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. `1 m//s`
B. `1.5 m//s`
C. `0.5 m//s`
D. `2 m//s`

Answer

c

Explanation

At t=2 s
`y=(1)/([1+(x-1)^(2)])`
or `x-vt=x-1 implies 1=vt`
`implies1=vxx2`
`impliesv=0.5 m//s`