Consider a progressive wave train 
for which
only, hence 
and
depend only on k (or L or T = 
.
The case considered is for a wave type where increases
with T (as in a short gravity wave) and 
for given T.
The propagation paths of given periods (say 
and 
)
are straight lines on the 
- plane since
is constant for given T.
However, since increases with T for this case, the
number of waves between the propagation paths for and
increases with time, i.e. the dispersion manifests itself
in the creation of more waves.
However, if the total energy is conserved, then this must be spread
among all the waves and the amplitudes of the waves accordingly must
decrease with time.
The region of the maximum amplitude (i.e., the maximum of the group
envelope) advances at the group speed appropriate to the period of
these waves near the maximum (dashed line in the above figure).
Individual waves, such as those identified as A, B, C in the figure, advance faster than the group as a whole and eventually will disappear as they propagate out of the region of significant energy density. New waves are formed in the rear to more than offset the number lost through the front of the wave group.