Approximation of the acoustic radiation impedance of a cylindrical pipe

Details Approximation of the acoustic radiation impedance of a cylindrical pipe Approximation of the acoustic radiation impedance of a cylindrical pipe

2008-11-21

arxiv.org/abs/0811.3625v1

J. Sound Vib. 322(1-2), 255-263, 2009

Physics

Classical Physics

Journal of Sound and Vibration (2008) accepted

Scientific paper

10.1016/j.jsv.2008.11.008

Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and mathematical principles are met, like hermitian symmetry for the reflection coefficient (identical behaviour of positive and negative frequencies) and causality for the impulse response. A non causal but more accurate expression is also proposed that is suitable for frequency-domain applications. The formulae are obtained by analytical and numerical fitting to reference results from Levine & Schwinger for the unflanged case and extracted from the radiation impedance matrix given by Zorumski for the infinite flanged case.

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