Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide

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.

Scattering analysis of a flexible trifurcated lined waveguide structure with step-discontinuities

“…Mathematically, the corresponding governing problems consist of Helmholtz or Laplace equations along with suitable boundary conditions. A variety of these problems has been solved using the Wiener-Hopf technique; see, for instance, [6][7][8]. On the other hand, Lawrie and Abrahams [9] considered membrane-bounded geometrical designs and accordingly considered problems with high-order boundary conditions.…”

Diffraction of EM-wave by a slit of finite width with Dirichlet conditions in cold plasma

“…Also, a few years back, the scattering problem of plane waves by a discontinuous edge contour is studied with the three-dimensional boundary diffraction wave theory [15]. Evidently, the multitude of prior investigations dedicated to the study of classical problems of line source and point source diffractions of acoustic and electromagnetic waves by half-planes of diverse variations signifies the importance of the subject [14,[16][17][18]. Jones [14] investigated the electromagnetic wave diffraction from a line source by a perfectly conducting half-plane.…”

“…Subsequently, Jones [16] observed the diffraction problem of acoustic waves due to a line source by a hard half-plane. Later on, Ayub et al [17,18] examined the acoustic wave scattering by taking soft-hard half-planes, coming from the line and point sources.…”

Reflected field analysis of soft–hard pentafurcated waveguide

“…Hassan and Rawlins 14 explained the propagation of sound radiations in a planar trifurcated lined duct and obtained a closed-form solution. Ayub and colleagues [15][16][17] analyzed the diffraction of dominant mode on acoustic wave propagation in a trifurcated lined duct with different boundary conditions. They have also presented solutions by using the Wiener-Hopf technique.…”