Kink wave cutoff frequency as a function of altitude, from analytical models (see legend, left column) and from our numerical simulations (right column). We show the analytical predictions of Spruit (1981, SP81), Snow et al. (2017, Sn17), and Lopin & Nagorny (2017, LN17) (coloured lines). For the last model, we computed the cutoff frequency for different values of z₀, the ‘base of the atmosphere’. We show the cutoff altitude (z_c) for the four simulations that we ran with different driver frequencies (black symbols). The cutoff altitudes are computed with different thresholds t_r, indicated in the legend and described in the text.