency range in which all dimensions of the enclosure are much less than the wavelength. The results are valid throughout the range from adiabatic to isothermal conditions in the enclosure. The effect is equivalent to placing an additional, frequency-dependent complex impedance in parallel with the adiabatic compliance. As the thermal boundary layer grows to fill the cavity, the reactive part of the impedance varies smoothly from the adiabatic value to the isothermal value. In some microphones, this change in cavity stiffness is sufficient to modify the sensitivity. The resistive part of the additional cavity impedance varies as the inverse square root of frequency at high frequencies where the boundary layer has not grown to fill the enclosure. The thermal modification gives rise to a thermal noise whose spectral density varies asymptotically as l/f(3/2) above the isothermal transition frequency.