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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 |
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Answer» 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) |
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