The power spectra of low latitude (L<3), groundbased recordings of dayside geomagnetic pulsations in the 10--100 mHz band indicate that these pulsations come from discrete, driven field line resonances which are coupled to compressional, magnetohydrodynamic, cavity, or waveguide modes. The spectral bands of individual harmonics of the field line resonances seen by the magnetometers have envelopes which are typically 10's of mHz wide but also show a fine scale structure of almost equispaced peaks with separations of about 3 to 5 mHz. A WKB analysis of a cavity or waveguide model shows that the fine structure is likely due to field line resonances driven by waveguide modes with turning points within the plasmasphere and reflection at the dayside magnetopause. ¿ American Geophysical Union 1995