The amplitude of a wave disturbance propagating in the positive x-direction is given by `y = (1)/((1 + x))^(2)` at time `t = 0` and by `y = (1)/([1+(x - 1)^(2)])` at `t = 2 seconds`, `x and y` are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ............... m//s`.

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)`