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A transfer matrix for the input impedance of weakly tapered, dissipative cones as of wind instruments (L)
Timo Grothe1, Johannes Baumgart2, Cornelis J Nederveen3
1Erich-Thienhaus-Institut, Hochschule für Musik Detmold, Detmold, Germany.
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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