  In the present work, we analyze the corrections caused by an anomalous
dispersion relation, suggested in several quantum gravity models, upon the
speed of sound in a weakly interacting Bose--Einstein Condensate, trapped in a
potential of the form $V(r)\sim r^{2}$. We show that the corresponding ground
state energy and consequently, the associated speed of sound, present
corrections respect to the usual case, which may be used to explore the
sensitivity to Planck--scale effects on these relevant properties associated
with the condensate. Indeed, we stress that this type of macroscopic bodies may
be more sensitive, under certain conditions, to Planck--scale manifestations
than its constituents. In addition, we prove that the inclusion of a trapping
potential, together with many--body contributions, improves the sensitivity to
Planck--scale signals, compared to the homogeneous system.
