Local-density sound speed of a condensate ($c(\mathbf{r})=\sqrt{[\mu -V(\mathbf{r})]/m}$)

In occupied bulk regions where density-gradient energy is negligible, the stationary relation $g\rho =\mu -V$ gives speed of sound $c=\sqrt{g\rho /m}$. Empty regions do not have an imaginary physical speed of sound; the bulk condensate formula is simply inapplicable there.