A wave in which the crest and trough or compression and rarefaction travel toward is called progressive wave. In progressive wave, the crest and trough or compression and rarefaction changes its position continuously and the velocity of move equals to the velocity of wave.
Consider a wave travelling along positive X-axis with a velocity “v” as in figure. If y be the displacement of the particle at “o” then,
Consider a particle at “p” which is at a distance x from point “p”. Since the particle at “o” and “p” are not in the same phase. Then displacement of the particle “y” given by,