  The presence of neutral species in a plasma has been shown to greatly affect
the properties of magnetohydrodynamic waves. For instance, the interaction
between ions and neutrals through momentum transfer collisions causes the
damping of Alfv\'en waves and alters their oscillation frequency and phase
speed. When the collision frequencies are larger than the frequency of the
waves, single-fluid magnetohydrodynamic approximations can accurately describe
the effects of partial ionization, since there is a strong coupling between the
various species. However, at higher frequencies, the single-fluid models are
not applicable and more complex approaches are required. Here, we use a
five-fluid model with three ionized and two neutral components, which takes
into consideration Hall's current and Ohm's diffusion in addition to the
friction due to collisions between different species. We apply our model to
plasmas composed of hydrogen and helium, and allow the ionization degree to be
arbitrary. By means of the analysis of the corresponding dispersion relation
and numerical simulations, we study the properties of small-amplitude
perturbations. We discuss the effect of momentum transfer collisions on the
ion-cyclotron resonances and compare the importance of magnetic resistivity,
ion-neutral and ion-ion collisions on the wave damping at various frequency
ranges. Application to partially ionized plasmas of the solar atmosphere are
performed.
