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?

Explanation

In terms of power function of pulse is given by `y=(a)/(b+(x-+vt)^(2))`
A comparison of given equations with the above reveals
`(x-+vt)^(2)=(x-1)^(2)` for `t=2s`
i.e., `vt=1` for `t=2s`, i.e., `v=((1)/(2))=0.5m//s`