  The response of a medium to a sudden localized perturbation (a "splash") will
be explained for isotropic media within the framework of linear response
theory. In this theory splashes result from the interference of the collective
excitations of the medium, with the outcome determined by the interplay between
their phase and group velocities as well as the sign of the latter. The salient
features of splashes are controlled by the existence of extremal values of the
phase and the group velocities: the group velocity gives the expansion rate of
the locus of the points where new wavefronts nucleate or existing ones
disappear, while the phase velocity determines the large-time expansion rate of
a group of wavefronts. If the group velocity is negative in a spectral range
and takes on a minimal value within it, then converging wavefronts will be
present in the splash. These results are relevant to the studies of several
experimentally viable setups, such as a splash on the surface of deep water due
to a small pebble or a raindrop, a splash in the two-dimensional electron gas
caused by a short voltage pulse applied with the tip of a scanning tunneling
microscope, or a bulk splash in superfluid $^{4}He$ due to formation of an
electron bubble. Specifically, the gross features of the latter are determined
by five extremal velocities. Additionally, due to the existence of a negative
group velocity spectral range, some of the wavefronts in superfluid $^{4}He$
splash are converging.
