Abstract
The acoustic field of a source moving at a subsonic velocity in a regular waveguide with perfectly reflecting boundaries is considered. The acceleration of the source is assumed to be small. In a moving coordinate system, the asymptotics of the wave field is obtained. This asymptotics is inapplicable near the critical cross sections, for which the Doppler frequency of the source coincides with the frequency of the waveguide mode under consideration. It is demonstrated that, in this case, the wave field can be represented locally by a special type of integral, which is analyzed by the saddle-point method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. E. Hawker, “A normal mode theory of acoustic Doppler effect in the oceanic waveguide,”J. Acoust. Soc. Am.,65, No. 3, 675–681 (1979).
V. S. Buldyrev, “The acoustic field of a source moving in an inhomogeneous layer covering a homogeneous half-space,”Zap. Nauchn. Semin. LOMI,156, 35–48 (1986).
V. I. Il'ichev, V. S. Rabinovich, E. A. Rivelis, and U. V. Khokha, “On the acoustic field of a moving narrow-band source in oceanic waveguides,”Dokl. Akad. Nauk SSSR,304, No. 5, 1123–1127 (1989).
V. M. Babich, V. S. Buldyrev, and I. A. Molotkov,Space-Time Ray Method [in Russian], Leningrad Univ. Press, Leningrad (1985).
V. M. Babich and V. S. Buldyrev,Asymptotic Methods in Short-Wavelength Diffraction Problems [in Russian], Nauka, Moscow (1972).
N. S. Grigor'eva, “Short-wavelength asymptotics of the solution of the problem on a point source moving in an inhomogeneous nonstationary medium,”Zap. Nauchn. Semin. LOMI,165, 42–51 (1987).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 71–78.
This work was supported in part by the Russian Foundation for Basic Research under grant 95-01-01285a.
Rights and permissions
About this article
Cite this article
Buldyrev, V.S., Sokolov, A.V. & Starkov, A.S. The acoustic field of a high-frequency source moving in a waveguide. J Math Sci 96, 3327–3331 (1999). https://doi.org/10.1007/BF02172808
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02172808