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arXiv · 2303.12750

A Transfer Matrix for the Input Impedance of weakly tapered Cones as of Wind Instruments

Timo Grothe·Johannes Baumgart·Cornelis J. Nederveen
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Abstract

A formula for the local acoustical admittance in a conical waveguide with viscous and thermal losses given by Nederveen [(1969) Acoustical Aspects of Woodwind Instruments (Frits Knuf, Amsterdam)] is rewritten as an impedance transmission matrix. Based on a self-consistent approximation for the cone, it differs from other one-dimensional transmission matrices used in musical acoustics, which implicitly include the loss model of a cylinder. The resonance frequencies of air columns calculated with this transmission matrix are in better agreement with more comprehensive models. Even for long cones with a slight taper, there is no need to discretize along the axis.

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Timo Grothe, Johannes Baumgart, Cornelis J. Nederveen. 2023-03-22. A Transfer Matrix for the Input Impedance of weakly tapered Cones as of Wind Instruments. https://doi.org/10.1121/10.0020270

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