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(C) The displacement equation for a simple harmonic wave is given by:$y = \frac{10}{\pi} \sin \left(2000 \pi t - \frac{\pi x}{17}ight) 	ext{ cm}$Co

Vedclass · Accepted Answer

$10^{-3} \,s, 200 \,ms^{-1}$

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(C) The displacement equation for a simple harmonic wave is given by:$y = \frac{10}{\pi} \sin \left(2000 \pi t - \frac{\pi x}{17}ight) 	ext{ cm}$Comparing this with the standard wave equation $y = a \sin(\omega t - kx)$:Here,amplitude $a = \frac{10}{\pi} 	ext{ cm} = \frac{10}{\pi} 	imes 10^{-2} 	ext{ m}$.Angular frequency $\omega = 2000 \pi 	ext{ rad/s}$.$1$. Period $(T)$:$\omega = \frac{2\pi}{T} = 2000 \pi$$T = \frac{2\pi}{2000 \pi} = \frac{1}{1000} 	ext{ s} = 10^{-3} 	ext{ s}$.$2$. Maximum velocity $(v_{\max})$:$v_{\max} = \omega a$$v_{\max} = (2000 \pi) 	imes \left(\frac{10}{\pi} 	imes 10^{-2}ight) 	ext{ m/s}$$v_{\max} = 2000 	imes 10 	imes 10^{-2} = 200 	ext{ m/s}$.Thus,the period is $10^{-3} 	ext{ s}$ and the maximum velocity is $200 	ext{ m/s}$.

The displacement $y$ (in $cm$) in case of a simple harmonic wave is given by $y=\frac{10}{\pi} \sin \left(2000 \pi t-\frac{\pi x}{17}\right)$. The period and maximum velocity of the particles in the medium will respectively be

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