Abstract
In this paper, we have made Wiener-Hopf analysis of an acoustic plane wave by a semi-infinite hard duct that is placed symmetrically inside an infinite soft/hard duct. The method of solution is integral transform and Wiener-Hopf technique. The imposition of boundary conditions result in a 2 × 2 matrix Wiener-Hopf equation associated with a new canonical scattering problem which is solved by using the pole removal technique. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. These systems of linear algebraic equations are solved numerically. The graphs are plotted for sundry parameters of interest. Kernel functions are also factorized.
Similar content being viewed by others
References
Hassan M., Rawlins A.D.: Radiation from a two dimensional duct. Can. J. Phys. 1, 375–384 (1997)
Büyükaksoy A., Polat B.: A bifurcated waveguide problem. ARI 51, 196–202 (1999)
Snakowska A.: Diffraction of sound waves at the opening of a soft cylindrical duct. Eur. Phy. J. Spec. Top. 154, 201–205 (2008)
Ayub M., Tiwana M.H., Mann A.B.: Propagation of sound in a duct with mean flow. Commun. Nonlinear Sci. Numer. Simul. 14, 3578–3590 (2009)
Jones D.S.: Diffraction by three semi-infinite planes. Proc. R. Soc. Lond. A 404, 299–321 (1986)
Asghar S., Ayub M., Ahmad B.: Point source diffraction by three half planes in a moving fluid. Wave Motion 15, 201–220 (1992)
Polat B.: Plane wave diffraction by a semi-infinite soft/hard parallel-plate waveguide. Can. J. Phys. 76, 771–784 (1998)
Rawlins A.D.: Two waveguide trifurcation problems. Math. Proc. Camb. Phil. Soc. 121, 555–573 (1997)
Idemen M.: A new method to obtain exact solutions of vector Wiener-Hopf equations. ZAMM Z. Angew. Math. Mech. 59, 656–658 (1979)
Büyükaksoy A., Topsakal E., Idemen M.: Plane wave diffraction by a pair of parallel soft and hard overlapping half-planes. Wave Motion 20(3), 273–282 (1994)
Abrahams I.D.: Scattering of sound by two parallel semi-infinite screens. Wave Motion 9, 289–300 (1987)
Büyükaksoy, A., Tayyar, I.H., Uzgören, G.: Influence of the junction of perfectly conducting and impedance parallel plate semi-infinite waveguides to the dominant mode propagation, First European Conference on Antennas and Propagation, Eu CAP Nice France (2006)
Tayyar I.H., Büyükaksoy A., Isikyer A.: A Wiener-Hopf analysis of the parallel plate waveguide with finite length impedance loading. Radio Sci. 43, RS5005 (2008)
Ayub M., Tiwana M.H., Mann A.B.: Influence of acoustic dominant mode propagation in a trifurcated lined duct with different impedances. Phys. Scr. 81, 035402 (2010)
Rawlins A.D.: Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface. Proc. R. Soc. Lond. A 36, 65–91 (1978)
Noble B.: Methods based on the Wiener-Hopf technique, 2nd edn. Chelsea, New York (1988)
Morse P.M., Feshbach H.: Methods of theoretical physics, vol. 12. Mc Graw-Hill, New York (1953)
Jones D.S.: The theory of electromagnetism. Pergamon, London (1964)
Titchmarsh E.C.: Theory of fourier integrals. Oxford University Press, Oxford (1937)
Mittra R., Lee S.W.: Analytical techniques in the theory of guided waves. McMillan, New York (1971)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ayub, M., Tiwana, M.H. & Mann, A.B. Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide. Arch Appl Mech 81, 701–713 (2011). https://doi.org/10.1007/s00419-010-0444-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-010-0444-5