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. `2.5 m//s`
B. `0.25 m//s`
C. `0.5 m//s`
D. `5 m//s`

Answer

C

Explanation

`y = (1)/(1 + x^(2)) (t = 0)`
`y = (1)/(1 + (x - 2v)^(2)) (t = 2)`
Now comparing
`x - 2v = x - 1`
`v = 0.5 (m)//(sec)`