A stationary wave is represented by y = 10 si | vedclass

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(A) The standard equation for a stationary wave is given by $y = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y = 10 \sin \frac{

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$4$

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(A) The standard equation for a stationary wave is given by $y = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y = 10 \sin \frac{\pi x}{4} \cos 20 \pi t$,we find the wave number $k = \frac{\pi}{4} \ cm^{-1}$.The wave number $k$ 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 $\frac{\lambda}{2}$.Therefore,the distance $= \frac{8 \ cm}{2} = 4 \ cm$.

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

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