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  4. The displacement of a wave is represented by y = 0.6 × 10-3 sin (500 t - 0.05 x) where all the quantities are in their proper units. The maximum particle velocity (in ms-1) of the medium is

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Q. The displacement of a wave is represented by $y = 0.6 \times 10^{-3} \, \sin (500\, t - 0.05\, x)$ where all the quantities are in their proper units. The maximum particle velocity (in $ms^{-1}$) of the medium is

KEAMKEAM 2018Waves

Solution:

$\because$ The displacement of wave
$y =0.6 \times 10^{-3} \sin (500\, t-0.05\, x)$
$\therefore \, v =\frac{d y}{d t}=0.6 \times 10^{-3} \times 500 \sin (500\, t-0.05\, x)$
$v =0.3 \sin (500\, t-0.05\, x)$
For maximum particle velocity,
$\sin (500 t-0.05 x)=1$
Hence, $V_{\max }=0.3\, ms ^{-1}$