  We study wave propagation in a draining bathtub: a fluid-mechanical black
hole analogue in which perturbations are governed by a Klein-Gordon equation on
an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub
geometry possesses an (effective) horizon, an ergosphere and null circular
orbits. We propose that a `pulse' disturbance may be used to map out the
light-cone of the effective geometry. First, we apply the eikonal approximation
to elucidate the link between wavefronts, null geodesic congruences and the
Raychaudhuri equation. Next, we solve the wave equation numerically in the time
domain using the method of lines. Starting with Gaussian initial data, we
demonstrate that a pulse will propagate along a null congruence and thus trace
out the light-cone of the effective geometry. Our numerical results reveal
features, such as wavefront intersections, frame-dragging, winding and
interference effects, that are closely associated with the presence of null
circular orbits and the ergosphere.
