Sound and light Doppler effects

Abstract: Although electromagnetic and acoustic waves profoundly differ in their nature, comparing their Doppler effects is instructive and reveals persistent conceptual traps. The principle of the Doppler effect was presented by Christian Doppler in 1842 long before the advent of relativity theory, but while the relativistic Doppler effect is now well established, its non-relativistic version retrospectively called classical, suffers from misleading intuitions such as: (1) there is no transverse classical Doppler effect; (2) the Galilean Doppler effect corresponds to the relativistic one without Lorentz dilation factor. Additional pitfalls concern the sound Doppler effect which, in addition to being Galilean, results from asymmetric contributions of the sources and receptors and depends on a material medium for its propagation, possibly modifying the effective velocity of the wave. Moreover, contrary to light, the information on the sound Doppler effect and the location of the source are transmitted through different channels, sound and light respectively, thereby complicating data interpretation and increasing confusion. A thorough revision is proposed here addressing these issues and providing a complete set of new candidate Doppler formulas, non-collinear, two- and three-dimensional and in their angular and linear versions.