Acoustic radiation pressure in the near field

Abstract Langevin's acoustic radiation pressure on an absorbing target has been stated in numerous plane wave theories as being given by twice the kinetic acoustic energy density, by the total acoustic energy density or by acoustic intensity divided by the speed of sound. In a non-plane wave, which is the rule and not the exception in reality, these three quantities are no longer equal to one another. An expression for the radiation pressure in a three-dimensional sound field is derived from the literature. Although including the plane wave result as a special application, it is not in general equal to any of the three quantities mentioned, but is something different, the numerical values of which are discussed for the sound field of a continuously vibrating, circular piston source. The plane wave result that the radiation force on a large absorber is equal to the acoustic power divided by the speed of sound turns out not to be strictly valid in the piston field and it should be replaced by a slightly different formula.

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