Two travelling waves produce a standing wave | vedclass

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(B) For a node,the amplitude of the standing wave must be zero.Given the equation ${y} = 1.0 \, 	ext{mm} \cos(1.57 \, 	ext{cm}^{-1} x) \sin(78.5 \,

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(B) For a node,the amplitude of the standing wave must be zero.Given the equation ${y} = 1.0 \, 	ext{mm} \cos(1.57 \, 	ext{cm}^{-1} x) \sin(78.5 \, 	ext{s}^{-1} t)$,the spatial part is $\cos(1.57 \, 	ext{cm}^{-1} x)$.Setting the spatial part to zero: $\cos(1.57 \, 	ext{cm}^{-1} x) = 0$.This occurs when the argument is an odd multiple of $\frac{\pi}{2}$. For the node closest to the origin $(x > 0)$,we take the first positive value:$1.57 \, 	ext{cm}^{-1} x = \frac{\pi}{2}$.Using $\pi \approx 3.14$,we have $1.57 \approx \frac{\pi}{2}$.Therefore,$x = \frac{\pi}{2 	imes 1.57} \, 	ext{cm} = \frac{1.57}{1.57} \, 	ext{cm} = 1 \, 	ext{cm}$.

Two travelling waves produce a standing wave represented by the equation,
${y} = 1.0 \, \text{mm} \cos(1.57 \, \text{cm}^{-1} x) \sin(78.5 \, \text{s}^{-1} t)$
The node closest to the origin in the region ${x} > 0$ will be at ${x} = \dots \, \text{cm}$.

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Two travelling waves produce a standing wave represented by the equation,${y} = 1.0 \, \text{mm} \cos(1.57 \, \text{cm}^{-1} x) \sin(78.5 \, \text{s}^{-1} t)$The node closest to the origin in the region ${x} > 0$ will be at ${x} = \dots \, \text{cm}$.