  The subject of this study is oscillations in the lower atmosphere in
coronal-hole regions, where the conditions are favorable for propagation
between the atmospheric layers. Based on spectroscopic observations in
photospheric and chromospheric lines, we analysed the features of the
oscillations that show signs of propagation between layers of the solar
atmosphere. Using the cross-spectrum wavelet algorithm, we found that both
chromospheric and photospheric signals under coronal holes share a range of
significant oscillations of periods around five minutes, while the signals
outside of coronal holes show no mutual oscillations in the photosphere and
chromosphere. The phase shift between the layers indicates a predominantly
upward propagation with partial presence of standing waves. We also tested the
assumption that torsional Alfv\'en waves propagating in the corona originate in
the lower atmosphere. However, the observed line-width oscillations, although
similar in period to the Alfv\'en waves observed earlier in the corona of
open-field regions, seem to be associated with other MHD modes. If we assume
that the oscillations that we observed are related to Alfv\'en waves, then
perhaps this is only through the mechanisms of the slow MHD wave
transformation.
