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 2026-08-03
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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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I apologize. I had intended to add the keyword regarding the Helmholtz-type cavity—which is discussed in Chapter 5 of the preprint—during the last round, but although I had entered the metadata, I failed to save the changes. If the addition of that keyword was previously rejected after your review, I am very sorry to ask you to review it again. I apologize for the repeated revisions and for the trouble this causes you, and I would appreciate it if you could review the submission.
