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. 0.5
B. 1
C. 2
D. 4

Answer

A

Explanation

We rewrite the given equations as `y = (1)/(1 + (x - vt)^(2))`
For t = 0, this becomes `y = (1)/([1 + (x -2v)^(2)]] = (1)/([1 + (x -1)^(2)]]`
implies `2v = 1 or v = 0.5 m//s`