Question

If equation of transverse wave is $y=x_{0} \cos 2 \pi\left(n t-\frac{x}{\lambda}\right)$. Maximum velocity of particle is twice of wave velocity, if $\lambda$ is-

• A. $\pi / 2x_{0}$
• B. $2\lambda x_{0}$
• C. $\pi x$
• D. $\pi x_0$

Answer 1

Answer: (D)

$y=x_{0} \cos 2 \pi\left(n t-\frac{x}{\lambda}\right)$
$y=x_{0} \cos \frac{2 \pi}{\lambda}(v t-x)$
$[\therefore v=n \lambda]$
$\left(\frac{d y}{d t}\right)_{\max }=x_{0} \times \frac{2 \pi}{\pi} v=2 v$ (given)
$\therefore \lambda=\pi x_{0}$