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Generalized Analysis of Sound Scattering by Diffusing Walls

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The two-dimensional, generalized diffraction theory is developed for a periodic diffusing wall, consisting of walls of arbitrary rectangular profile and of arbitrary acoustic impedance at the bottom. From the boundary conditions to be satisfied by the plane waves in the free half-space and the eigenwaves in the walls, a simultaneous infinite system of linear equations is derived from which the sound reflection of the wall can be solved. Two examples are given. One of them is used to demonstrate the effect of the present theory, emphasizing the importance of the evanescent waves to the total scattered field. Another one is concerned with the quadratic-residue (QR) sequence diffuser and shows again that this kind of diffuser is favourable.

Zusammenfassung

Die zweidimensionale, verallgemeinerte Beugungstheorie wird für eine periodische Streuwand entwickelt, die aus beliebigen, rechteckigen Vertiefungen mit beliebiger akustischer Bodenimpedanz zusammengesetzt ist. Aus den Randbedingungen, die durch die ebenen Wellen im freien Halbraum und durch die Eigenwellen in den Vertiefungen zu erfüllen sind, wird ein lineares, unendliches Gleichungssystem hergeleitet, wodurch die Schallreflexion an der Wand berechnet werden kann. Zwei Beispiele werden angeführt. Das eine dient dazu, die Wirkung der angegebenen Theorie zu zeigen, wobei die Bedeutung der blindgedämpften Wellen für das gesamte Streufeld betont werden soll. Das andere behandelt den auf quadratischen Restfolgen (QR) basierenden Diffusor und zeigt erneut, daß diese Art von Diffusor vorteilhaft ist.

Sommaire

On applique à une paroi diffusante périodique la théorie généralisée de la diffraction bidimen-sionnelle. La paroi est constituée de «puits» munis chacun d'un profil rectangulaire arbitraire dont le fond présente une impédance également arbitraire. Les conditions de raccordement entre les ondes planes pouvant se propager dans le demi-espace libre et les ondes correspondant aux modes propres dans les puits fournissent un système infini d'équations linéaires. En le résolvant on peut en déduire la réflexion acoustique de la paroi. Deux exemples sont développés: l'un sert à démontrer une des conséquences de la théorie présentée, à savoir l'importance des ondes évanescentes dans la composition du champ total diffracté; l'autre concerne le diffuseur séquentiel à «résidus quadratiques», dont on retrouve les particularités intéressantes.
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Document Type: Research Article

Publication date: October 1, 1983

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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