Q159 / 160 · WBJEE 2012 · Physics

A progressive wave moving along $x$ -axis is represented by $y=A \sin \left[\frac{2 \pi}{\lambda}(v t-x)\right]$ The wavelength $(\lambda)$ at which the maximum particle velocity is 3 times the wave velocity is

  • A
    $\frac{\mathrm{A}}{A}$
  • B
    $2 \mathrm{A}(3 \pi)$
  • C
    $\left(\frac{3}{4}\right) \pi A$
  • Correct answer
    D
    $(2 / 3) \pi A$

Solution

$y=A \sin \left[\frac{2 \pi}{\lambda}(v t-x)\right]$ $v=\frac{2 \pi}{\lambda} V A$ $$ \begin{aligned} \left(v_{p}\right)_{\max } &=3 v \\ \lambda &=\frac{2 \pi}{3} A \end{aligned} $$

Hence, the correct answer is option: 'D'.

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