It has been seen in chapter 6 that
a progressive wave and a standing wave, with the same wavelength and amplitude,
have the same z-dependence and a different x and t dependence.
This means that we can use the results obtained in chapter 7 to
initialise a progressive wave. This is done by first initialising a standing
wave,
as described in section 7.2,
and allowing it to
evolve for a quarter period. The magnitude of the horizontal
velocity 
is then found at 
and
the magnitude of the vertical velocity 
at
. The density profile 
is found at any value of
x. A progressive wave can then be initialised with
density 
and velocities 
and 
.
The interface 
is imposed by shifting each column
of sites by an amount 
to produce the interface. Values shifted off
the grid are discarded. Sites near the boundary which
are not assigned a new value
retain their original value.