stationary waves Interference of two waves of same frequency traveling in opposite direction, results in zero energy flow. Particles of the medium vibrate with varying amplitude. This often happens when a wave is reflected back along the same path, as in the case of waves on a string or air column inside a pipe.

If the wave equation for +x direction is,

y₊ = a sin (w t-kx)

and for -x direction,

y_- = a sin (w t+kx)

where we have substituted -x for x. Adding the two equations,

y =y₊+y_- =2a sin (w t) cos (kx) (s19)

which shows that amplitude varies as 2a cos (kx). At points of maximum amplitude (anti node) the amplitude is 2a, while at the minimum it is zero (node).The distance between a node and its adjoining antinode is l /4.