  We give an account of the gravitational memory effect in the presence of the
exact plane wave solution of Einstein's vacuum equations. This allows an
elementary but exact description of the soft gravitons and how their presence
may be detected by observing the motion of freely falling particles. The
theorem of Bondi and Pirani on caustics (for which we present a new proof)
implies that the asymptotic relative velocity is constant but not zero, in
contradiction with the permanent displacement claimed by Zel'dovich and
Polnarev. A non-vanishing asymptotic relative velocity might be used to detect
gravitational waves through the "velocity memory effect", considered by
Braginsky, Thorne, Grishchuk, and Polnarev.
