  Being directly observed in the Doppler shift and imaging data and indirectly
as quasi-periodic pulsations in solar and stellar flares, slow magnetoacoustic
waves offer an important seismological tool for probing many vital parameters
of the coronal plasma. A recently understood active nature of the solar corona
for magnetoacoustic waves, manifested through the phenomenon of wave-induced
thermal misbalance, led to the identification of new natural mechanisms for the
interpretation of observed properties of waves. A frequency-dependent damping
of slow waves in various coronal plasma structures remains an open question, as
traditional wave damping theories fail to match observations. We demonstrate
that accounting for the back-reaction caused by thermal misbalance on the wave
dynamics leads to a modification of the relationship between the damping time
and oscillation period of standing slow waves, prescribed by the linear theory.
The modified relationship is not of a power-law form and has the equilibrium
plasma conditions and properties of the coronal heating/cooling processes as
free parameters. It is shown to readily explain the observed scaling of the
damping time with period of standing slow waves in hot coronal loops.
Functional forms of the unknown coronal heating process, consistent with the
observed frequency-dependent damping, are seismologically revealed.
