Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct

Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct

Acoustic wave propagation in hard-walled ducts is of interest in many fields including vehicle design, musical instruments acoustics, and architectural and environmental noise-control. For the case of small sinusoidal perturbation of the cross-section, it is possible to derive simple though approxim...

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Main Authors: Silvio Del Giudice, Giancarlo Bernasconi
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/267291
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spelling doaj-c87082fb8eba4052a5aa24973b3682332020-11-24T21:28:01ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/267291267291Acoustic Response of a Sinusoidally Perturbed Hard-Walled DuctSilvio Del Giudice0Giancarlo Bernasconi1Department of Electronics, Information and Bioengineering, Polytechnic University of Milan, Via Ponzio 34/5, 20133 Milan, ItalyDepartment of Electronics, Information and Bioengineering, Polytechnic University of Milan, Via Ponzio 34/5, 20133 Milan, ItalyAcoustic wave propagation in hard-walled ducts is of interest in many fields including vehicle design, musical instruments acoustics, and architectural and environmental noise-control. For the case of small sinusoidal perturbation of the cross-section, it is possible to derive simple though approximate analytical formulas of its plane wave acoustic reflection and transmission spectral response that resembles the optical situation of uniform Bragg gratings. The proof is given here, starting from the “horn equation” and then exploiting the coupled-modes theory. Examples of the results obtained with these analytical formulas are shown for some sinusoidally perturbed ducts and compared to results obtained through a numerical method, revealing a very good agreement.http://dx.doi.org/10.1155/2013/267291
collection DOAJ
language English
format Article
sources DOAJ
author Silvio Del Giudice
Giancarlo Bernasconi
spellingShingle Silvio Del Giudice
Giancarlo Bernasconi
Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
Mathematical Problems in Engineering
author_facet Silvio Del Giudice
Giancarlo Bernasconi
author_sort Silvio Del Giudice
title Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
title_short Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
title_full Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
title_fullStr Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
title_full_unstemmed Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct
title_sort acoustic response of a sinusoidally perturbed hard-walled duct
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description Acoustic wave propagation in hard-walled ducts is of interest in many fields including vehicle design, musical instruments acoustics, and architectural and environmental noise-control. For the case of small sinusoidal perturbation of the cross-section, it is possible to derive simple though approximate analytical formulas of its plane wave acoustic reflection and transmission spectral response that resembles the optical situation of uniform Bragg gratings. The proof is given here, starting from the “horn equation” and then exploiting the coupled-modes theory. Examples of the results obtained with these analytical formulas are shown for some sinusoidally perturbed ducts and compared to results obtained through a numerical method, revealing a very good agreement.
url http://dx.doi.org/10.1155/2013/267291
work_keys_str_mv AT silviodelgiudice acousticresponseofasinusoidallyperturbedhardwalledduct
AT giancarlobernasconi acousticresponseofasinusoidallyperturbedhardwalledduct
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