A new theory of Rayleigh radiation pressure

The present paper deals with the Rayleigh radiation pressure which is defined as the time-averaged force per unit area of the wall of a closed vessel when an acoustic field is applied. Previous theories on the Rayleigh radiation pressure are examined critically and erroneous results are noted and rectified. A new theory of radiation pressure on a partially reflecting plate is developed as a function of the linear reflection coefficient and transmission coefficient of the plate. It is shown that the time-averaged Lagrangian pressure does not depend on the Lagrangian coordinate and that the effects of acoustic straining cannot be disregarded even in the presence of reflected waves in a closed tube. The present theory is applicable to various types of reflectors. The principal conclusion of this work is that the Rayleigh radiation pressure on a perfectly absorbing plate and that on a perfectly reflecting plate are both given by (γ+1)‹E›/4, where γ is the ratio of specific heats of the medium and ‹E› is the time-averaged energy density.