Wave theories of heating of the chromosphere, corona and solar wind due to photospheric fluctuations are strengthened by the existence of the wave coherency observed up to the transition region. The coherency of intensity oscillations of solar spicules was explored using the Solar Optical Telescope (SOT) on the Hinode spacecraft with increasing height above the solar limb in the active region. We used time sequences near the south-east region from the Hinode/SOT for the Ca II H line obtained on 2015 April 3 and applied the de-convolution procedure to the spicule to illustrate how effectively our restoration method works on fine structures such as spicules. Moreover, the intensity oscillations at different heights above the solar limb were analysed through wavelet transforms. Afterwards, the phase difference was measured between oscillations at two heights in search of evidence for coherent oscillations. The results of the wavelet transformations revealed dominant period peaks for 2, 4, 5.5 and 6.5 min at four separate heights. The dominant frequencies for a coherency level higher than 75 per cent were found to be around 5.5 and 8.5 mHz. Mean phase speeds of 155-360 km s (1) were measured. We found that the mean phase speeds increased with height. The results suggest that the energy flux carried by coherent waves into the corona and heliosphere may be several times larger than previous estimates that were based solely on constant velocities. We provide compelling evidence for the existence of upwardly propagating coherent waves.