We focus on a polar coronal hole region to find any evidence of dissipation
of propagating slow magneto-acoustic waves. We obtained time-distance and
frequency-distance maps along the plume structure in a polar coronal hole. We
also obtained Fourier power maps of the polar coronal hole in different
frequency ranges in 171~\AA\ and 193~\AA\ passbands. We performed intensity
distribution statistics in time domain at several locations in the polar
coronal hole. We find the presence of propagating slow magneto-acoustic waves
having temperature dependent propagation speeds. The wavelet analysis and
Fourier power maps of the polar coronal hole show that low-frequency waves are
travelling longer distances (longer detection length) as compared to
high-frequency waves. We found two distinct dissipation length scales of wave
amplitude decay at two different height ranges (between 0--10 Mm and 10--70 Mm)
along the observed plume structure. The dissipation lengths obtained at higher
height range show some frequency dependence. Individual Fourier power spectrum
at several locations show a power-law distribution with frequency whereas
probability density function (PDF) of intensity fluctuations in time show
nearly Gaussian distributions. Propagating slow magneto-acoustic waves are
getting heavily damped (small dissipation lengths) within the first 10~Mm
distance. Beyond that waves are getting damped slowly with height. Frequency
dependent dissipation lengths of wave propagation at higher heights may
indicate the possibility of wave dissipation due to thermal conduction,
however, the contribution from other dissipative parameters cannot be ruled
out. Power-law distributed power spectra were also found at lower heights in
the solar corona, which may provide viable information on the generation of
longer period waves in the solar atmosphere.Comment: corrected typos and grammar, In press A&
