This paper analyses the response and receptivity of the hypersonic boundary layer
over a wedge to free-stream disturbances including acoustic, vortical and entropy
fluctuations. Due to the presence of an attached oblique shock, the boundary layer is
known to support viscous instability modes whose eigenfunctions are oscillatory in the
far field. These modes acquire a triple-deck structure. Any of three elementary types
of disturbances with frequency and wavelength on the triple-deck scales interacts with
the shock to generate a slow acoustic perturbation, which is reflected between the
shock and the wall. Through this induced acoustic perturbation, vortical and entropy
free-stream disturbances drive significant velocity and temperature fluctuations within
the boundary layer, which is impossible when the shock is absent. A quasi-resonance
was identified, due to which the boundary layer exhibits a strong response to a continuum
of high-frequency disturbances within a narrow band of streamwise wavenumbers.
Most importantly, in the vicinity of the lower-branch neutral curve the slow acoustic
perturbation induced by a disturbance of suitable frequency and wavenumbers is in
exact resonance with a neutral eigen mode. As a result, the latter can be generated directly
by each of three types of free-stream disturbances without involving any surface
roughness element. The amplitude of the instability mode is determined by analysing
the disturbance evolution through the resonant region. The fluctuation associated
with the eigen mode turns out to be much stronger than free-stream disturbances due
to the resonant nature of excitation and in the case of acoustic disturbances, to the
well-known amplification effect of a strong shock. Moreover, excitation at the neutral
position means that the instability mode grows immediately without undergoing
any decay, or missing any portion of the unstable region. All these indicate that this
new mechanism is particularly efficient. The boundary-layer response and coupling
coefficients are calculated for typical values of parameters.