1.

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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