Question

The amplitude of a wave disturbance propagating in the positive x-direction is given by y =1/ (1 + x²) at time t = 0 and by y = 1/[1 + (x – 1)² at t = 2 seconds, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is

• A. 1 ms⁻¹
• B. 0.5 ms⁻¹
• C. 1.5 ms⁻¹
• D. 2 ms⁻¹

Answer 1

Answer: (B)

0.5 ms⁻¹

Answer 2

Writing the general expression for y in terms of x as

y = $\frac{1}{1 + (x - vt)^{2}}$ at t = 0, y = 1/ (1 + x)². At t = 2 s,

y = $\frac{1}{1 + \lbrack x - v(2)\rbrack^{2}}$

Comparing with the given equation we get 2v = 1 and v = 0.5 m/s.