Derivation of Rossiter Formula in Cavity Resonance
DOI:
https://doi.org/10.31224/7028Keywords:
cavity sound, cavity noise, cavity resonance, cavity resonance frequency, Rossiter fomula, Rossiter's equation, Green's function, vorticity, Powell's equation, Powell equation, whistle noise, whistle sound, whistling sound, whistling noise, Rossiter's formula, vortex, Helmholtz-type cavity, Helmholtz resonance, Helmholtz resonator, HelmholtzAbstract
Research on automobile whistling and suction sounds has been conducted in the past. For cavity resonance, a type of whistling sound, the cavity resonance frequency has been determined using Rossiter's empirical equation. Therefore, limiting the study to the one-dimensional case, Rossiter formula was derived by solving a system of three differential equations. In addition, equations for the stability conditions of cavity resonance and the sound pressure were derived. Finally, the results were verified through numerical calculations, and reasonable conclusions were obtained.
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Posted
2026-05-10 — Updated on 2026-08-31
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Copyright (c) 2026 Takuya Yabu
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Starting from Equation (68) in Chapter 5, I have added further mathematical derivations and discussion, specifically covering the two-dimensional and three-dimensional cases. No other changes have been made. I sincerely apologize for the inconvenience of asking you to review the material again, and I would appreciate it if you could review the changes.
