All the expressions above are for progressive waves travelling, with
celerity 
, in the positive x-direction. For each situation
considered the real part of the interface has the form
and the velocity has the form (where we are now considering only the real part)
where 
and 
are also
functions of the frequency and
wavenumber and 
may be zero.
The corresponding expressions for a standing wave can be found by
considering the superposition of two waves travelling in opposite directions
with the same frequency and with half the amplitude 
. These
two waves have interfaces and velocities given by
The interface 
and the velocities 
and 
of the corresponding standing wave are
the sum of the two progressive waves:
Thus if a progressive wave is damped at a rate 
: 
then a standing wave will be damped at the same rate.
The ratio of the interface amplitude to the amplitudes of the
horizontal and vertical
velocities, 
and respectively, are the same for
progressive
and standing waves as is the frequency. The x and t dependence are different.