The standing wave in a medium is expressed as | vedclass

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(D) The given equation of the standing wave is $y = 0.2 \sin(0.8 x) \cos(3000 t) \, m$.Comparing this with the standard equation $y = A \sin(kx) \cos(

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None of these

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(D) The given equation of the standing wave is $y = 0.2 \sin(0.8 x) \cos(3000 t) \, m$.Comparing this with the standard equation $y = A \sin(kx) \cos(\omega t)$,we get the wave number $k = 0.8 \, rad/m$.The relationship between wave number $k$ and wavelength $\lambda$ is $k = \frac{2\pi}{\lambda}$.Thus,$\lambda = \frac{2\pi}{k} = \frac{2\pi}{0.8} = \frac{20\pi}{8} = 2.5\pi \, m$.The distance between two consecutive points of minimum displacement (nodes) or maximum displacement (antinodes) is given by $\frac{\lambda}{2}$.Distance $= \frac{\lambda}{2} = \frac{2.5\pi}{2} = 1.25\pi \, m = \frac{5\pi}{4} \, m$.Since $\frac{5\pi}{4} \, m$ is not among the given options,the correct choice is $(d)$.

The standing wave in a medium is expressed as $y = 0.2 \sin(0.8 x) \cos(3000 t) \, m$. The distance between any two consecutive points of minimum or maximum displacement is

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