Mode of sound radiation during forced vibrations of shells in compressible fluid

Radiation of sound from a vibrating sphere through a compressible fluid completely surrounding it is analyzed as a problem of forced vibrations, on the basis of the corresponding Helmholtz equation for the displacement potential. The solution to this equation describes the displacement potential as a series in spherical functions and yields the sound intensity in the fluid as a polynomial function, with positive coefficients, of the inverse square of distance from the center of the sphere. The significance of lower power terms increases while the effect of compressibility decreases with increasing distance from the sphere, in a manner which depends on the wave number and thus on the frequency.