Approximation of the acoustic radiation impedance of a cylindrical pipe

TL;DR

This paper presents new approximation formulas for the acoustic radiation impedance of cylindrical pipes, ensuring physical principles like causality and symmetry, with improved accuracy for frequency-domain applications.

Contribution

It introduces novel approximation formulas for radiation impedance that satisfy physical principles and are derived from analytical and numerical fitting to reference data.

Findings

Formulas meet hermitian symmetry and causality principles

Non-causal expression offers higher accuracy for frequency-domain use

Approximations are validated against established reference results

Abstract

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.