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?

Answer

A

Explanation

As `y = (1)/(1 + x)^(2)`
At `t = 0 and x = 0` , we get `y = 1`.
Also at `t = 2 and x = 1, again y = 1`.
The wave pulse has travelling a distance of `1m` in `2sec`.
:. `v = (1)/(2) = 0.5 m//s^(-1)`