Question

The amplitude of a wave disturbance propagating in the positive x-direction is given by $y=\frac{1}{1-x^2}$ at $t=0$ and $y=\frac{1}{2+x^2-2x}$ at $t=2s$, where $x$ and $y$ are in meter. Assuming that the shape of the wave disturbance does not change during the propagation, the speed of the wave is:

• A. $0.5m/s$
• B. $1m/s$
• C. $1.5m/s$
• D. $2m/s$

Answer 1

The correct option is A $0.5m/s$

Given

$y=1/(1+x²)$ at $t=0$ sec

$y=1/[1+(x-1\left)²\right]$ at $t=2$ sec

in second case graph shift right direction by 1 unit. ,(see graph)

Here it is clear that the shape of wave doesn't change. and wave move in 2 sec , $1$ m in positive x direction.

so, wave moves 1 m in 2 sec .

so, velocity of wave = displacement of wave / time taken

$v=\frac{d}{t}$

$v=\frac{1}{2}=0.5m/s$

hence, velocity of wave = 0.5 m/s