Quiet-time compressional Pc5 pulsations observed within the dawnside equatorial magnetosphere often exhibit frequency doubling, in which the northward component of the magnetic field oscillates at frequencies twice as great as those of the azimuthal or radial component. We use THEMIS-A ESA plasma velocity moments and gyrophase observations of suprathermal ions on November 7, 2007 to argue against proposed explanations for the frequency doubling that invoke either the radial or azimuthal sloshing of plasma and magnetic field gradients past the observing spacecraft, or the combined effects of non-adiabatic radial flux gradients and drift-bounce resonances, in favor of an explanation in terms of meridional oscillations in the equatorial line of nodes for antisymmetric field-line motion. The latter enables near-equatorial spacecraft to observe two magnetic field strength enhancements, one north and one south of the line of nodes, per wave cycle. Many mechanisms have been proposed to account for the compressional Pc5 pulsations themselves. We show that their characteristics are compatible with predictions for the ballooning-mirror instability. In combination with the antisymmetric electric fields expected for the instability, drift shell splitting on stretched magnetic field lines results in non-resonant suprathermal ions streaming alternately parallel and antiparallel to the magnetic field. The significance of the pulsations lies in the possibility that they may further energize already energetic ions in the radiation belts via drift-bounce resonances.