Approximation formulae for the acoustic radiation impedance of a cylindrical pipe

Fabrice Silva (1) , Philippe Guillemain (1) , Jean Kergomard (1) , Bastien Mallaroni (1) , Andrew N. Norris (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 Mechanical & Aerospace Engineering

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 Zorum-ski for the infinite flanged case.

Mots clés: cylindrical pipe; Acoustic radiative impedance

Domaines: Acoustique [physics.class-ph]

Fabrice Silva, Philippe Guillemain, Jean Kergomard, Bastien Mallaroni, Andrew N. Norris. Approximation formulae for the acoustic radiation impedance of a cylindrical pipe. Journal of Sound and Vibration, 2009, 322 (1-2), pp.255-263. ⟨10.1016/j.jsv.2008.11.008⟩. ⟨hal-00226659⟩