Searching for the Second Harmonic

To mathematically model the oscillations of a spherical bubble, either the time-dependent volume V(t) or the radius R(t) can be used as the dependent variable. A recent exchange between the advocates of the volume approach and the radius approach concerns in apparent discrepancy in the predicted nonlinear acoustic emissions from a bubble subject to a time-periodic external pressure field. This letter attempts to resolve the discrepancy via an examination of the arguments offered by both sides. In addition, some general comments on nonlinear harmonic and subharmonic emissions from acoustically forced bubble oscillations are presented.