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The study rigorously investigates the propagation of sound waves from an infinite duct lined with three different finite acoustically absorbing materials. Due to multiple discontinuity points, the mode matching method effectively solved the problem. The mathematical equations involved are highly complex due to three distinct and finite linings. To overcome this, a numerical solution is obtained, and the effects of the geometry's parameters on the transmission loss are thoroughly examined. As the length of the finite acoustic absorbing lining increases, the transmission loss decreases. In addition, the graphs clearly illustrate the substantial influence that the choice of absorbing lining can have on transmission loss. These findings hold great relevance for absorber systems, highlighting the importance of careful selection in order to achieve optimal performance. The obtained results are compared with another study, and complete agreement is observed, indicating the study's accuracy and reliability. [ABSTRACT FROM AUTHOR]

This study delves into the analysis of acoustic waves emanating from a ring source in an infinite cylindrical duct. The duct is equipped with an acoustically absorbing lining on its outer surface when z is less than l, and is perforated when z is greater than l. The inclusion of acoustically absorbing lining results in a substantial increase in the complexity of the equations compared to the scenario without such lining. Through rigorous efforts, these intricate equation systems are numerically solved, and graphs are generated across various parameter values. Furthermore, by adjusting the parameter values, a physical resemblance is established with an existing study in the literature, showcasing impeccable alignment in the results. [ABSTRACT FROM AUTHOR]

In this study, the analysis of sound waves from a coaxial pipe with a perforated screen and a partial acoustic absorbing lining is investigated. The geometry under consideration consists of an infinite pipe placed in a semi-infinite cylindrical pipe such that the inner surface of the outer pipe is covered with a partial acoustic absorbing lining. Because of the partial lining, the solution is obtained with both the Jones' method and the Mode-Matching method. The effects of the problem parameters such as perforated screen and partial lining on the radiation phenomenon are presented. [ABSTRACT FROM AUTHOR]

In this paper, the Wiener-Hopf method is studied to solve the radiation of acoustic waves from a perforated part through an infinite channel. At first the boundary value problem involving a Helmholtz equation with mixed-boundary conditions is formulated into a Wiener Hopf equation by applying the Fourier transform. After that the Wiener-Hopf kernel is split into two functions that are analytic in specified regions of the complexplane and equation is solved analytically. Finally, numerical results showing the effect of the problem's parameters (channel radius, frequency, etc.) on the radiation phenomenon are graphically displayed. [ABSTRACT FROM AUTHOR]

Radiation of sound waves by a coaxial rigid duct with perforated screen is investigated by using the Mode Matching technique in conjunction with the Jones' Method. The geometry of the problem consists semi-infinite outer duct and infinite inner duct. It is assumed that the duct walls are fully rigid. The solution of current study contains an infinite sets of coefficients satisfying an infinite systems of linear algebraic equations. These systems are truncated at a certain number and then solved numerically. The effects of open and perforated case, frequency and porosity on the radiation phenomenon are shown graphically. In the present study, perforated screen makes the problem more interesting when it is compared with the unperforated screen. In this context, solution of the problem is compered numerically with similar studies, which are used different method to obtain Wiener–Hopf equation, existing in the literature. As a result, it is observed that in the absence of a perforated screen, there is a perfect agreement between the two results. [ABSTRACT FROM AUTHOR]

An analytical solution is obtained for the diffraction problem. In an infinite cylindrical duct, the sound waves are emanating by a ring source. The duct is rigid for z < l and perforated for z > l. The mixed boundary value problem is defined by a Wiener Hopf equation, by using the Fourier transform technique. Then the numerical solution is obtained. The influence of the parameters of the problem on the diffraction phenomenon is displayed graphically. The present study can be used as a model for different applications. Reducing noise in exhaust systems, ventilation systems are some of these applications. [ABSTRACT FROM AUTHOR]

In the present work, the radiation of sound waves from a coaxial duct is considered. This coaxial duct has an inner wall which is infinite and has piecewise acoustically absorbent material, while the outer wall is semi-infinite and rigid. The analytical solution of the problem is found by means of the Wiener-Hopf technique. Applying the Fourier transformation to the boundary value problem, the explicit expression for the scattered field is obtained. In the end, some numerical results are displayed for different parameters and compared to rigid case. [ABSTRACT FROM AUTHOR]

In this paper, diffraction of sound waves through a lined cavity is analyzed rigorously. The inner–outer surfaces of the cavity and the base of the cavity are coated with three different absorbing linings. By using the Fourier transform technique in conjunction with the Mode-Matching method, the related boundary value problem is formulated as a Wiener–Hopf equation. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The graphical results are also presented which show that how efficiently the sound diffraction can be reduced by selection of problem parameters. [ABSTRACT FROM AUTHOR]

Radiation of sound waves from a semi-infinite cylindrical duct with perforated end whose outer wall is coated with acoustically absorbent material is investigated by using the Wiener-Hopf technique in conjunction with the mode matching technique. A semi-infinite duct with a perforated screen can be used as a model for many engineering applications, such as noise reduction in exhausts of automobile engines, in modern aircraft jet, and turbofan engines. In particular, we aim to find the effects of outer lining and perforated end to sound pressure level for the underlying problem by using the standard Wiener-Hopf and mode matching techniques. We also present some numerical illustrations by determining the sound pressure level for different parameters such as soft and rigid outer surface, with and without perforated end, etc. Such investigations are useful in the reduction of noise effects generated through variety of sources. [ABSTRACT FROM AUTHOR]

The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with the Wiener-Hopf technique. The solution is obtained by modification of the Wiener- Hopf technique and involves an infinite series of unknowns which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound diffraction are studied. A perfect agreement is observed when the results of radiated field are compared numerically with a similar work existing in the literature. [ABSTRACT FROM AUTHOR]

An analytical solution is presented for the problem of radiation of sound waves from a semi-infinite circular cylindrical coated pipe which is partially lined from inside. By stating the total field in duct region in terms of normal waveguide modes (Dini's series) and using the Fourier transform technique elsewhere, we obtain a Wiener–Hopf equation whose solution involving three sets of infinitely many unknown expansion coefficients satisfying three systems of linear algebraic equations. This system is solved numerically and the influence of some parameters (pipe radius, impedances, extension, etc.) on the radiation phenomenon is displayed graphically. [ABSTRACT FROM AUTHOR]