We present the results of shock-turbulence interactions in hypersonic flows in air using direct numerical simulation (DNS) and linear interaction analysis (LIA). The DNS calculations are conducted with the HTR solver for various shock strengths (Mach number), turbulence intensities and scales (turbulent Mach number and Taylor-scale Reynolds number). The HTR solver is a Navier–Stokes solver purpose-built for conducting direct numerical simulations of hypersonic flows characterized by high enthalpies (M. Di Renzo et al. Computer Physics Communications 261, 107733, 2021). These results are compared with linear theory in the fast-reaction limit. It necessitates the prior determination of equilibrium conditions downstream of the shock for the unperturbed scenario, a task facilitated by the Combustion Toolbox. Subsequent to this, we address the perturbed scenario which encompasses weakly isotropic vortical disturbances, employing a refined Fourier analysis technique. In this respect, this work is a natural extension of (C. Huete et al., Phys. Fluids, 33, 086111, 2021) that made use of LIA to study the amplification of turbulence across hypersonic shocks moving in single-species diatomic gases. The primary focus of this study is the examination of how dilatational energy ahead of the shock influences the Reynolds stress components. Furthermore, we explore the impact of vibrational excitation on turbulence amplification, employing two distinct thermodynamic models: the calorically perfect gas model and the calorically imperfect gas model with frozen chemistry.