The equation of a stationary wave along a str | vedclass

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(B) The standard equation for a stationary wave is $y = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y = 5 \sin \left( \frac{\pi

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$3$

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(B) The standard equation for a stationary wave is $y = A \sin(kx) \cos(\omega t)$.Comparing this with the given equation $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos(40 \pi t)$, we identify the wave number $k = \frac{\pi}{3} \ cm^{-1}$.The relationship between the wave number $k$ and the wavelength $\lambda$ is $k = \frac{2\pi}{\lambda}$.Substituting the value of $k$: $\frac{\pi}{3} = \frac{2\pi}{\lambda}$, which gives $\lambda = 6 \ cm$.The separation between two adjacent nodes in a stationary wave is given by $\frac{\lambda}{2}$.Therefore, the separation $= \frac{6 \ cm}{2} = 3 \ cm$.

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \left( \frac{\pi x}{3} \right) \cos (40 \pi t)$. Here $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is: (in $cm$)

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