Sound diffraction around screens and wedges for arbitrary point source locations

Journal of the Acoustical Society of America

Volumn 69, Issue 5, 1981, Pages 1266-1276

  Hadden, W James ^a   Pierce, Allan D ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVES;

EID: 0019565848     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.385809     Document Type: Article

References (15)

1. An extensive bibliography of relevant earlier literature (in-cluding contributions by Poincare, Sommerfeld, and Mac-Donald) is given by H. G. Garnir, Bulletin de la Soci§t§ Royale des Sciences de Libge 21, 207–231 (1952)
2. The standard “handbook” article for this subject is J. J. Bowman and T. B. A. Senior, “The Wedge,” Chap. 6 in Electromagnetic and Acoustic Scattering by Simple Shapes, edited by J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi (North-Holland, Amsterdam, 1969), pp. 252–283
3. T. J. I. A. Bromwich, “Diffraction of Waves by a Wedge,” Proc. Lond. Math. Soc. 14, 450–463 (1915)
4. H. S. Carslaw, “Diffraction of Waves by a Wedge of any angle,” Proc. Lond. Math. Soc. 18, 291–306 (1920)
5. F. J. W. Whipple, “Diffraction by a Wedge and Kindred Problems,” Proc. Lond. Math. Soc. 16, 94–111 (1918) (see p. 103)
6. F. Oberhettinger, “On Asymptotic Series for Functions occurring in the Theory of Diffraction of Waves by Wedges,” J. Math. Phys. 34, 245–255 (1956) (J. Math. Phys., Cambridge, MA)
7. A. D. Pierce, “Diffraction of Sound around Corners and over Wide Barriers,” J. Acoust. Soc. Am. 55, 941—955 (1974)
8. A. A. Tuzhilin, “New Representation of Diffraction Fields in Wedge-Shaped Regions with Ideal Boundaries,” Sov. Phys. Acoust. 9, 168–172 (1963)
9. P. Ambaud and A. Bergassoli, “Le problfeme du difedre en acoustique” (The Problem of the Wedge in Acoustics), Acustica 27, 291–298 (1972)
10. The result is compatible with Rayleigh's conclusion (Sec. 280 in Theory of Sound) that mean square power radiated by a source with given volume velocity amplitude at a vertex of a cone should be inversely proportional to the solid angle of the cone, such that the pressure amplitude at given radial distance r is inversely proportional to the product of the cone's solid angle and r. That Rayleigh's analysis applies to the case of a source on a wedge's edge was pointed out by R. V. Waterhouse, “Diffraction Effects in a Random Sound Field,” J. Acoust. Soc. Am. 35, 1610–1620 (1963)
11. W. Gautschi, “Error Function and Fresnel Integrals,” in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965), pp. 295–329
12. The term “Fresnel number” in the present paper is used in the same sense as in Z-Maekawa i “noise Reduction by Screens,” Paper F13 in 5 Congres International d'Acoustique, Vol. la, edited by D. E. Commins (Georges Thone, Liege, 1965). The result derived in the present paper is analogous to what Maekawa derives from the “Kirchhoff theory.”
13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1965), 3.381 4
14. See, for example, M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), 4th ed., pp. 568–569. The result is due to A. Sommerfeld, Math. Ann. 47, 317—374 (1896)
15. P. J. Davis and I. Polonsky, “Numerical Interpolation, Differentiation, and Integration,” in Handbook of Mathematical Functions (Dover New Yprk, 1965), pp. 875—924. See pp. 890 and 923