Question

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

Options

• 1

• 3

• 2

• 4

Answer 1

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

Explanation:

Equation of a wave,

at t = 0, y = `1/(1 + x^2)`

at t = t, y = `1/(1 + (x - vt)^2)`

at t = 1, y = `1/(1 + (x - v)^2)` ..........(i)

When (i) is compared to the given equation,

y = `1/(1 + (x - 2)^2)`

So, ν = 2 m/s