  We consider the dynamics of vortex strings and sound waves in superfluids in
the phenomenological Landau-Ginzburg equation. We first derive the vortex
equation where the velocity of a vortex is determined by the average fluid
velocity and the density gradient near the vortex. We then derive the effective
action for vortex strings and sound waves by the dual formulation. The
effective action might be useful in calculating the emission rate of sound
waves by moving vortex strings.

Condensed Matter