Slow waves are commonly observed on the entire solar atmosphere. Assuming a thin flux tube approximation, the cut-off periods of slow-mode magneto-acoustic-gravity waves that travel from the photosphere to the corona were obtained in Costa et al. (2018). In that paper, however, a typo in the specific heat coefficient at constant pressure $c_{mathrm{p}}$ value led to an inconsistency in the cut-off calculation, which is only significant at the transition region. Due to the abrupt temperature change in the region, a change of the mean atomic weight (by a factor of approximately two) also occurs, but is often overlooked in analytical models for simplicity purposes. In this paper, we revisit the calculation of the cut-off periods of magneto-acoustic-gravity waves in Costa et al. (2018) by considering an atmosphere in hydrostatic equilibrium with a temperature profile, with the inclusion of the variation of the mean atomic weight and the correction of the inconsistency aforementioned. In addition, we show that the cut-off periods obtained analytically are consistent with the corresponding periods measured in observations of a particular active region.
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