but could you please derive them

shanmukhaadithyaakkiraju Consider that , a wave form is traveling right along the x axis from left.

Since the particles are oscillating in simple harmonic motion ,then It will maintain y = A sinθ

When t =0, point P is at x distance right from O has phase difference, then oscillation of particle at P maintain y = A sin

Phase difference at λ is 2 π ; at x is (2π/ λ)x
So, y = A sin (2π/ λ)x

Phase velocity - v ; time - t

Wave travels right with v at t then phase lag between particle at origin O and particle of right go on increasing since wave proceeds away from O towards right.

The equation of motion of particle at right is :

y = A sin [( 2π/ λ ) x - ωt] = A sin (kx - ωt)

For left is :

y = A sin ( kx + ωt)


Hope it helps