Radiation reaction and runaway solutions in acoustics

A solution is given to the acoustical field equations when the source of the field is a sphere undergoing radial pulsations. This solution, which is exact within the usual linear approximation, is used to investigate two topics of interest in electrodynamics. The first is the indirect calculation of the radiation reaction. An alternative to the usual method is presented which does not involve equating the average radiated power to the average work done by the source. It is also shown that the acoustic field separates into two, a radiating field and a nonradiating retarded field, with the latter field possessing some interesting properties. The second topic is the demonstration that runaway solutions can occur when the acoustic source is mechanically coupled to the acoustic field. Using the exact solution, it is shown that this is an artifact arising from the inappropriate use of perturbation theory. The paper also discusses possible applications to electrodynamics.