Power Spectral Density (PSD) in wavenumber-frequency space for the vertical flow speed v_z, taken at various heights in the computational domain; Z = −2 Mm (upper-convection zone), Z = 0 Mm (photosphere), Z = 4 Mm (above the chromosphere), and Z = 12 Mm (low corona). For the photospheric slice, the typical acoustic-gravity wave cut-off frequencies are indicated, given the average pressure, density, and magnetic field strength. Classically, waves in the shaded region are evanescent (under the assumption of a stably stratified atmosphere). For completeness the lamb-mode (ω  =  c_sk_⊥) and f-mode () dispersion relations are shown with dotted and dash-dotted lines respectively. Elsewhere, the pressure-modes generated due to the computational set-up are highlighted. These ‘box modes’ have a clear impact on the PSD of the velocity fluctuations up in the low corona.