A standing wave is formed by the superpositio | vedclass

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(A) The given equation for the standing wave is $y(x, t) = 0.5 \sin(\frac{5\pi}{4}x) \cos(200\pi t)$.Comparing this with the standard equation of a st

Vedclass · Accepted Answer

$160$

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(A) The given equation for the standing wave is $y(x, t) = 0.5 \sin(\frac{5\pi}{4}x) \cos(200\pi t)$.Comparing this with the standard equation of a standing wave,$y(x, t) = 2A \sin(kx) \cos(\omega t)$,we identify the angular frequency $\omega$ and the wave number $k$.Here,$\omega = 200\pi 	ext{ rad/s}$ and $k = \frac{5\pi}{4} 	ext{ rad/m}$.The speed $v$ of the individual travelling waves that form the standing wave is given by the ratio of the angular frequency to the wave number:$v = \frac{\omega}{k} = \frac{200\pi}{5\pi/4} = 200\pi 	imes \frac{4}{5\pi} = 160 	ext{ m/s}$.

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