If the direction of propagation is opposite we can get standing waves.
For simplicity we take the case of equal amplitudes :
The x and t dependence has factorized and I no longer have a
traveling wave. This wave is special in that the amplitude of the
oscillatory disturbance varies as a function of distance.
In particular at some
points it vanishes.
A standing wave does not propagate but is characterized by a
pattern of nodes and maxima in the time dependent oscillation. The
nodes are separated by distance, 
, such that
We have a number of neat experiments illustrating standing waves which I briefly describe in the following.