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

At `t=0,y=(1)/((1+x)^(2))`
For y to be maximum, `x=0`,
`therefore y_(max)=1`
`y=(1)/(1+(x-1)^(2))" at "t=2s`
or `y_(max)=1` when `x=1`.
It means that in 2 sec, the wave has moved a distance of 1 m.
`therefore` Velocity = `("distance")/("time")=(1)/(2)=0.5ms^(-1)`