Interaction of reed and acoustic resonator in clarinetlike systems

TL;DR

This paper investigates the mechanisms behind sound emergence in clarinet-like instruments by analyzing reed-bore interactions, modeling various factors influencing oscillation thresholds, frequencies, and bifurcation types to better understand musical performance dynamics.

Contribution

It introduces advanced models of reed-bore coupling including viscothermal losses and vena contracta effects, and provides analytical approximations near oscillation thresholds to clarify bifurcation behavior.

Findings

Reed damping influences register selection.

Reed motion-induced flow affects oscillation frequencies.

Analytical solutions clarify bifurcation conditions.

Abstract

Sound emergence in clarinetlike instruments is investigated in terms of instability of the static regime. Various models of reed-bore coupling are considered, from the pioneering work of Wilson and Beavers ["Operating modes of the clarinet", J. Acoust. Soc. Am. 56, 653--658 (1974)] to more recent modeling including viscothermal bore losses and vena contracta at the reed inlet. The pressure threshold above which these models may oscillate as well as the frequency of oscillation at threshold are calculated. In addition to Wilson and Beavers' previous conclusions concerning the role of the reed damping in the selection of the register the instrument will play on, the influence of the reed motion induced flow is also emphasized, particularly its effect on playing frequencies, contributing to reduce discrepancies between Wilson and Beavers' experimental results and theory, despite discrepancies still remain concerning the pressure threshold. Finally, analytical approximations of the oscillating solution based on Fourier series expansion are obtained in the vicinity of the threshold of oscillation. This allows to emphasize the conditions which determine the nature of the bifurcation (direct or inverse) through which the note may emerge, with therefore important consequences on the musical playing performances.