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 the given equation $y = 0.8 \cos \left( \frac{\pi

Vedclass · Accepted Answer

$20$

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(A) The standard equation of a stationary wave is given by $y = A \cos(kx) \sin(\omega t)$.Comparing the given equation $y = 0.8 \cos \left( \frac{\pi x}{20} ight) \sin(200 \pi t)$ with the standard form,we identify the wave number $k$ as:$k = \frac{2\pi}{\lambda} = \frac{\pi}{20}$.Solving for the wavelength $\lambda$:$\lambda = 20 	imes 2 = 40 \, cm$.The separation between two consecutive nodes in a stationary wave is given by $\frac{\lambda}{2}$.Therefore,the separation = $\frac{40}{2} = 20 \, cm$.

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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