M.H. Tiwana

DIFFRACTION OF PLANE WAVES BY A SLIT IN AN INFINITE SOFT-HARD PLANE

We have studied the problem of diffraction of plane waves by a finite slit in an infinitely long soft-hard plane. Analysis is based on the Fourier transform, the Wiener-Hopf technique and the method of steepest descent. The boundary value problem is reduced to a matrix Wiener-Hopf equation which is solved by using the factorization of the kernel matrix. The diffracted field, calculated in the farfield approximation, is shown to be the sum of the fields (separated and interaction fields) produced by the two edges of the slit. Some graphs showing the effects of various parameters on the diffracted field produced by two edges of the slit are also plotted.

Influence of acoustic dominant mode propagation in a trifurcated lined duct with different impedances

In this study, we analyzed the diffraction of the acoustic dominant mode in a parallel-plate trifurcated waveguide with normal impedance boundary conditions in the case where surface impedances of the upper and lower infinite plates are different from each other. The acoustic dominant mode is incident in a soft/hard semi-infinite duct located symmetrically in the infinite lined duct. The solution of the boundary value problem using Fourier transform leads to two simultaneous modified Wiener–Hopf equations that are uncoupled using the pole removal technique. Two infinite sets of unknown coefficients are involved in the solution, which satisfy two infinite systems of linear algebraic equations. These systems are solved numerically. The new kernel functions are factorized. Some graphical results showing the influence of sundry parameters of interest on the reflection coefficient are presented.

Acoustic Wave Propagation in a Trifurcated Lined Waveguide

The diffraction of sound from a semi-infinite soft duct is investigated. The soft duct is symmetrically located inside an acoustically lined but infinite duct. A closed-form solution is obtained using integral transform and Jones’ method based on Wiener-Hopf technique. The graphical results are presented, which show how effectively the unwanted noise can be reduced by proper selection of different parameters. The kernel functions are factorized with different approaches. The results may be used to design acoustic barriers and noise reduction devices. The analysis of the effects of unwanted noise has been an active area of research because of its technological importance. This study is im portant in connection with exhaust system, steam valves, internal combustion engines of aircraft and vehicles, turbofan engines, and ducts and pipes. The analysis of wave scattering by such structures is an important area of noise reduction and relevant for many applications. Continued interest in the problem of noise reduction has attracted the attention of many scientists, physicists, and numerical simulists. Many interesting mathematical models for the reduction of noise are discussed by several authors. In view of historical perspectives the story goes that Rawlins � 1� was the first to show that the duct with a thin acoustically absorbent lining is an effective method which can be used to reduce the unwanted noise within a waveguide. As a sound attenuator, the acoustic performance of a duct can be increased significantly by lining its walls with an acoustically absorbent material � 2� .K och� 3� discussed the problem of noise reduction from the engineering point of view, namely, in rectangular chambers, circular and annular geometries in the absence of mean flow situation. In another paper � 4� , Koch discussed

Diffraction of waves by an oscillating source and an oscillating half plane

In this paper we have studied the problem of diffraction of cylindrical acoustic waves (emanating from a harmonic time dependent source) by an oscillating half plane. An analytical solution, using spatial and temporal Fourier transforms, complex Fourier series, the Wiener-Hopf technique and the method of steepest descent, is constructed. Some graphs showing the effects of various parameters on the diffracted field are also presented.

Analysis of Diffraction of Dominant Mode in an Acoustic Impedance Loaded Trifurcated Duct

The paper presents the analytical description of diffraction phenomena of sound at the opening of a two dimensional semi-infinite acoustically soft duct. This soft duct is symmetrically located inside an infinite duct with normal impedance boundary conditions in the case where the surface acoustic impedances of the upper and lower infinite plates are different from each other. A matrix Wiener- Hopf equation associated with a new canonical scattering problem is solved explicitly. A new kernel function arose for the problem and has been factorized. The graphical results are also presented which show how effectively the unwanted noise can be reduced by proper selection of different parameters.