Prop-2-yn-1-ol NMR spectrum differences
The chemical shift of protons in polar groups can vary a lot between solvents of different polarity, because the average electron density around the proton changes. Hydrogen bonding etc. A nice overview can be gotten from the article NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist. 

For example water shifts from 4.79ppm in water($D_2O$) down to 0.4ppm in d6-benzene. Or the OH group of ethanol from 0.5 in benzene to 1.3 in chloroform to 4.6(!) in DMSO. The methyl and methene groups otoh just shift by 0.3 ppm max. between solvents.

The signals in your spectra are sharp, because there is either a fast exchange, meaning the peak comes at the average CS of both positions of the proton, or no exchange. Slow exchange (either statistically or because the reaction is slow) leads to broadening.

(Slow = exchange happens on the NMR timescale, a millisecond plus/minus a few decades, depending on your $T_{2}$ etc.)