Question

The displacement of a particle of the medium due to a wave moving in the positive $x-$ direction is given by $y=\frac{1}{(1+x^2)}$ at time $t=0$ and by $y=\frac{1}{1+{(x-1)}^2}$ at $t=2$ second, where $x$ and $y$ are in metre. The velocity of the wave in $\text{m/s}$ is

• A. $0.5$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A

$0.5$

The general equation of a progressive wave travelling in $+x$ direction is $y=f(x-vt)$

We rewrite the given equations as $y=\frac{1}{1+(x-vt{)}^2}$
For $t=0$, this becomes $y=\frac{1}{(1+x^2)}$
and for $t=2s$, this becomes $y=\frac{1}{[1+(x-2v{)}^2]}=\frac{1}{[1+(x-1{)}^2]}$
$\Rightarrow 2v=1$ or $v=0.5\text{m/s}$