  The equations describing a two-component cosmological fluid with linearized
density perturbations are investigated in the small wavelength or large $k$
limit. The equations are formulated to include a baryonic component, as well as
either a hot dark matter (HDM) or cold dark matter (CDM) component. Previous
work done on such a system in static spacetime is extended to reveal some
interesting physical properties, such as the Jeans wavenumber of the mixture,
and resonant mode amplitudes. A WKB technique is then developed to study the
expanding universe equations in detail, and to see whether such physical
properties are also of relevance in this more realistic scenario. The Jeans
wavenumber of the mixture is re-interpreted for the case of an expanding
background spacetime. The various modes are obtained to leading order, and the
amplitudes of the modes are examined in detail to compare to the resonances
observed in the static spacetime results. It is found that some conclusions
made in the literature about static spacetime results cannot be carried over to
an expanding cosmology.
