  The influence of a weak random potential on the collective modes of a trapped
interacting Bose-Einstein condensate at zero temperature is calculated in the
limit when the correlation length of the disorder is smaller than the healing
length of the superfluid. The problem is solved in the Thomas-Fermi limit by
generalizing the superfluid hydrodynamic equations to allow for the presence of
weak disorder. We find that the disorder-induced frequency-shifts of the
low-energy excitations can be of the same order of magnitude as the beyond
mean-field corrections in the normal interaction recently observed
experimentally.
