  Compressible disturbances propagate in a plasma in the form of
magnetoacoustic waves driven by both gas pressure and magnetic forces. In
partially ionized plasmas the dynamics of ionized and neutral species are
coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves
propagating through a partially ionized medium are affected by the ion-neutral
coupling. The degree to which the behavior of the classic waves is modified
depends on the physical properties of the various species and on the relative
value of the wave frequency compared to the ion-neutral collision frequency.
Here, we perform a comprehensive theoretical investigation of magnetoacoustic
wave propagation in a partially ionized plasma using the two-fluid formalism.
We consider an extensive range of values for the collision frequency,
ionization ratio, and plasma $\beta$, so that the results are applicable to a
wide variety of astrophysical plasmas. We determine the modification of the
wave frequencies and study the frictional damping due to ion-neutral
collisions. Approximate analytic expressions to the frequencies are given in
the limit case of strongly coupled ions and neutrals, while numerically
obtained dispersion diagrams are provided for arbitrary collision frequencies.
In addition, we discuss the presence of cutoffs in the dispersion diagrams that
constrain wave propagation for certain combinations of parameters. A specific
application to propagation of compressible waves in the solar chromosphere is
given.
