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. `0.2m//s`
B. `0.5m//s`
C. `0.3m//s`
D. `0.4m//s`

Answer

B

Explanation

Here, at `t=0, y=(1)/(1+x^(2))` or`1+x^(2)=(1)/(y)`
`x^(2)=(1)/(y)-1=(1-y)/(y)` or `x=((1-y)/(y))^(1//2)`
Also at `t=2s`
`y=(1)/([1+(x-1)^(2)])` or `[1+(x-1)^(2)]=(1)/(y)`
`(x-1)^(2)=(1)/(y)-1=(1-y)/(y)` or `(x-1)=((1-y)/(y))^(1//2)`
`x=1+((1-y)/(y))^(1//2),`As `upsilon=(x_(2)-x_(1))/(t_(2)-t_(1))`
Here, `x_(2)=[1+((1-y)/(y))^(1//2)]` and `x_(1)=((1-y)/(y))^(1//2)`
`t^(2)-t^(1)=2-0=2s`
`:. upsiklon=(1)/(2-0)=0.5ms^(-1)`