Aims. We focus on a polar coronal hole region to find any evidence of dissipation of propagating slow magneto-acoustic waves. Methods. 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 Å and 193 Å passbands. We performed intensity distribution statistics in time domain at several locations in the polar coronal hole. Results. 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 of intensity fluctuations in time show nearly Gaussian distributions. Conclusions. 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.