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
0e4346ca-1a26-481d-8241-f83730f6b0e4
April 2008
Sinayoko, Samuel
0e4346ca-1a26-481d-8241-f83730f6b0e4
Joseph, P.F.
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McAlpine, A.
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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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Published date: April 2008
Keywords:
duct acoustics, directivity function, directivity with flow, multi-mode
Organisations:
University of Southampton
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Local EPrints ID: 66672
URI: http://eprints.soton.ac.uk/id/eprint/66672
PURE UUID: 295f09cf-39e7-4dac-9d19-230f136481e8
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Date deposited: 08 Jul 2009
Last modified: 14 Mar 2024 02:42
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Author:
Samuel Sinayoko
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