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Scattering of Sound by a Hollow, Hard Sphere with an Opening

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In this paper the scattering on a hollow sphere with infinitely thin, hard walls and an opening is calculated in order to provide benchmark solutions for BEM and FEM methods. The calculations are based on an expansion into products of Bessel or Neumann functions and Legendre Polynomials. Solutions are obtained by minimizing the residual errors on the surface and in the opening of the sphere. This leads to infinite sets of linear equations which include certain Wigner 3j symbols. An implementation of the recursion for these symbols is presented. Criteria for the truncation of the infinite set of equations are discussed, good results are obtained for 2 < kr 0 < 30, k and r 0 denoting the wavenumber and the radius of the sphere respectively. The results are in agreement with the asymptotic calculations of Morse and Feshbach regarding the position of the first resonance, some difference found at low wave numbers for the surface velocity field is discussed.
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Document Type: Research Article

Publication date: 2006-07-01

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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