  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.
