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Versuch einer relativistischen Schalltheorie bewegter Körper

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This paper deals with the transformation of a sound field existing in a medium at rest to a reference system which is moving uniformly with respect to the medium. By use of the Galilei-Transformation the functional structure of the acoustical wave equation is changed in such a way, that its integration is generally very difficult. To overcome this obstacle the “Mach-Transformation” is introduced which, owing to its mathematical identity with the Lorentz-Transformation, saves the invariance of the wave equation. For convenience, the “Mach-Transformation” is written in accordance with the “Four-Vector World” originated by Minkowski. While the space and time metric of Mach's system of reference deviates from the acoustical abilities of man, it requires as an observer a somewhat artificial “demon”. In order to interpret the observations of this demon a further “Mach-Galilei-Transformation” is introduced which translates the physical effects to be expected into the Galilean language of a real observer. The general theory is demonstrated by three examples: (1) The Doppler-Effect of a moving sound source. (2) The diffraction of sound by a travelling sphere. (3) The principles of sound detection of an invisible object. The last chapter points on same basic problems of relativistic acoustics not solved by the present paper.

Zusammenfassung

Die vorliegende Arbeit beschäftigt sich mit der Transformation des Schallfeldes in einem ruhenden Medium auf ein relativ zu diesem gleichförmig bewegtes Bezugssystem. Die Galilei-Transformation verändert die Wellengleichung derart, daß deren unmittelbare Integration erschwert wird. Dagegen bleibt die Wellengleichung gegen die ,,Mach-Transformation“ invariant, die zwar mit der Lorentz-Transformation mathematisch identisch ist, deren physikalisch zulässigen Anwendungsbereich jedoch wesentlich erweitert. Die Mach-Transformation wird in der Minkowskischen, vierdimensionalen Schreibweise benutzt. Die Machsche Metrik des transformierten Schallfeldes ist zwar einem nur virtuellen Beobachter [,,Dämon“] angepaßt, wird jedoch mittels der Mach-Galilei-Transformation eindeutig der Terminologie eines realen Beobachters erschlossen. Die allgemeine Theorie wird auf den Dopplereffekt einer bewegten Schallquelle, die Schalldispersion an einer wandernden Kugel und die Grundlagen der akustischen Ortung angewandt. Der Schluß enthält Hinweise auf die Problematik der relativistischen Akustik.

Sommaire

Ce travail s'occupe de transformer le champ acoustique dans un milieu au repos en un champ relatif à un système de référence en mouvement uniforme par rapport au dit milieu. La transformation de Galilée a l'inconvénient de modifier l'équation des ondes d'une telle manière que les intégrales en deviennent beaucoup plus difficiles à calculer. Par contre cette équation demeure invariante vis-à-vis de la transformation de Mach, laquelle du reste est mathématiquement identique à la transformation de Lorentz mais en élargit substantiellement le domaine des applications physiquement acceptables. Cette transformation de Mach sera mise en pratique avec lécriture quadridimensionnelle de Minkowski. En principle la métrique de Mach du champ acoustique après transformation n'est acceptable que par des observateurs virtuels («démons»), mais grâce à la transformation de Mach-Galilée elle peut être étendue d'une manière univoque à la terminologie d'un observateur réel. La théorie générale ainsi obtenue est appliquée successivement à l'effet Doppler d'une source sonore en mouvement, à la dispersion acoustique d'une sphère mobile et à l'établissement des principes fondamentaux de la localisation des sources acoustiques On conclut sur les horizons nouveaux et la problématique de l'acoustique relativiste.
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Document Type: Research Article

Publication date: February 1, 1982

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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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