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The displacement of a wave disturbance p...

The displacement of a wave disturbance propagating in the positive x-direction is given by
`y =(1)/(1 + x^(2))`at `t = 0` and `y =(1)/(1 +(x - 1)^(2))` at `t =2s`
where, `x` and `y` are in meter. The shape of the wave disturbance does not change during the propagation. what is the velocity of the wave?

Text Solution

Verified by Experts

Let the wave velocity is `v` towards right.
(Displacement at `t = 0, x = x`)
=[Displacement at `t = 2 s, x = x + v(2)`]
`rArr (1)/(1 + x^(2)) = (1)/(1+(1+ x + 2v)^(2)`
`rArr v = -0.5 m//s`.
The negative sign indicates that wave is travelling towards left.
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