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Establish a relation between wave speed and particle speed. |
Answer» Equation of the wave is represented by: y = A sin (ωt - kx) Differentiating it with respect to t, we get O = A cos (ωt - kx) [ω - k.dx/dt] And the velocity of wave, dx/dy = ω/k Similarly the velocity of the particle dx/dy = ωA cos (ωt - kx) And the acceleration of a point particle is given by d2y/dt2 = ω2 A sin (ωt - kx) ....(i) Differentiating the y with respect to x dx/dy = -Ak cos (ωt - kx) and d2y/dx2 = -Ak2 sin (ωt - kx) ...(ii) From eqn. (i) and eqn. (ii) we get d2y/dx2 = v2 d2y/dx2 |
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