The equation of a stationary wave is y = 0.8 | vedclass

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(A) The standard equation of a stationary wave is given by $y = A \cos(kx) \sin(\omega t)$.Comparing this with the given equation $y = 0.8 \cos \left(

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$20$

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(A) The standard equation of a stationary wave is given by $y = A \cos(kx) \sin(\omega t)$.Comparing this with the given equation $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin(200 \pi t)$,we get the wave number $k = \frac{\pi}{20}$.We know that $k = \frac{2 \pi}{\lambda}$,so $\frac{2 \pi}{\lambda} = \frac{\pi}{20}$.Solving for wavelength $\lambda$,we get $\lambda = 40 \, cm$.The distance between two consecutive nodes in a stationary wave is given by $\frac{\lambda}{2}$.Therefore,the separation is $\frac{40}{2} = 20 \, cm$.

The equation of a stationary wave is $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin (200 \pi t)$,where $x$ is in $cm$ and $t$ is in $sec$. The separation between consecutive nodes will be .... $cm$.

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