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The Scattering of Sound by a Hard Sphere Above an Impedance Ground

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The classical problem of acoustic diffraction by an acoustically hard sphere irradiated by a point source is reviewed. Experimental measurements are conducted in an anechoic chamber to examine the validity and accuracy of such a formulation. The theoretical analysis is further extended for the study of scattering of sound by a hard sphere above a realistic outdoor ground surface of finite impedance. The solutions to problems are analyzed in an exact fashion using the technique of separation of variables and appropriate wave field expansions. Incorporating the image method, the numerical solutions can be generated by systematically analyzing the multi-scattering interaction between the sphere and the image sphere above a hard and an impedance ground. The effect of ground impedance on the reflected sound fields is taken into account by using the approximate analytical solution known as the Weyl-van der Pol formula. The total sound field can be expressed in four components: the incident field and its reflection, and the scattered fields from the real sphere and its image. An approximate method is proposed to determine the scattering coefficients for a hard sphere not too close to the ground. The approximate method can substantially reduce the computational time for the calculation of the sound fields. It is found that the theoretical predictions derived from the approximate method are in good agreement with the results obtained by using the exact solution. Indoor experimental measurements are also carried out for the validation of the proposed theoretical models.
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Document Type: Research Article

Publication date: March 1, 2004

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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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