Medium-frequency waves in the ion-electron two-fluid plasma with frequencies between the electron gyrofrequency and the ion gyrofrequency are studied. The dispersion relations and the Friedrichs diagrams of the group velocities are plotted with color-coded electric-field information. The group-velocity distributions and the properties of the electric fields can help us explain the observed dynamic spectra of waves when the waves are generated by a localized broadband disturbance. Possible sources of such disturbances are explored. One of them is the magnetic trapped energetic electrons with pitch angles greater than 70°. The dynamic spectra of the waves generated by these energetic electrons are ray-angle dependent. For the ray angle greater than 2°, the dynamic spectra of the rising-tone quasielectromagnetic chorus waves are characterized by a frequency gap near half of the electron gyrofrequency. The dynamic spectra of the rising tone chorus waves without the frequency gap can only be found when either the ray angle is less than 2° or when the lower-band chorus waves are quasielectrostatic. Lightning from the neutral atmosphere provides another type of localized disturbance. Depending on the magnetic latitude, lightning can result in two types of falling-tone electromagnetic whistler waves. One of them is the low- k ⊥ whistler waves with highly field-aligned phase velocity and group velocity. The other is the high- k ⊥ whistler waves with highly field-aligned group velocity but with phase velocity almost perpendicular to the background magnetic field. The results of this study will provide a road map for future studies of the waves in this frequency range.