On the acoustic radiation pressure on spheres

Although frequent reference is made to acoustic radiation pressure in treatises and memoirs on sound, there appears to be no systematic theoretical development of the subject enabling actual pressures on obstacles of simple geometrical form to be calculated. In the audible range of acoustic frequencies, it is possible to devise, in a number of ways, means of measuring pressure amplitudes in sound waves as first order effects. At supersonic frequencies, however, these methods are no longer serviceable. When the dimensions of resonators of diaphragms become comparable with the wave-length, the physical effects which enable the pressure amplitude to be measured involve intractable diffraction problems, while the extremely high frequencies and small amplitudes involved make the employment of stroboscopic methods of observation extremely difficult. It has been shown, however, that at supersonic frequencies the acoustic radiation pressures on spheres and discs become sufficiently large to be measured easily, at any rate, in liquids. The mean pressure is generally assumed to be proportional to the energy density in the neighbourhood of the obstacle, and on this basis relative measurements can be made, for instance, in the radiation field of a supersonic oscillator. Such formulæ may be obtained without restriction as to wave-length, for spheres in plane progressive and stationary radiation fields, and the magnitude of the pressure is found to be of entirely different orders of magnitude in the two cases.