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))`
`:. 1+x^(2)=(1)/(y)`
or `x^(2)=(1)/(y)-1=(1-y)/(y)`
`x=((1-y)/(y))^(1//2)=x_(1), ` say …(i)
At `t=2s, y=(1)/([1+(x-1)^(2)])`
or `(1+9x-1)^(92)=(1)/(y)`
`(x-1)^(2)=((1)/(y)-1)=(1-y)/(y)`
`x=1+((1-y)/(y))^(1//2)=x_(2),` say ...(ii)
No, velocity of wave, `v=(x_(2)-x_(1))/(t_(2)-t_(1))=(1)/(2-0)`
`=0.5m//s.`