Doppler effect considered as a distortion of time, application to an engineering case

Jean Varnier

doi:10.5802/crmeca.312

Research article

Doppler effect considered as a distortion of time, application to an engineering case

Jean Varnier ^1,²

¹ French Aeronautical and Astronautical Association, 3AF, 75016 Paris, France
² National Office for Aerospace Studies and Research, ONERA, 92320 Châtillon, France

Comptes Rendus. Mécanique, Volume 353 (2025), pp. 863-877

Abstract (Original language)
Résumé

The ground-based listening of aircraft, rockets, or space launchers, and the simulation of recorded acoustic spectra with a view to civilian or military applications, raise the problem of the distortion by the Doppler effect of the spectrum emitted by the sound sources, in addition to other problems related to the sound propagation in atmosphere. We propose a solution to the direct problem—the characteristics of the sound source and its trajectory are known—based on an original time approach to the Doppler effect. This study shows in fact that it is not necessary to distinguish between frequency and sound level variations, both being directly related to the ratio of the emission to the reception durations of a chosen signal sequence. The developed method has a character of generality and can be applied without restriction in most cases (e.g. variable speed of the mobile, curved trajectory, atmosphere with wind and temperature gradients) using an acoustic propagation code, but remains obviously applicable in an isotropic environment to simple or complex cases, for example when the observer is moving.

L’écoute au sol d’avions, de fusées ou de lanceurs spatiaux, ainsi que la simulation de spectres acoustiques enregistrés en vue d’applications civiles ou militaires, soulèvent le problème de la distorsion par effet Doppler du spectre émis par les sources sonores, en plus d’autres problèmes liés à la propagation du son dans l’atmosphère. Nous proposons une solution au problème direct – les caractéristiques de la source sonore et sa trajectoire étant connues – basée sur une approche temporelle originale de l’effet Doppler. Cette étude montre en effet qu’il n’est pas nécessaire de distinguer les variations de fréquence et de niveau sonore, toutes deux étant directement liées au rapport des durées d’émission et de réception d’une séquence de signaux choisie. La méthode développée présente un caractère général et peut être appliquée sans restriction dans la plupart des cas (par exemple, vitesse variable du mobile, trajectoire courbe, atmosphère avec gradients de vent et de température) à l’aide d’un code de propagation acoustique, mais est évidemment applicable en environnement isotrope à des cas simples ou complexes, par exemple lorsque l’observateur est en mouvement.

Received: 2025-05-25
Revised: 2025-06-30
Accepted: 2025-06-30
Published online: 2025-07-18

DOI: 10.5802/crmeca.312

Keywords: Aeroacoustics, Doppler effect, Time approach, Sound power spectrum, Sonic boom, Atmospheric propagation
Mots-clés : Aéroacoustique, Effet Doppler, Approche temporelle, Spectre de puissance acoustique, Bang sonique, Propagation atmosphérique

Author's affiliations:

Jean Varnier ^{1, 2}

¹ French Aeronautical and Astronautical Association, 3AF, 75016 Paris, France
² National Office for Aerospace Studies and Research, ONERA, 92320 Châtillon, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Doppler effect considered as a distortion of time, application to an engineering case},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {863--877},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {353},
     doi = {10.5802/crmeca.312},
     language = {en},
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Jean Varnier. Doppler effect considered as a distortion of time, application to an engineering case. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 863-877. doi: 10.5802/crmeca.312

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