Two-dimensonal unsteady compressible flows are studied numerically for the caseof interactions between a initially steady flow and a periodically perturbed compressible flow. Two numerical schemes employed: implicit LU-ADI FDM & explicit Roe`s FDS FVM. The numerical methods are tested for four basic flows with appropriate numerical boundary conditions; acoustic wave propagations through a uniform duct with inflow excitation, through a uniform duct with wall excitation, through a bump inside a duct and a transonic steady flow over a circular arc bump duct. It turns out the methods are suitable for the simulation of low frequency wave propagations through the flow medium as well as for steady flow. Finally, calculations are carried out for the flow over an arc bump channel with periodically perturbed inflow conditions near transonic speeds. In general, periodic motions in the flow fields, including the shock on the bump. are clearly observed for the harmonic perturbation, At the region far downstream from the bump, a harmonic motion is observed. However, near the shock regions, higher hamonic motions are also observed for the harmonic perturbation. This might be due to the nonlinear and area-change effects near the bump.