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Generalized formulation of acoustics

Abstract : In 1937, Janowski and Spandöck experimentally demonstrated the curvature of sound rays travelling at grazing incidence above absorbing materials. 30 years later, Cremer and Müller showed that this curvature was created by the surface admittance of the material ; however, they were not able to demonstrate the curvature of the rays. By making use of the stress-energy tensor, introduced in Acoustics by Morse and Ingard, we show that this formalism, borrowed from the general relativity theory, makes it possible to derive the curvature of grazing rays, provided that general coordinates are adopted so that the metric tensor adapts itself to the admittance at the boundary. We show that the metric tensor can be arbitrarily defined, with the only condition that the normal derivative of the velocity potential be null.Absorption is then taken into account by the residual Christoffel symbols that define normal derivation of the stress-energy tensor at the boundary. A generalized formulation of energy conservation is then obtained. It generalizes earlier work on energy propagation in corridors and flat rooms.
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Submitted on : Friday, September 13, 2019 - 5:38:49 PM
Last modification on : Friday, July 31, 2020 - 11:28:08 AM


  • HAL Id : hal-02288067, version 1


Jean-Dominique Polack, Aidan Meacham, Roland Badeau. Generalized formulation of acoustics. Congrès Français de Mécanique, Aug 2019, Brest, France. ⟨hal-02288067⟩



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