Let y = 1/ 1 + x^2 at t = 0s be the amplitude of the wave propagating in the positive x- direction.

Question

Let. y = \(\frac{1}{1+ x^2}\) at t = 0s be the amplitude of the wave propagating in the positive x-direction. At t = 2s, the amplitude of the wave propagating becomes y = \(\frac{1}{1 + (x - 2)^2}\). Assume that the shape of the wave does not change during propagation the velocity of the wave is ....

(a) 0.5 ms^-1 

(b) 1.0 ms^-1 

(c) 1.5 ms^-1 

(d) 2.0 ms^{​​​​​​​-1}

Answer 1

(b) 1.0 ms^-1

The general expression y in terms of x

\(y = \frac {1}{1 + (x - vt)^2}\)

The shape of wave does not change, also wave move in 2 sec, 2m in positive ‘x’ direction. So, wave moves 2 m in 2 sec.

∴  The velocity of the wave = \(\frac{displacement}{time}\) = \(\frac{2}{2}\); v = 1 ms^-1