Question

The disturbance $y(x,t)$ of a wave propagating in the positive x-direction is given by $y=\frac{1}{1+x^2}$ at time $t=0$ and by $y=\frac{1}{\left[1+\left(x-1^2\right)\right]}$ at $t=2s,$ where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in $m/s$ is

• A. 2.0
• B. 4.0
• C. 0.5
• D. 1.0

Answer 1

Answer: (C)

The equation of wave at any time is obtained by putting $X=x-vt$
$y=\frac{1}{1+x^2}\frac{1}{1+{\left(x-vt\right)}^2}\dots \left(i\right)$
We know at $t=2sec$,
$y=\frac{1}{1+{\left(x-1\right)}^2}\dots \left(ii\right)$
On comparing $\left(i\right)$ and $\left(ii\right)$ we get
$vt=1$
$V=\frac{1}{t}$
As $t=2sec$
$\therefore V=\frac{1}{2}=0.5m/s.$