  We address theoretically the puzzling discontinuity of the radial quadrupole
mode frequency observed in a trapped Fermi gas across the BEC-BCS crossover. We
apply the scaling transformation to a two-channel model of a resonant Fermi
superfluid and argue that the frequency downshift in the crossover region is
due to Feshbach coupling of the molecular Bose-Einstein condensate (BEC) to the
surrounding Fermi sea. The Bose and Fermi components of the gas act as coupled
macroscopic oscillators. The frequency jump corresponds to the point where the
closed-channel molecules are entirely converted into the Fermi sea. This
implies linear scaling of the "critical" detuning between the scattering
channels with the Fermi energy, which can be readily verified in an experiment.
