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Sound field of a source moving in an inhomogeneous layer on a homogeneous halfspace

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Abstract

Equations are suggested in the present paper for the amplitudes and instantaneous frequencies of sound waves generated by a moving source. The equations are derived by means of the Space-Time Ray (STR) method and by the two-scale expansion method (the method of horizontal rays and vertical modes).

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Literature cited

  1. B. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. II, Nauka, Moscow (1965).

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  2. R. M. Lewis, “Formal theory of traveling waves,” in: Quasioptics [Russian translation], Mir (1966).

  3. A. N. Guthrie, R. M. Fitzgerald, D. A. Nutile, and Y. D. Shaffer, “Long-range low-frequency CW propagation in the deep ocean: Antiqua-New Foundland,” J. Acoust. Soc. Amer.,56, No. 1, 58–69 (1974).

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  4. K. E. Hawker, “A normal mode theory of acoustic Doppler effects in the oceanic waveguide,” J. Acoust. Soc. Am.,65, No. 3, 675–681 (1979).

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  5. V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, The Space-Time Ray Method — Linear and Nonlinear Waves [in Russian], Leningrad State Univ. (1985).

  6. N. A. Razumovskii, “The Green's function of a weakly inhomogeneous waveguide,” J. Sov. Math.,30, No. 5 (1985).

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 35–48, 1986.

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Buldyrev, V.S. Sound field of a source moving in an inhomogeneous layer on a homogeneous halfspace. J Math Sci 50, 1702–1711 (1990). https://doi.org/10.1007/BF01097099

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  • DOI: https://doi.org/10.1007/BF01097099

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