|Propagating slow waves are often observed in polar plume/inter plume regions and active region fan loops. These waves cause periodic disturbances in intensity and are mostly identified from the alternate slanted ridges in the space-time maps. One of the interesting features of these waves is that they get rapidly damped as they propagate along the supporting structure. Thermal conduction, compressive viscosity, radiation, gravitational stratification, and area divergence, are believed to be some of the causes for a change in the wave amplitude. From theoretical modelling, it was found that the thermal conduction and area divergence can account for the observed decay even when gravitation stratification is present. Our recent results indicate that the damping in these waves is frequency-dependent and it qualitatively supports the damping due to thermal conduction. Further, we did a detailed quantitative analysis which show different dependences of damping lengths on frequency in polar and on-disk regions. Comparison of these results with those expected from the linear wave theory suggests a significant contribution from sources other than thermal conduction for the damping of slow waves, particularly in the polar region.