Optimal lower bound of the resonance widths for a Helmhotz tube-shaped resonator

TL;DR

This paper provides an optimal lower bound for the resonance widths in a simple 2D Helmholtz tube-shaped resonator, advancing understanding of resonance behavior in such structures.

Contribution

It introduces a precise analysis of the transition zone in a 2D Helmholtz resonator to establish an optimal lower bound on resonance widths.

Findings

Derived an optimal lower bound for resonance widths

Analyzed the transition zone where oscillations begin

Enhanced understanding of resonance behavior in tube-shaped resonators

Abstract

The study of the resonances of the Helmholtz resonator has been broadly described in previous works. Here, for a simple tube-shaped two dimensional resonator, we can perform a careful analysis of the transition zone where oscillations start to appear. In that way, we obtain an optimal lower bound of the width of the resonances.