The amplitude of wave distance propagating in the positive X-direction is given by y = `(1)/((1 + x)^(2))` at time t = 0 and y = `(1)/(1 + (x - 1)^(2))` at t = 1 seconds here x and y are in metre. The shape of wave disturbance does not change during propagation. The velocity of wave is :

Options

A. `2 ms^(-1)`
B. `15 ms^(-1)`
C. `1 ms^(-1)`
D. `0.5 ms^(-1)`

Answer

D

Explanation

The general equation is y = `(1)/(1 + (x - v)^(2))`
at t = 0 sec `" " y = (1)/(1 + x^(2))`
At t = 2 sec. `" " y = (1)/(1 + (x - 2v)^(2)) `
comparing this with `y = (1)/(1 + (x - 1)^(2))`
We have 2v = 1 `rArr " " v = 0.5 ms^(-1)`.
correct choice is d.