External Tonehole Interactions in Woodwind Instruments

TL;DR

This paper introduces a new method, TMMI, to account for external tonehole interactions in woodwind instruments, improving the accuracy of impedance calculations over traditional TMM by considering radiated sound effects.

Contribution

The paper proposes the Transfer-Matrix Method with external Interaction (TMMI), enhancing traditional models by including external tonehole effects and validating it against FEM and experimental data.

Findings

External interactions increase radiated energy.

They slightly lower lower resonance frequencies.

They significantly alter response near and above cutoff frequency.

Abstract

The classical Transfer-Matrix Method (TMM) is often used to calculate the input impedance of woodwind instruments. However, the TMM ignores the possible influence of the radiated sound from toneholes on other open holes. In this paper a method is proposed to account for external tonehole interactions. We describe the Transfer-Matrix Method with external Interaction (TMMI) and then compare results using this approach with the Finite Element Method (FEM) and TMM, as well as with experimental data. It is found that the external tonehole interactions increase the amount of radiated energy, reduce slightly the lower resonance frequencies, and modify significantly the response near and above the tonehole lattice cutoff frequency. In an appendix, a simple perturbation of the TMM to account for external interactions is investigated, though it is found to be inadequate at low frequencies and for holes spaced far apart.