Consider a waves moves along the positive direction of x with a velocity v. Let the displacement at any instant at time t at x = 0 is
y = a sin ωt
Here, v to be the wave velocity. We have form for λ displacement phase change is 2π so for x displacement the phase change Q = \(\frac {2π}λ\)x so we get
y = a sin (ωt - Q)
y = a sin (ωt - \(\frac {2π}λ\)x)
y = t (vt - x)
y = a sin \(\frac {2π}λ\) (vt - x)