Computing the Sound of the Sea in a Seashell

TL;DR

This paper presents a constructive, universal algorithm for computing the resonances of any Helmholtz resonator with a bounded, smooth boundary, advancing the ability to analyze acoustic properties of complex shapes.

Contribution

It introduces a positive, constructive approximation procedure for resonances of Helmholtz resonators with smooth, bounded chambers, regardless of shape.

Findings

Provides a universal algorithm for resonance computation.

Requires only boundary characteristic function evaluations.

Works for any bounded, smooth-chamber resonator.

Abstract

The question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $\mathcal C^2$. The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.