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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 267291, 6 pages
Research Article

Acoustic Response of a Sinusoidally Perturbed Hard-Walled Duct

Department of Electronics, Information and Bioengineering, Polytechnic University of Milan, Via Ponzio 34/5, 20133 Milan, Italy

Received 2 August 2013; Revised 18 October 2013; Accepted 19 October 2013

Academic Editor: Carlo Cattani

Copyright © 2013 Silvio Del Giudice and Giancarlo Bernasconi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.