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Preprint / Version 9

About 3D Cavity Resonance

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DOI:

https://doi.org/10.31224/7076

Keywords:

cavity resonance, three-dimention, Rossiter fomula, Rossiter's equation, cavity noise, cavity sound, whistle noise, whistling noise, whistle sound, whistling sound, Powell's equation

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, we limited our study to the three-dimensional case and clarified the physical phenomena that arise by solving a set of partial differential equations that explain the phenomenon. As a result, we were able to determine the frequency at which resonance increases, taking into account three-dimensional space. Finally, we were able to confirm the conditions under which resonance increases through numerical calculations.

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Posted

2026-05-15 — Updated on 2026-07-20

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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

In the nomenclature, I have added $f_x$, $f_{xr}$, and $\alpha$, and included the dimensions for $\alpha$ and $\beta$. I have revised Equation (2), removed the boundary condition $p=0$ in Section 2.4, modified Equations (15) through (22), updated the titles of Sections 3.3 and 3.4, and revised Equations (29) through (32). Concurrently, I have updated Table 1 and Figures 2 through 7 in Chapter 4, and revised the text of Chapter 4 accordingly. I sincerely apologize for the inconvenience of asking you to review the manuscript again, and I would greatly appreciate it if you could examine these changes.