The lifetimes of the acoustic vibrations of metal nanostructures depend sensitively on the properties of the environment, such as the acoustic impedance and viscosity. In order to accurately study these effects, they have to be separated from the damping processes that are inherent to the nanostructure. Here we show that this can be done experimentally by investigating individual gold nanowires suspended over a trench in air and liquid environments. The experiments were done by ultrafast pump-probe microscopy, recording transient absorption traces at the same point on the nanowire in both environments. These first experiments were performed with water, and the measured vibrational quality factors due to the presence of water were compared to continuum mechanics calculations for a cylinder in a homogeneous environment. Good agreement was found between the experimental quality factors and the calculated values. The continuum mechanics analysis shows that damping is dominated by the acoustic impedance of the solvent rather than by its viscosity for the nanowires in the present experiments. This experimental technique opens up the possibility of studying the effect of viscosity on the high frequency vibrational motions of nanostructures for a variety of liquids.