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. `2.0`
B. `4.0`
C. `0.5`
D. `1.0`

Answer

C

Explanation

The equation of wave at any time is obtained by putting `X=x-vt`
`Y=1/(1+x^2)=1/(1+(x-vt)^2)`......(i)
We know at t=2 sec
`y=1/(1+(x-1)^2)`.....(ii)
On comparing (i) and (ii) we get
`vt=1, v=l/t`
As `t=2 sec therefore v=1/2=0.5 m//s`