The present paper focuses on the analysis of aero-acoustics characteristic by appling different four boundary conditions. The high-order and high-resolution numerical schemes are used for discrete accurate computation of compressible flow. The four boundary conditions include extrapolation, characteristic boundary condition, zonal characteristic boundary condition. These boundary conditions are applied to the computation of two dimensional circular cylinder flows with Mach number of 0.3 and Reynolds number of 400. The computation results are validated against measurement data and other computation results for the Strouhal frequency of vortex shedding, the mean drag coefficient and root-mean-square lift for the unsteady periodic flow regime. The characteristics of secondary frequency is predicted by three kinds of boundary conditions.