  We consider the entropy associated to the phonons generated via the Hawking
mechanism in a sonic hole in a Bose-Einsten condensate. In a previous paper, we
looked at the (1+1)-dimensional case both in the hydrodynamic limit and in the
case when high-frequency dispersion is taken in account. Here, we extend the
analysis, based on the 't Hooft brick wall model, by including transverse
excitations. We show that they can cure the infrared divergence that appears in
the (1+1)-dimensional case, by acting as an effective mass for the phonons. In
the hydrodynamic limit, where high-frequency dispersion is neglected, the
ultraviolet divergence remains. On the contrary, in the dispersive case the
entropy not only is finite, but it is completely fixed by the geometric
parameters of the system.
