  High spatial and temporal resolution images of a sunspot, obtained
simultaneously in multiple optical and UV wavelengths, are employed to study
the propagation and damping characteristics of slow magnetoacoustic waves up to
transition region heights. Power spectra are generated from intensity
oscillations in sunspot umbra, across multiple atmospheric heights, for
frequencies up to a few hundred mHz. It is observed that the power spectra
display a power-law dependence over the entire frequency range, with a
significant enhancement around 5.5 mHz found for the chromospheric channels.
The phase-difference spectra reveal a cutoff frequency near 3 mHz, up to which
the oscillations are evanescent, while those with higher frequencies propagate
upwards. The power-law index appears to increase with atmospheric height. Also,
shorter damping lengths are observed for oscillations with higher frequencies
suggesting frequency-dependent damping. Using the relative amplitudes of the
5.5 mHz (3 minute) oscillations, we estimate the energy flux at different
heights, which seems to decay gradually from the photosphere, in agreement with
recent numerical simulations. Furthermore, a comparison of power spectra across
the umbral radius highlights an enhancement of high-frequency waves near the
umbral center, which does not seem to be related to magnetic field inclination
angle effects.
