Open Access
2013 Time-frequency Integrals and the Stationary Phase Method in Problems of Acoustic Waves Propagation from Moving Sources
G. Burlak , V. Rabinovich , J. R. Hernandez Juarez
Commun. Math. Anal. 14(2): 25-39 (2013).
Abstract

The paper is devoted to the applications of the time-frequency integrals and the two-dimensional stationary phase method for the problems of waves propagation from moving sources in acoustic dispersive media. Applying the stationary phase method we obtain the effective formula for the acoustic fields in the dispersive media generated by non-uniformly moving modulated source.

References

1.

D. I. Blokhintzev, Acoustics of Non-homogeneous Moving Media, Nauka, Moscow, 1981 (in Russian). D. I. Blokhintzev, Acoustics of Non-homogeneous Moving Media, Nauka, Moscow, 1981 (in Russian).

2.

F. A. Berezin and M. A. Shubin, The Schrödinger Equation, Kluwer, Dorderecht, Boston, London, 1991.  MR1186643 F. A. Berezin and M. A. Shubin, The Schrödinger Equation, Kluwer, Dorderecht, Boston, London, 1991.  MR1186643

3.

V. S. Buldyrev, Sound field produced by a source moving in a non-homogeneous layer lying on a homogeneous half-space. Zapis.sem.LOMI, 156 (1986), pp 35-49 (in Russian). V. S. Buldyrev, Sound field produced by a source moving in a non-homogeneous layer lying on a homogeneous half-space. Zapis.sem.LOMI, 156 (1986), pp 35-49 (in Russian).

4.

V. S. Buldyrev and N. S. Grigor'eva, Acoustic field generated by a moving atmosphere source in a fluid layer with variable thickness. Akusticheskii jurnal 39 (1993), pp 782-792, 1014-1024 (in Russian). V. S. Buldyrev and N. S. Grigor'eva, Acoustic field generated by a moving atmosphere source in a fluid layer with variable thickness. Akusticheskii jurnal 39 (1993), pp 782-792, 1014-1024 (in Russian).

5.

L. M. Brekhovskikh, Waves in Layered Media, New York, Academic Press, 1960.  MR112392 0558.73018 L. M. Brekhovskikh, Waves in Layered Media, New York, Academic Press, 1960.  MR112392 0558.73018

6.

N. Blestein and R. A. Handelsman, Asymptotic Extention of Integrals, Dover Publication Ink. New York, 1975. N. Blestein and R. A. Handelsman, Asymptotic Extention of Integrals, Dover Publication Ink. New York, 1975.

7.

L. Brilloin, Wave Propagation and Group Velocity, Academic Press, New York, NY, 4, 1960.  MR108217 0094.41601 L. Brilloin, Wave Propagation and Group Velocity, Academic Press, New York, NY, 4, 1960.  MR108217 0094.41601

8.

L. Cohen, Time-Frequency Analysis, Prentice Hall, 1995. L. Cohen, Time-Frequency Analysis, Prentice Hall, 1995.

9.

L. B. Felson and N. Marcuvitz, Radiation and Scattering of Waves, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973.  MR471626 L. B. Felson and N. Marcuvitz, Radiation and Scattering of Waves, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973.  MR471626

10.

T. Melamed and L. B. Felsen, Pulsed-beam propagation in lossless dispersive media. I. Theory, J. Opt. Soc. Am. A 15 (1998) pp 1268-1276. T. Melamed and L. B. Felsen, Pulsed-beam propagation in lossless dispersive media. I. Theory, J. Opt. Soc. Am. A 15 (1998) pp 1268-1276.

11.

M. V. Fedoryuk, Method of the Steepest Descent, Moscow 1977 (in Russian). M. V. Fedoryuk, Method of the Steepest Descent, Moscow 1977 (in Russian).

12.

V. L. Ginzburg, Radiation of uniformly moving sources (Vavilov-Cherenkov effect, Doppler effect in medium, Transition radiation and related phenomena. Progress in Optics 32, (1993) pp 267-312. V. L. Ginzburg, Radiation of uniformly moving sources (Vavilov-Cherenkov effect, Doppler effect in medium, Transition radiation and related phenomena. Progress in Optics 32, (1993) pp 267-312.

13.

V. L. Ginsburg, Theoretic Physics and Astrophysics, Moscow, Nauka, 1981.  MR637059V. L. Ginsburg, Theoretic Physics and Astrophysics, Moscow, Nauka, 1981.  MR637059

14.

V. L. Ginsburg, Propagation of Electromagnetic Waves in Plasma, Moscow, Nauka, 1960. V. L. Ginsburg, Propagation of Electromagnetic Waves in Plasma, Moscow, Nauka, 1960.

15.

J. D. Jackson, Classical Electrodynamics, J. Willey&Son Ink. New York, London, Sidney, 1962. J. D. Jackson, Classical Electrodynamics, J. Willey&Son Ink. New York, London, Sidney, 1962.

16.

J. V. Jelley, Cherenkov Radiation and Its Applications. Pergamon Press, London, 1958. J. V. Jelley, Cherenkov Radiation and Its Applications. Pergamon Press, London, 1958.

17.

K. Hawker, A normal mode theory of acoustic Doppler effects in the oceanic waveguide. J.Acoust.Soc.Am., 65 (1979), pp 675–681. K. Hawker, A normal mode theory of acoustic Doppler effects in the oceanic waveguide. J.Acoust.Soc.Am., 65 (1979), pp 675–681.

18.

