We present EIS/Hinode & SUMER/SoHO joint observations allowing the first spectroscopic detection of accelerating disturbances as recorded with coronal lines in inter-plume and plume regions of a polar coronal hole. From time-distance radiance maps, we detect the presence of propagating disturbances in a polar inter-plume region with a period of 15 to 20 min and a propagation speed increasing from 130+/-14 km/s just above the limb, to 330+/-140 km/s around 160" above the limb. These disturbances

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... can also be traced to originate from a bright region of the on-disk part of the coronal hole where the propagation speed was found to be in the range of 25+/-1.3 to 38+/-4.5 km/s, with the same periodicity. These on-disk bright regions can be visualized as the base of the coronal funnels. The adjacent plume region also shows the presence of propagating disturbance with the same range of period but with propagation speeds in the range of 135+/-18 to 165+/-43 km/s only. To our knowledge, this result provides first spectroscopic evidence of acceleration of propagating disturbances in the polar region close to the Sun (within 1.2 solar radii). We suggest that the waves are likely either Alfv'enic or fast magnetoacoustic in the inter-plume and slow magnetoacoustic in plume regions. This may lead to the conclusion that inter-plumes are preferred channel for the acceleration of the fast solar wind.