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Comparing Approaches to the Spherical and Planar Single Layer Potentials for Interior Sound Field Synthesis

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Practical approaches to sound field synthesis are described by the single layer potential for which spherical monopoles are driven by appropriate driving functions. This article reviews analytic derivations of known driving functions in the sound field synthesis literature in a consistent framework. It will be shown that the same fundamental methods hold for planar and spherical problems considering a continuous layer of spherical monopoles. The resulting single layer potential can be either solved explicitly as an inverse problem. On the other hand, the Helmholtz integral equation postulates the superposition of a single and a double layer potential which can be simplified to a single layer potential. This is achieved by imposing homogeneous boundary conditions on the involved scalar fields. The equivalent sound-soft scattering approach using the Dirichlet boundary condition on the pressure leads to similar driving functions as derived by the explicit solution. The well known Rayleigh integral equation using the Neumann Green's function incidentally yields an equivalent single layer potential driving function for the planar geometry only.
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Document Type: Research Article

Publication date: 01 September 2014

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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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