The equation of a standing wave in a string fixed at both ends is given as $y=2 A \sin k x \cos \omega t$ The amplitude and frequency of a particle vibrating at the mid of an antinode and a node are respectively

  • A

    $A, \frac{\omega}{2 \pi}$

  • B

    $\frac{A}{\sqrt{2}}, \frac{\omega}{2 \pi}$

  • C

    $A, \frac{\omega}{\pi}$

  • D

    $\sqrt{2} A, \frac{\omega}{2 \pi}$

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