The dissipation of an elastic wave in dry and wet glass bead packings is measured using multiple sound scattering. The interplay of a linear viscoelastic loss and a nonlinear frictional one is observed in dry media. The Mindlin model provides a qualitative description of the experiment, but fails to quantitatively account for the data due to grain roughness. In weakly wet media, we find that the dissipation is dominated by a linear viscous loss due to the liquid films trapped at the grain surface asperities. Adding more liquid enables us to form the capillary menisci but does not increase the energy loss.