A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by $y\left( {x,t} \right) = 0.5\sin\, \left( {\frac{{5\pi }}{4}x} \right)\,\cos\, \left( {200\,\pi t} \right)$. What is the speed of the travelling wave moving in the positive $x$ direction .... $m/s$ ? ($x$ and $t$ are in meter and second, respectively.)
JEE MAIN 2017, Diffcult
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Given, $y(x, t)=0.5 \sin \left(\frac{5 \pi}{4}x\right) \cos (200 \pi t)$
comparing with equation $-y(x, t)=2 a sin\mathrm{kx} \cos \omega \mathrm{t}$
$\omega=200 \pi, k=\frac{5 \pi}{4}$
speed of travelling wave
$v=\frac{\omega}{k}=\frac{200 \pi}{5 \pi / 4}=160 \mathrm{m} / \mathrm{s}$
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