To investigate the interaction between hypersonic flow field and disturbance wave in free-stream

a high-order accuracy finite difference method was used to conduct directly numerical simulation of hypersonic transient flow field over a blunt cone under the action of slow acoustic wave. And Fourier frequency spectral analysis was used to study the temporal and spatial evolution of disturbance wave modes in boundary-layer. Results show that consecutive ∽-deformation appeares in bow shock and initial disturbance is enlarged greatly. The disturbance modes outside and inside the boundary-layer differ a lot. For spatial evolution (along the flow direction)

the low frequency perturbation modes are dominated within a nose radius; with the disturbance development from upstream to downstream

the high frequency components increase quickly and low frequency components are almost restrained from growth. The ratio between low frequency and high frequency components transforms quickly. In the downstream of the flow field

most of the low-frequency disturbance component are attenuated

or no longer increase; there only exists a special frequency range of unstable wave rapid growth in the boundary-layer. Viewed from the temporal evolution

the dependence of dominant mode on the excitation of upstream is bigger than that of the other mode. Mode competition exists in both the temporal and spatial evolution of disturbance wave modes in boundary-layer.