A transverse wave is passing through a stretched string with a speed of $20\ m/s.$ The tension in the string is $20\ N$. At a certain point $P$ on the string, it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.
Medium
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$40 \times 10^{-3}=\mathrm{mv}_{\mathrm{p}}^{2} \mathrm{v}=50 \times 10^{-3} \times \mathrm{v}_{\mathrm{p}}^{2} \times 20$
$\frac{4}{100}=v_{p}^{2} \Rightarrow 0.2 \mathrm{\,m} / \mathrm{s}=\mathrm{v}_{\mathrm{p}}=20 \mathrm{\,cm} / \mathrm{s}$
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