Studies of acoustic vibrations in nanometre-scale particles can provide fundamental insights into the mechanical properties of materials because it is possible to precisely characterize and control the crystallinity and geometry of such nanostructures. Metal nanoparticles are of particular interest because they allow the use of ultrafast laser pulses to generate and probe high-frequency acoustic vibrations, which have the potential to be used in a variety of sensing applications. So far, the decay of these vibrations has been dominated by dephasing due to variations in nanoparticle size. Such inhomogeneities can be eliminated by performing measurements on single nanoparticles deposited on a substrate, but unknown interactions between the nanoparticles and the substrate make it difficult to interpret the results of such experiments. Here, we show that the effects of inhomogeneous damping can be reduced by using bipyramidal gold nanoparticles with highly uniform sizes. The inferred homogeneous damping is due to the combination of damping intrinsic to the nanoparticles and the surrounding solvent; the latter is quantitatively described by a parameter-free model.