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A Powerful Asymptotic Solution for Sound Propagation above an Impedance Boundary

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A very powerful solution is developed to the problem of sound radiation from a point source above an impedance plane. It is valid for any location of the source and the receiver and for an arbitrary impedance of the plane. The only condition is k 0 R 2≫1, R 2 being the distance from image source to receiver and ko is the wavenumber. The solution is expressed in terms of the complementary error function and gives an accuracy that is comparatively difficult to obtain by numerical integration of the exact solution.


Es wird eine äußerst leistungsfähige Lösung für das Problem der Schallabstrahlung einer Punktschallquelle über einer Impedanzebene hergeleitet. Sie ist gültig für alle Quellen und Empfängerpositionen und für beliebige Impedanzen der Ebene. Einzuhalten ist lediglich die Bedingung k 0 R 2≫1, wobei R 2 der Abstand zwischen Spiegelquelle und Empfänger ist und k 0 die Wellenzahl. Die Lösung wird mit Hilfe der komplementären Fehlerfunktion formuliert. Sie liefert eine Genauigkeit, die durch numerische Integration der exakten Lösung nur schwer zu erreichen ist.


On apporte au problème du rayonnement d'une source sonore ponctuelle placée au dessus d'un plan caractérisé par une impédance une solution riche d'applications multiples. Cette solution est valable quelle que soit l'impédance du plan et quels que soient les emplacements de la source et du point de réception. La seule condition de validité est k 0 R 2≫1, k 0 étant le nombre d'onde et R 2 la distance du récepteur à l'image de la source dans le plan. La solution proposée s'exprime en termes contenant la fonction erreur et conduit à des résultats dont la précision est difficile à atteindre même par intégration numérique des solutions élémentaires exactes.
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Document Type: Research Article

Publication date: June 1, 1980

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  • 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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