Traffic noise and the hyperbolic plane
- DAMTP, CMS, WIlberforce Road, Cambridge CB3 0WA (United Kingdom)
We consider the problem of sound propagation in a wind. We note that the rays, as in the absence of a wind, are given by Fermat's principle and show how to map them to the trajectories of a charged particle moving in a magnetic field on a curved space. For the specific case of sound propagating in a stratified atmosphere with a small wind speed, we show that the corresponding particle moves in a constant magnetic field on the hyperbolic plane. In this way, we give a simple 'straightedge and compass' method to estimate the intensity of sound upwind and downwind. We construct Mach envelopes for moving sources. Finally, we relate the problem to that of finding null geodesics in a squashed anti-de Sitter spacetime and discuss the SO(3,1)xR symmetry of the problem from this point of view.
- OSTI ID:
- 21336121
- Journal Information:
- Annals of Physics (New York), Vol. 325, Issue 4; Other Information: DOI: 10.1016/j.aop.2009.12.007; PII: S0003-4916(09)00247-4; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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