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?

Options

A. `1ms^(-1)`
B. `0.5ms^(-1)`
C. `1.5ms^(-1)`
D. `2ms^(-1)`

Explanation

Writing the general expression for `y` in terms of `x` as
`y=(1)/(1+(x-vt)^(2))`. At `t=0`, `y=1//(1+x^(2))`. At `t=2s`, `y=(1)/(1+[x-v(2)]^(2))`
Comparing with the given equation we get `2v=1` and `v=0.5m//s`.