The equation of a stationary wave along a str | vedclass

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(B) The standard equation of a stationary wave is given by $y = 2a \sin \frac{2\pi x}{\lambda} \cos \omega t$.Comparing the given equation $y = 5 \sin

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$3$

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(B) The standard equation of a stationary wave is given by $y = 2a \sin \frac{2\pi x}{\lambda} \cos \omega t$.Comparing the given equation $y = 5 \sin \frac{\pi x}{3} \cos 40\pi t$ with the standard equation,we get the propagation constant $k = \frac{2\pi}{\lambda} = \frac{\pi}{3}$.Solving for $\lambda$,we find $\lambda = 6 \ cm$.The separation between two adjacent nodes in a stationary wave is given by $\frac{\lambda}{2}$.Therefore,the separation = $\frac{6}{2} = 3 \ cm$.

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 seconds. The separation between two adjacent nodes is..... $cm$.

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