V. I. Il'ichev, V. S. Rabinovich, E. A. Rivelis, and U. V. Hoha, Acoustic field of a moving narrow-band source in oceanic waveguides. Dokl.Akad.Nauk SSSR, 304 (1989), pp 1123-1127 (in Russian). V. I. Il'ichev, V. S. Rabinovich, E. A. Rivelis, and U. V. Hoha, Acoustic field of a moving narrow-band source in oceanic waveguides. Dokl.Akad.Nauk SSSR, 304 (1989), pp 1123-1127 (in Russian).

19.

L. Kazandjian and L. Leviandier, A normal mode of the air to water sound transmission by a moving source. J.Acoustic Soc. Am. 96 (1994), pp 1732-1740. L. Kazandjian and L. Leviandier, A normal mode of the air to water sound transmission by a moving source. J.Acoustic Soc. Am. 96 (1994), pp 1732-1740.

20.

L. D. Landau and E. M. Lifshitz, Field Theory, Theoretical Physics II, Moscow, Nauka, 1988.  MR1017641 L. D. Landau and E. M. Lifshitz, Field Theory, Theoretical Physics II, Moscow, Nauka, 1988.  MR1017641

21.

L. D. Landau and E. M. Lifshitz, Theorical Physics, Vol. 8, Electrodynamics of Continuous Media, Moscow, Nauka, 1982. L. D. Landau and E. M. Lifshitz, Theorical Physics, Vol. 8, Electrodynamics of Continuous Media, Moscow, Nauka, 1982.

22.

G. Lighthill, Waves in Fluids, Cambridge University Press, 1978.  MR642980 G. Lighthill, Waves in Fluids, Cambridge University Press, 1978.  MR642980

23.

P. H. Lim and J. M. Ozard, On the underwater acoustic field of a moving point source, I, Range-independent environment. J.Acoustic Soc. Am. 95 (1994), pp 131-137; II Range-dependent environment, J.Acoustic Soc. Am. 95 (1994), pp 138-151. P. H. Lim and J. M. Ozard, On the underwater acoustic field of a moving point source, I, Range-independent environment. J.Acoustic Soc. Am. 95 (1994), pp 131-137; II Range-dependent environment, J.Acoustic Soc. Am. 95 (1994), pp 138-151.

24.

H. Medwin and C. S. Clay, Fundamentas of Acoustical Oceanography, Academic Press, Boston San Diego New York, 1998. H. Medwin and C. S. Clay, Fundamentas of Acoustical Oceanography, Academic Press, Boston San Diego New York, 1998.

25.

O. A. Obrezanova and V. S. Rabinovich, Acoustic field of a source moving along stratified waveguide surface. Akusticheskii jurnal. 39 (1993), pp 517-521 (in Russian). O. A. Obrezanova and V. S. Rabinovich, Acoustic field of a source moving along stratified waveguide surface. Akusticheskii jurnal. 39 (1993), pp 517-521 (in Russian).

26.

S. M. Grudsky, O. A. Obrezanova, and V. S. Rabinovich, Sound propagation from a moving air source in the ocean covered by ice. Akusticheskii jurnal, 41 (1995), pp 1-6 (in Russian). S. M. Grudsky, O. A. Obrezanova, and V. S. Rabinovich, Sound propagation from a moving air source in the ocean covered by ice. Akusticheskii jurnal, 41 (1995), pp 1-6 (in Russian).

27.

O. A. Obrezanova and V. S. Rabinovich, Acoustic field generated by moving sources in stratified waveguides. Wave Motion, 27 (1998), pp 155-167.  MR1606865 10.1016/S0165-2125(97)00039-5 O. A. Obrezanova and V. S. Rabinovich, Acoustic field generated by moving sources in stratified waveguides. Wave Motion, 27 (1998), pp 155-167.  MR1606865 10.1016/S0165-2125(97)00039-5

28.

L. Szabo, Causal theories and data for acoustic attenuation obeying a frequency power law. J. Acoust. Soc. Am. 97 (1995), pp 14-24. L. Szabo, Causal theories and data for acoustic attenuation obeying a frequency power law. J. Acoust. Soc. Am. 97 (1995), pp 14-24.

29.

H.Shmidt and W.A.Kuperman, Spectral and modal representation of the Doppler-shifted field in ocean waveguides. J.Acoustic Soc. Am. 95 1 (1994), pp 386-395. H.Shmidt and W.A.Kuperman, Spectral and modal representation of the Doppler-shifted field in ocean waveguides. J.Acoustic Soc. Am. 95 1 (1994), pp 386-395.

30.

K. R. Waters and M. S. Hughes, G. H. Brandenburger, and J. G. Miller, On a time-domain representation of the Kramers-Kronig dispersion relations. J. Acoust. Soc. Am. 108 (2000), pp 2114-2119. K. R. Waters and M. S. Hughes, G. H. Brandenburger, and J. G. Miller, On a time-domain representation of the Kramers-Kronig dispersion relations. J. Acoust. Soc. Am. 108 (2000), pp 2114-2119.

31.

A. Sommerfield, Lectures on Theoretical Physics, Academic Press, New York, NY, 1950. A. Sommerfield, Lectures on Theoretical Physics, Academic Press, New York, NY, 1950.
Copyright © 2013 Mathematical Research Publishers
G. Burlak , V. Rabinovich , and J. R. Hernandez Juarez "Time-frequency Integrals and the Stationary Phase Method in Problems of Acoustic Waves Propagation from Moving Sources," Communications in Mathematical Analysis 14(2), 25-39, (2013). https://doi.org/
Published: 2013
Vol.14 • No. 2 • 2013
Back to Top