For a stationary wave,Y = 10 sin left( frac{p | vedclass

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(A) The standard equation for a stationary wave is given by $y = 2a \sin(kx) \cos(\omega t)$,where $k = \frac{2\pi}{\lambda}$.Comparing the given equa

Vedclass · Accepted Answer

$7.5$

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(A) The standard equation for a stationary wave is given by $y = 2a \sin(kx) \cos(\omega t)$,where $k = \frac{2\pi}{\lambda}$.Comparing the given equation $Y = 10 \sin \left( \frac{\pi x}{15} ight) \cos (48 \pi t)$ with the standard form,we identify the wave number $k = \frac{\pi}{15} 	ext{ cm}^{-1}$.Since $k = \frac{2\pi}{\lambda}$,we have $\frac{2\pi}{\lambda} = \frac{\pi}{15}$.Solving for wavelength $\lambda$,we get $\lambda = 30 	ext{ cm}$.The distance between a node and the successive antinode in a stationary wave is given by $\frac{\lambda}{4}$.Therefore,the distance $= \frac{30}{4} = 7.5 	ext{ cm}$.

For a stationary wave,$Y = 10 \sin \left( \frac{\pi x}{15} \right) \cos (48 \pi t) \text{ cm}$,the distance between a node and the successive antinode is (in $\text{ cm}$)

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