### 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 f32 above the isothermal transition frequency.

Original language | English (US) |
---|---|

Pages (from-to) | 1364-1370 |

Number of pages | 7 |

Journal | Journal of the Acoustical Society of America |

Volume | 123 |

Issue number | 3 |

DOIs | |

State | Published - Mar 19 2008 |

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### All Science Journal Classification (ASJC) codes

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics

### Cite this

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*Journal of the Acoustical Society of America*, vol. 123, no. 3, pp. 1364-1370. https://doi.org/10.1121/1.2832314

**Thermal boundary layer effects on the acoustical impedance of enclosures and consequences for acoustical sensing devices.** / Thompson, Stephen C.; LoPresti, Janice L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Thermal boundary layer effects on the acoustical impedance of enclosures and consequences for acoustical sensing devices

AU - Thompson, Stephen C.

AU - LoPresti, Janice L.

PY - 2008/3/19

Y1 - 2008/3/19

N2 - 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 f32 above the isothermal transition frequency.

AB - 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 f32 above the isothermal transition frequency.

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U2 - 10.1121/1.2832314

DO - 10.1121/1.2832314

M3 - Article

C2 - 18345825

AN - SCOPUS:40749134047

VL - 123

SP - 1364

EP - 1370

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 3

ER -