Question

The graph shows three waves travelling with same velocity, that are separately sent along a string, which is under a certain tension along $x-$axis. If ${\omega }_1,{\omega }_2$ and ${\omega }_3$ are their angular frequencies respectively, then,

• A. ${\omega }_1={\omega }_3>{\omega }_2$
• B. ${\omega }_1>{\omega }_2>{\omega }_3$
• C. ${\omega }_2>{\omega }_1={\omega }_3$
• D. ${\omega }_1={\omega }_2={\omega }_3$

Answer 1

The correct option is A ${\omega }_1={\omega }_3>{\omega }_2$

We know that, $T=2\pi /\omega$
and $T$ corresponds to one complete cycle

Now, $v=f\lambda =\frac{\omega }{2\pi }\lambda \dots \left(1\right)$
If $\lambda$ is more, $\omega$ will be less for a given medium.
From the given graph, it is clear that,
${\lambda }_1={\lambda }_3......\left(2\right)$
$\text{and}{\lambda }_2>{\lambda }_1......\left(3\right)$

$\text{From}\left(1\right),\left(2\right)\text{and}\left(3\right)$, we can write,
${\omega }_1={\omega }_3\text{and}{\omega }_2<{\omega }_1$

Hence, $\left(A\right)$ is the correct answer.