Waves in the 1-Hz frequency band are often seen by both ground observations of magnetic fields and satellite observations of electric and magnetic fields. Comparison between the ground and satellite observations of these waves is complicated by the fact that such waves must pass through the strongly inhomogeneous and collisional ionosphere. While this is true for ULF waves at lower frequencies as well, waves near 1 Hz are more strongly affected since their wavelength is comparable with the scale size of the ionospheric minimum in the Alfvén speed; therefore they can be trapped and, in the case of compressional waves, ducted in this region of low Alfvén speed. A model is developed to describe the propagation of waves in this frequency range through the ionosphere. A variety of ionospheric models for this propagation have been used to assess the ground signatures of these waves under various conditions. This model is used to study the transient response of the ionosphere to an increase in the field-aligned current. The strength of the ground signal depends strongly on both the Pedersen and Hall conductivities of the ionosphere. Ground signatures are strongest when the Hall conductivity is greater than the Pedersen conductivity. An underdamped signature is seen when the conductivities are high, while an overdamped waveform results for low conductivities. The fundamental mode of the shear mode Alfvén resonator is found not to couple to a ducted compressional wave, while higher harmonics of the wave are readily ducted through the ionospheric waveguide.