For the stationary wave y = 4 sin left( frac{ | vedclass

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(A) The standard equation for a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi x}{\lambda} \right) \cos (\omega t)$.Comparing the given e

Vedclass · Accepted Answer

$7.5$

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(A) The standard equation for a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi x}{\lambda} \right) \cos (\omega t)$.Comparing the given equation $y = 4 \sin \left( \frac{\pi x}{15} \right) \cos (96 \pi t)$ with the standard form,we get:$\frac{2 \pi}{\lambda} = \frac{\pi}{15}$.Solving for $\lambda$:$\lambda = 30$.The distance between a node and the next consecutive antinode is given by $\frac{\lambda}{4}$.Therefore,the distance $= \frac{30}{4} = 7.5$.

For the stationary wave $y = 4 \sin \left( \frac{\pi x}{15} \right) \cos (96 \pi t)$,the distance between a node and the next antinode is

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