Acoustic energy quantities and radiation force in higher approximation

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Abstract
Extending the familiar linear acoustics treatment, the acoustic energy density, the acoustic energy flux density (acoustic intensity), and the acoustic radiation stress tensor in a three-dimensional acoustic field in a lossless and nondispersive fluid are calculated up to any order of approximation. The formulas obtained are used to discuss the question of the validity limitations of the familiar second-order result for the relation between radiation pressure and intensity. This question is important in connection with the widespread use of the radiation force method for ultrasonic power measurements. An answer is given by calculating the third- and fourth-order expressions for the specific case of a plane-progressive wave impinging on a perfect absorber. The result is that in the whole amplitude range covered by current ultrasonic medical equipment (therapeutic and diagnostic), the third- and fourth-order correction to the second-order formula is less than 1% and can thus be neglected.

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