A high-order spectral difference flow solver is used to perform direct numerical simulations (DNS) of a hypersonic laminar boundary layer on an ultrasonically absorptive coating (UAC), in order to analyze the stabilizing effects of such a material on the laminar-turbulent transition. The UAC is modeled in the simulations by a time-domain impedance boundary condition, which is calibrated to replicate the acoustic response of the UAC over a broad spectral range. The frequency-dependence damping effectiveness is investigated, as are any other side effects the porous coating might have on the mean flow. It is found that the second-mode instability, which dominates the high-Mach number flow regime, is strongly suppressed for all excitation frequencies considered. The DNS solutions are also found to compare favorably with linearized stability theory. Finally, a side effect of theUACis the modification of the medium dispersive properties and the change of the perturbation group velocity.