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. `2ms^(-1)`
B. `0.5ms^(-1)`
C. `3ms^(-1)`
D. `1ms^(-1)`

Answer

B

Explanation

At `t=0`, `x_(1)=sqrt((1-y)/(y))`, At `t=2`, `x_(2)=1+sqrt((1-y)/(y))`.
to have same value i.e., `y=1`, we get `x_(1)=0`, `x_(2)=1`
`:.` Velocity `V=(x_(2)-x_(1))/(t_(2)-t_(1))`