Wavelet phase difference between the photospheric and chromospheric umbral velocities around 08:13 UT. Top panel: phase difference at every location in the selected region. The power of the WCS of frequencies higher than that indicated by the vertical dotted line is above the 95% confidence level. The blue line represents the expected phase difference for linear wave propagation in a gravitationally stratified atmosphere with radiative losses (T₀ = 4160 K, Δz = 900 km, τ_R = 20). Bottom panel: coherence of the phase difference. The phase differences where the confidence is below 95% (frequencies below the vertical dotted line in the top panel) and with coherence below the threshold (horizontal dashed line in the bottom panel) are unreliable.