  We have performed self-consistent calculations of the dynamical response of
the (111) surface of the noble metals Cu, Ag, and Au. Our results indicate that
the partially occupied surface-state band in these materials yields the
existence of acoustic surface plasmons with linear dispersion at small wave
vectors. Here we demonstrate that the sound velocity of these low-energy
collective excitations, which had already been predicted to exist in the case
of Be(0001), is dictated not only by the Fermi velocity of the two-dimensional
surface-state band but also by the nature of the decay and penetration of the
surface-state orbitals into the solid. Our linewidth calculations indicate that
acoustic surface plasmons should be well defined in the energy range from zero
to $\sim 400$ meV.
