The sound field of a pulsating sphere in unsteady rectilinear motion

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Abstract
A sphere, whose radius changes in time, moves with non-uniform speed along a straight line through an inviscid compressible fluid. The acoustic velocity potential is determined asymptotically when the characteristic speed U0 of the sphere is small compared with the mean sound speed c0 in the fluid. It is assumed that both the sphere radius and the translational speed vary slowly, with appreciable change on a time scale t0 = a0/U0, where a0 is a characteristic radius; furthermore, the sphere is assumed to be compact, in the sense that the ratio between its radius and a typical wavelength is small. The sound field is expressed by means of moving source and dipole potentials in a fashion that appears simpler and more general than previously given.

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