Time evolution of the standing fast excitation given by Eqs. (33)–(34) with the density model given by Eq. (35). The continuous line represents the v_x component, while the v_z component is plotted with a dotted line (its amplitude has been multiplied by a factor 10 for visualisation purposes). The vertical dashed lines represent the locations of the transition between the corona and photosphere. For this simulation ka = π/9, v₀/v_A = 1, k_xa = 1.5, c_s/v_A = 0.2, ρ_ph/ρ_c = 10⁸, w/a = 0.25.