The Mean Pressure and Velocity in a Plane Acoustic Wave in a Gas

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Abstract
The one‐dimensional wave equation is discussed to the second order of approximation by means of a transformation that carries the equation from the Eulerian to the Lagrangean form. Airy's solution to this equation in Lagrangean form has been shown by Fubini to be an excellent approximation to an exact solution of Earnshaw's equation of motion; therefore, Airy's solution is chosen as the basis for much of this discussion. An expression for the local mean hydrostatic pressure in a plane progressive wave is obtained by transforming Airy's solution from particle to local coordinates. In a similar way, the particle velocity in fixed coordinates is shown to possess a time‐independent component proportional to, and in a direction opposite to, the intensity vector This d.c. counter‐velocity is predicted without recourse to viscous forces and is compatible with zero average mass velocity. For a sound pressure level of 151 decibels in air there should exist a steady particle velocity of 1 cm/sec. Small particles suspended in the field can, under certain circumstances, acquire this velocity. An approximate treatment is suggested for handling second‐effects arising from stationary field configurations. The influence of viscosity is discussed qualitatively. One purpose of this paper is to correlate work in the field which has not so far been published in this country.

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