Oscillation frequency (upper plot) and growth rate (lower plot) of the modes ℓ = 1 calculated in units of the post-shock frequency v_sh/r_sh, for γ = 4/3, as a function of the shock distance in the model with cooling using (α, β) = (3/2, 5/2) (dashed lines) and in the adiabatic approximation (solid lines). The fundamental mode (in red) and the first three overtones (green, orange, blue) are displayed. The grey horizontal line in the upper plot indicates the Lamb frequency at the shock. The fundamental mode becomes dominated by higher overtones as its frequency becomes too low for acoustic propagation (${\omega }_r<{\omega }_{\mathrm{Lamb}}^{\mathrm{sh}}$).