The Rayleigh equations for a multi-sinusoidal periodic surface

Journal of the Acoustical Society of America

Volumn 103, Issue 2, 1998, Pages 683-694

  Purcell, Anthony ^a  

^a Box 1388 ^*  (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL;

EID: 0031935252     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.421237     Document Type: Article

References (22)

1. Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Vol. 2.
2. J. L. Uretsky, "The scattering of plane waves from periodic surfaces," Ann. Phys. (N.Y.) 33, 400-427 (1965).
3. R. F. Millar, "On the Rayleigh assumption in scattering by a periodic surface," Proc. Cambridge Philos. Soc. 65, 773-791 (1969).
4. R. Petit and M. Cadilhac, "Sur la diffraction d'une onde plane par un réseau infiniment conducteur," C. R. Acad. Sci. Paris, Ser. B 262, 468-471 (1966).
5. A. Purcell, "Reflection coefficients for scattering from a pressure-release, sinusoidal surface," J. Acoust. Soc. Am. 100, 2919-2936 (1996).
6. F. Oberhettinger, Fourier Expansions (Academic, New York, 1973).
7. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U.P., New York, 1980), 2nd ed.
8. D. Berman, "Simulations of rough interface scattering," J. Acoust. Soc. Am. 89, 623-636 (1991).
9. B. J. Kachoyan and C. Macaskill, "Acoustic scattering from an arbitrarily rough surface," J. Acoust. Soc. Am. 82, 1721-1726 (1987).
10. L. Fortuin, "Survey of literature on reflection and scattering of sound waves at the sea surface," J. Acoust. Soc. Am. 47, 1209-1228 (1970).
11. G. C. Bishop and J. Smith, "A scattering model for nondifferentiable periodic surface roughness," J. Acoust. Soc. Am. 91, 744-770 (1992).
12. N. R. Hill and V. Celli, "Limit of convergence of the Rayleigh method for surface scattering," Phys. Rev. B 79, 2478-2481 (1978).
13. P. M. van den Berg and R. J. Fokkema, "The Rayleigh hypothesis in the theory of reflection by a grating," J. Opt. Soc. Am. 69, 27-31 (1979).
14. R. L. Holford, "Scattering of sound waves at a periodic, pressure-release surface: An exact solution," J. Acoust. Soc. Am. 70, 1116-1128 (1981).
15. V. A. Wassiljeff, "Verallgemeinerung einer Summenformel von Neumann und Lommel," Z. Angew. Math. Phys. 20, 389-403 (1969).
16. W. C. Meecham, "On the use of the Kirchhoff approximation for the solution of reflection problems," J. Rational Mech. Anal. 5, 323-334 (1956).
17. E. R. Hansen, A Table of Series and Products (Prentice-Hall, Englewood Cliffs, NJ, 1973), Eq. 57.17.31.
18. Stephen Wolfram, The Mathematica Book (Wolfram Media/Cambridge U.P., New York, 1996), 3rd ed.
19. T. J. Bromwich, An Introduction to the Theory of Infinite Series (Chelsea, New York, 1991), 3rd ed.
20. D. F. McCammon and S. T. McDaniel, "Application of a new theoretical treatment to an old problem-Sinusoidal pressure release boundary scattering," J. Acoust. Soc. Am. 78, 149-156 (1985).
21. D. F. McCammon and S. T. McDaniel, "Surface reflection: On the convergence of a series solution to a modified Helmholtz integral equation and the validity of the Kirchhoff approximation," J. Acoust. Soc. Am. 79, 64-70 (1986).
22. D. Berman and J. Perkins, "Rayleigh method for scattering from random and deterministic interfaces," J. Acoust. Soc. Am. 88, 1032-1044 (1990).