The effect of thermal boundary conditions on linear stability of stationary convective flow in a horizontal layer subjected to the longitudinal temperature gradient and propagating acoustic wave is studied. Two-dimensional shear instability and three-dimensional monotonic and oscillatory instabilities are analyzed. The stability maps for different acoustic Reynolds number values with respect to different perturbation types are obtained. The stabilization under the influence of acoustic wave at low Prandtl numbers is demonstrated. It takes place when two-dimensional shear or three-dimensional oscillatory instability modes are most dangerous. Three-dimensional monotonic mode is destabilized by acoustic influence. Energy analyses for two-dimensional and monotonic three-dimensional modes of instability is carried out. (C) 2015 Elsevier Ltd. All rights reserved.