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Fundamental Investigation into the directivity function of multi-mode sound fields from ducts

Fundamental Investigation into the directivity function of multi-mode sound fields from ducts
Fundamental Investigation into the directivity function of multi-mode sound fields from ducts
Multi-mode sound radiation from hard-walled semi-infinite ducts with uniform subsonic flow is investigated theoretically. An analytic expression, valid in the high frequency limit, is derived for the multi-mode directivity function in the forward arc of the duct for a general family of mode distribution function. The multi-mode directivity depends on the amplitude of each mode, and on the single mode directivity functions. The amplitude of each mode is expressed as a function of cut-off ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles and for equal power per mode. The single mode directivity functions are obtained analytically by applying a Lorentz Transformation to the zero flow solution. The analytic formula for the multi-mode directivity with flow is derived by assuming total transmission of power at the open-end of the duct. The high frequency formula is compared to exact numerical solutions from the Wiener Hopf technique and for a flanged duct. The agreement is shown to be excellent.
duct acoustics, directivity function, directivity with flow, multi-mode
Sinayoko, Samuel
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Sinayoko, Samuel
0e4346ca-1a26-481d-8241-f83730f6b0e4
Joseph, Phillip
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Mcalpine, Alan
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Sinayoko, Samuel (2008) Fundamental Investigation into the directivity function of multi-mode sound fields from ducts. University of Southampton, Institute of Sound and Vibration Research, Masters Thesis, 119pp.

Record type: Thesis (Masters)

Abstract

Multi-mode sound radiation from hard-walled semi-infinite ducts with uniform subsonic flow is investigated theoretically. An analytic expression, valid in the high frequency limit, is derived for the multi-mode directivity function in the forward arc of the duct for a general family of mode distribution function. The multi-mode directivity depends on the amplitude of each mode, and on the single mode directivity functions. The amplitude of each mode is expressed as a function of cut-off ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles and for equal power per mode. The single mode directivity functions are obtained analytically by applying a Lorentz Transformation to the zero flow solution. The analytic formula for the multi-mode directivity with flow is derived by assuming total transmission of power at the open-end of the duct. The high frequency formula is compared to exact numerical solutions from the Wiener Hopf technique and for a flanged duct. The agreement is shown to be excellent.

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More information

Published date: April 2008
Keywords: duct acoustics, directivity function, directivity with flow, multi-mode
Organisations: University of Southampton

Identifiers

Local EPrints ID: 66672
URI: https://eprints.soton.ac.uk/id/eprint/66672
PURE UUID: 295f09cf-39e7-4dac-9d19-230f136481e8
ORCID for Alan Mcalpine: ORCID iD orcid.org/0000-0003-4189-2167

Catalogue record

Date deposited: 08 Jul 2009
Last modified: 28 Jun 2018 00:34

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