The equation of a stationary wave along a str | vedclass

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(C) The given equation of the stationary wave is $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$.Comparing this with the standard equation

Vedclass · Accepted Answer

$3$

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(C) The given equation of the stationary wave is $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$.Comparing this with the standard equation of a stationary wave,$y = A \sin(kx) \cos(\omega t)$,where $k = \frac{2\pi}{\lambda}$.From the given equation,the wave number $k = \frac{\pi}{3}$.Since $k = \frac{2\pi}{\lambda}$,we have $\frac{2\pi}{\lambda} = \frac{\pi}{3}$.Solving for $\lambda$,we get $\lambda = 6 \ cm$.The separation between two adjacent nodes in a stationary wave is given by $\frac{\lambda}{2}$.Therefore,the separation $= \frac{6 \ cm}{2} = 3 \ cm$.

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40 \pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is .... $cm$.

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