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Derivation of Rossiter Formula in Cavity Resonance

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DOI:

https://doi.org/10.31224/7028

Keywords:

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

Abstract

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.

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Posted

2026-05-10 — Updated on 2026-05-11

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Copyright (c) 2026 Takuya Yabu

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Version justification

I mistake Equation (2), so I correct this. I also correct from Equation (5) to Equation (15), and Equation (21). I calucurate again and change Table 1, Fig.2 and Fig.3. I sincerely apologize for the inconvenience caused by having to go through the review process again and I appreciate your cooperation.