  A dark soliton becomes unstable when it is incident on a background density
gradient, and the induced instability results in the emission of sound.
Detailed quantitative studies of sound emission are performed for various
potentials, such as steps, linear ramps and gaussian traps. The amount of sound
emission is found to be a significant fraction of the soliton energy for
typical potentials. Continuous emission of sound is found to lead to an
apparent deformation of the soliton profile. The power emitted by the soliton
is shown to be parametrised by the square of the displacement of the centre of
mass of the soliton from its density minimum, thus highlighting the
significance of the inhomogeneity-induced soliton deformation.
