  We compute the entanglement entropy associated to the Hawking emission of a
$(1+1)$-dimensional acoustic black hole in a Bose-Einstein condensate. We use
the brick wall model proposed by 't Hooft, adapted to the momentum space, in
order to tackle the case when high frequency dispersion is taken in account. As
expected, we find that in the hydrodynamic limit the entropy only depends on
the size of the box in the near-horizon region, as for gravitational
$(1+1)$-dimensional black holes. When dispersion effects are considered, we
find a correction that depends on the square of the size of the near-horizon
region measured in units of healing length, very similar to the universal
correction to the entropy found in the case of spin-1/2 Heisenberg XX chains.
