Comment on 'Sound velocity and multibranch Bogoliubov spectrum of an elongated Fermi superfluid in the BEC-BCS crossover'

The work by T. K. Ghosh and K. Machida [Phys. Rev. A 73, 013613 (2006) and cond-mat/0510160] on the sound velocity in a cylindrically confined Fermi superfluid obeying a power-law equation of state is shown to make use of an improper projection of the sound wave equation. This inaccuracy fully accounts for the difference between their results and those previously reported by Capuzzi [Phys. Rev. A 73, 021603(R) (2006) and cond-mat/0509323]. In this Comment, we show that both approaches lead exactly to the same result when the correct weight function is used in the projection. Plots of the correct behavior of the phonon and monopole-mode spectra in the BCS and unitary limits and in the BEC regime are also shown.