Abstract
The influence of the presence and magnitude of asymmetrical undercutting of the toneholes of woodwind instruments on the change in their effective radius and the corresponding shift of the eigenfrequencies of the air duct is considered. Within the framework of the electro-acoustic analogy, a tonehole with an asymmetrical undercutting along the axis of the main bore is presented as a cascade connection of two holes with different radii (undercutting and not undercutting parts of the hole), and with a sideway undercutting-in the form of a parallel connection. Formulas for numerical calculations are given that make it possible to determine the effective radius of such holes for the open state in the low-frequency approximation. Based on the obtained dependencies, using the transmission-matrix method, the eigenfrequencies of an air duct with one hole were calculated and compared with the results of computer modeling in the COMSOL Multiphysics 5.6 program. It is shown that increasing the degree and angle of undercutting leads to an increase in the effective radius, a displacement of the "center of gravity" of the sound hole along the main bore axis, and has effect on the shift of resonant frequency.
Published Version
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