The nature of the anomalies observed in the helium-atom scattering (HAS) and electron energy-loss (EELS) spectra of hydrogenated W(110) surfaces is investigated by calculating the full dispersion of the Rayleigh mode, using density-functional perturbation theory. We find excellent agreement between our calculations and the upper anomalous branch which is observed with both HAS and EELS. The lower branch-which is only detected by HAS-is instead not predicted. A hitherto unrecognized mechanism possibly responsible for the appearance of the second branch is proposed.