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.

中文翻译：

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内衬圆柱腔对声波的衍射

在本文中，声波通过内衬腔的衍射进行了严格的分析。腔体的内外表面和腔体底部涂有三种不同的吸收衬里。通过将傅立叶变换技术与模式匹配方法结合使用，相关的边值问题被表述为 Wiener-Hopf 方程。在该解中，涉及满足两个无限线性代数方程组的未知系数的两个无限集合。该系统的数值解是针对问题参数的各种值获得的。还提供了图形结果，表明通过选择问题参数可以如何有效地减少声音衍射。