The displacement $y($ in $\mathrm{cm})$ 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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Aicharya · Accepted Answer

Displacement equation in SHM is given as $ y=\frac{10}{\pi} \sin \left(2000 \pi t-\frac{\pi x}{17}ight) \mathrm{cm} $ Comparing with wave equation, $ y=a \sin (\omega t-k x) $ $ \begin{aligned} & 	ext { We get, } \quad a=\frac{10}{\pi} \mathrm{cm}=\frac{10}{\pi} 	imes 10^{-2} \mathrm{~m} \ & \omega=2000 \pi \ & \Rightarrow \quad \frac{2 \pi}{T}=2000 \pi \ & \Rightarrow \quad T=0.001 \mathrm{~s} \Rightarrow T=10^{-3} \mathrm{~s} \ & \end{aligned} $ Maximum velocity, $ \begin{aligned} v_{\max } & =\omega a=2000 \pi 	imes \frac{10}{\pi} 	imes 10^{-2} \ & =2 	imes 10^2=200 \mathrm{~ms}^{-1} \end{aligned} $

The displacement $y($ in $\mathrm{cm})$ in case of a simple harmonic wave is given by $y=\frac{10}{\pi} \sin…

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