A transfer matrix for the input impedance of weakly tapered, dissipative cones as of wind instruments (L)

Timo Grothe; Johannes Baumgart; Cornelis J Nederveen

doi:10.1121/10.0020270

A transfer matrix for the input impedance of weakly tapered, dissipative cones as of wind instruments (L)

J Acoust Soc Am. 2023 Jul 1;154(1):463-466. doi: 10.1121/10.0020270.

Authors

Timo Grothe¹, Johannes Baumgart², Cornelis J Nederveen³

Affiliations

¹ Erich-Thienhaus-Institut, Hochschule für Musik Detmold, Detmold, Germany.
² Dresden, Germany.
³ Pijnacker, The Netherlands.

PMID: 37489912
DOI: 10.1121/10.0020270

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.