For this case
, hence
(1.24) and (1.25) reduce to
and
, which imply S =
.
Moreover,
and
hence from (1.31)
.
Thus contours of S and M are straight parallel lines of
slope
on the x, t-plane.
It follows that
from (1.19) also depends only
on
.
It has the same spatial form for all t or the same temporal
form for all x.
An example is a plane acoustic wave.
If it were otherwise, then sound would not be a useful
mode of communication, since receivers at different
distances from a sound source would get different messages
unless
= constant.