  We derive the dynamics of magnetohydrodynamic waves in two-fluid partially
ionized plasmas and to compare the results with those obtained under
single-fluid description. Two-fluid magnetohydrodynamic equations are used,
where ion-electron plasma and neutral particles are considered as separate
fluids. Dispersion relations of linear magnetohydrodynamic waves are derived
for simplest case of homogeneous medium. Frequencies and damping rates of waves
are obtained for different parameters of background plasma. We found that two-
and single-fluid descriptions give similar results for low frequency waves.
However, the dynamics of MHD waves in two-fluid approach is significantly
changed when the wave frequency becomes comparable or higher than ion-neutral
collision frequency. Alfven and fast magneto-acoustic waves attain their
maximum damping rate at particular frequencies (for example, the peak frequency
equals 2.5 ion-neutral collision frequency for 50 % of neutral Hydrogen) in
wave spectrum. The damping rates are reduced for higher frequency waves. The
new mode of slow magneto-acoustic wave appears for higher frequency branch,
which is connected to neutral hydrogen fluid. The single-fluid approach
perfectly deals with slow processes in partially ionized plasmas, but fails for
time-scales smaller than ion-neutral collision time. Therefore, two-fluid
approximation should be used for the description of relatively fast processes.
Some results of single-fluid description, for example the damping of
high-frequency Alfven waves in the solar chromosphere due to ion-neutral
collisions, should be revised in future.
