Diffraction of Waves by a Wedge of any Angle

Carslaw, H. S.

doi:10.1112/plms/s2-18.1.291

Cited by 55 publications

(36 citation statements)

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“…It can be observed from the figure that the solutions of Senior and Maliuzhinets are in harmony, but deviate from the field expression of Raman and Krishnan. Since the total diffracted fields of Senior and Maliuzhinets are equal to zero on the surfaces of the half-plane, they do not satisfy the boundary condition, given in Equation (2).…”

Section: Numerical Comparisonmentioning

confidence: 99%

“…The evaluation of the complex integral yielded to the uniform expressions of the scattered fields in terms of the Fresnel functions. The method of Sommerfeld was applied to more general case of the conducting wedge by Carslaw [2]. The impedance surfaces are more realistic in the modeling of the scatterers since an object does not generally reflect all of the incoming energy.…”

Section: Introductionmentioning

confidence: 99%

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Scattering by an Impedance Half-Plane: Comparison of the Solutions of Raman/Krishnan and Maliuzhinets/Senior

Umul

2009

PIER M

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Abstract-There are three approaches for the solution of the diffraction problem of plane waves by an impedance half-plane in the literature. The diffracted field expressions, obtained by the related methods, are compared numerically. The examination of the scattered field shows that the most reliable solution is the field representation of Raman and Krishnan. Since the diffracted fields of Senior and Maliuzhinets do not compensate the discontinuities of the geometrical optics waves at the transition regions.

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Section: Numerical Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scattering by an Impedance Half-Plane: Comparison of the Solutions of Raman/Krishnan and Maliuzhinets/Senior

Umul

2009

PIER M

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“…[4][5][6][7] Ideally, such designs should be based on a comprehensive and accurate theory of sound diffraction around barrieri. In practice, however, the inherent complexities associated with the development of such a theory have necessitated the introduction of a variety of approximations and idealizations.…”

Section: Introductionmentioning

confidence: 99%

Aircraft noise propagation

Zaporozhets¹,

Tokarev²,

Attenborough³

2011

Aircraft Noise

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“…Indeed Reiche (1912), who gives a solution for the diffraction of a plane wave by a right angled wedge (in the form of geometrical acoustic terms and real integrals which represent the diffracted field) thanks Sommerfeld for supplying the appropriate 'ansatz' to obtain the solution! Carslaw (1920), was an early convert to Sommerfeld's method, but later gave up using the idea of Riemann surfaces, and instead used the more modern approach of using periodic Green's functions. However, Sommerfeld's method gave exact solutions which made apparent the geometrical acoustic and diffracted wave contributions for the half plane and the right angle wedge.…”

Section: Introductionmentioning

confidence: 99%

“…where (r, θ) are cylindrical polar coordinates has been shown by Carslaw (1920) to be given by It has also been shown by Carslaw that…”

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confidence: 99%

Plane-wave diffraction by a rational wedge

Rawlins

1987

Proc. R. Soc. Lond. A

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In this paper new expressions for the acoustic field produced when a plane wave source of sound is diffracted by a soft, hard or mixed soft/hard wedge whose angle can be expressed as a rational multiple of π are given. The solution is expressed in terms of geometrical acoustic source terms and real integrals which represent the diffracted field. The expressions are in a form which allows easy calculation of the acoustic field. Uniformly valid expressions for the far field are also given for all values of the angular variable. The general result obtained includes as special cases, Sommerfeld' s solution for diffraction by a half plane, Reiche's result for the diffraction by a right angled wedge, and a new representation for the solution of the problem of diffraction by a mixed soft/hard half plane.-3-

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Diffraction of Waves by a Wedge of any Angle

Cited by 55 publications

References 0 publications

Scattering by an Impedance Half-Plane: Comparison of the Solutions of Raman/Krishnan and Maliuzhinets/Senior

Scattering by an Impedance Half-Plane: Comparison of the Solutions of Raman/Krishnan and Maliuzhinets/Senior

Aircraft noise propagation

Plane-wave diffraction by a rational wedge

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