Question

Derive the expression for the particle displacement of a plane progressive harmonic wave. Prove that particle velocity is a head of particle displacement in phase by

Answer 1

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)