# The displacement y (in cm) produced by a simple harmonic wave is given by $y= \frac{10}{\pi}\sin(2000 \pi t- \frac{\pi x}{17})$the periodic time and maximum velocity of the particles in the medium will respectively be Option 1) $10^{-3}$sec and 330 m/s Option 2) $10^{-4}$ sec and 20 m/s Option 3) $10^{-3}$ sec and 200 m/s Option 4) $10^{-2}$ sec and 2000 cm/s.

P Prateek Shrivastava

As we learnt in

Relation between phase velocity and wave speed -

$V_{P}= -V\: \frac{dy}{dx}$

- wherein

$V_{P}=$ particle velocity

$V =$ wave velocity

$\frac{dy}{dx}=$ slope of curve

$y=\frac{10}{\pi}.sin(2000\pi t-\frac{\pi x}{17})$

$\omega = 2000 \pi\:\:\:=>T=\frac{2\pi}{\omega}=\frac{1}{1000}=10^{-3}\:sec$

& particle velocity $V_{p}=\frac{dy}{dt}$

$V_{p}=\frac{dy}{dt}=\frac{10}{\pi}.(2000 \pi).cos(2000 \pi t-\frac{\pi\:x}{17})$

$V_{p}^{max}=\frac{10}{\pi}\times 2000 \pi=\:20,000\:cm/s\:=200\:m/sec$

Option 1)

$10^{-3}$sec and 330 m/s

This option is incorrect.

Option 2)

$10^{-4}$ sec and 20 m/s

This option is incorrect.

Option 3)

$10^{-3}$ sec and 200 m/s

This option is correct.

Option 4)

$10^{-2}$ sec and 2000 cm/s.

This option is incorrect.

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