Four-dimensional Treatment of Linear Acoustic Fields and Radiation Pressure

A general expression of acoustic radiation pressure is here derived on the basis of the linear theory of classical fields. Following this theory, the acoustic energy, the sound intensity and the sound momentum density are introduced, together with the 3 × 3 wave-momentum flux density tensor, as components of a 4 × 4 acoustic energy-momentum tensor in a unified space-time approach, formally similar to the relativistic formulation of electromagnetism. The related conservation laws are then expressed by the condition of vanishing 4-divergence of this tensor, showing in particular that the so-called radiation pressure is nothing but a consequence of the momentum conservation law for the acoustic field. As an application, the radiation pressure is computed explicitly in two cases: a plane wave reflected on a flat wall and the field in the interior of an open organ pipe. In the latter case, indirect measurements of the radiation pressure have been also performed by an intensimetric technique, allowing to determine the complex reflection amplitude at the pipe's end. Finally, as an appendix of the paper, the angular momentum conservation and the analogy between the acoustic and electromagnetic radiation pressure are analyzed to some extent.