Numerical analysis was conducted for a hypersonic flow around a 5-degree half-angle sharp cone in order to examine wave propagation in the hypersonic boundary layer by computational fluid dynamics (CFD) and global stability analysis based on the computed flow field. Periodic signals were clearly found in the pressure fluctuations on the wall and moved downstream. The power spectrum of the wall pressure suggested that characteristic frequency appeared in the region predicted by linear stability theory for the second-mode waves, while the lower mode was also enhanced in the downstream side. Dynamic mode decomposition (DMD) as a global stability analysis was applied to the CFD data for finding the characteristic mode of which the frequency may be identified in the wall pressure spectrum since the DMD can extract the predominant modes with their growth rates and frequencies. The predominant dynamic modes obtained from the pressure field and those from the velocity field were different because the former depends on acoustic waves but the latter indicates entropy waves. The correlation of these modes may suggest the mode transfer in the hypersonic boundary layer.