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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 516982, 8 pages
http://dx.doi.org/10.1155/2015/516982
Research Article

Sound Propagation in a Duct with Wall Corrugations Having Square-Wave Profiles

Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 14 April 2015; Revised 17 June 2015; Accepted 18 June 2015

Academic Editor: Hakim Naceur

Copyright © 2015 Muhammad A. Hawwa. 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.

Abstract

Acoustic wave propagation in ducts with rigid walls having square-wave wall corrugations is considered in the context of a perturbation formulation. Using the ratio of wall corrugation amplitude to the mean duct half width, a small parameter is defined and a two levels of approximations are obtained. The first-order solution produces an analytical description of the pressure field inside the duct. The second-order solution yields an analytical estimate of the phase speed of waves transmitting through the duct. The effect of wall corrugation density on acoustic impedance and wave speeds is highlighted. The analysis reveals that waves propagating in a duct with square-wave wall corrugation are slower than waves propagating in a duct with sinusoidal wave corrugation having the same corrugation wavelength.