  When impacted by a rigid object, a thin elastic membrane with negligible
bending rigidity floating on a liquid pool deforms. Two axisymmetric waves
radiating from the impact point propagate. In the first place, a longitudinal
wave front -- associated with in-plane deformation of the membrane and
traveling at constant speed -- separates an outward stress free domain with a
stretched but flat domain. Then, in the stretched domain a dispersive
transverse wave travels at a wave speed that depends on the local stretching
rate. We study the dynamics of this fluid-body system and we show that the wave
dynamics is similar to the capillary waves that propagate at a liquid-gas
interface but with a surface tension coefficient that depends on impact speed.
We emphasize the role of the stretching in the membrane in the wave dynamics
but also in the development of a buckling instability that give rise to radial
wrinkles.
