Traffic noise and the hyperbolic plane
File(s)0911.1926v3.pdf (1.61 MB)
Accepted version
Author(s)
Gibbons, GW
Warnick, CM
Type
Journal Article
Abstract
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)×R symmetry of the problem from this point of view.
Date Issued
2010-01-04
Date Acceptance
2009-12-24
Citation
Annals of Physics, 2010, 325 (4), pp.909-923
ISSN
1096-035X
Publisher
Elsevier
Start Page
909
End Page
923
Journal / Book Title
Annals of Physics
Volume
325
Issue
4
Copyright Statement
© 2010 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Nuclear & Particles Physics
01 Mathematical Sciences
02 Physical Sciences
Publication Status
Published