  We consider a system of interacting bosons in one dimension at a two-body
resonance. This system, which is weakly interacting, is known to give rise to
effective three-particle interactions, whose dynamics is similar to that of a
two-dimensional Bose gas with two-body interactions, and exhibits an identical
scale anomaly. We consider the experimentally relevant scenario of a
harmonically trapped system. We solve the three-body problem exactly and
evaluate the shifts in the frequency of the lowest compressional mode with
respect to the dipole mode, and find that the effect of the anomaly is to
increase the mode's frequency. We also consider the weak-coupling regime of the
trapped many-boson problem and find, within the local density approximation,
that the frequency of the lowest compressional mode is also shifted upwards in
this limit. Moreover, the anomalous frequency shifts are enhanced by the higher
particle number to values that should be observable experimentally.
