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(C) The given equation of the stationary wave is $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$.Comparing this with the standard equatio

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$4$

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(C) The given equation of the stationary wave is $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$.Comparing this with the standard equation of a stationary wave,$y = 2A \sin (kx) \cos (\omega t)$,we get the propagation constant $k = \frac{\pi}{4} \ cm^{-1}$.We know that the propagation constant $k$ is related to the wavelength $\lambda$ by the formula $k = \frac{2\pi}{\lambda}$.Substituting the value of $k$: $\frac{\pi}{4} = \frac{2\pi}{\lambda}$.Solving for $\lambda$,we get $\lambda = 8 \ cm$.The distance between two consecutive nodes in a stationary wave is equal to half of the wavelength,which is $\frac{\lambda}{2}$.Therefore,the distance is $\frac{8 \ cm}{2} = 4 \ cm$.

$A$ stationary wave is represented by $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two consecutive nodes is (in $cm$)

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