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(D) The given wave equation is $y = (0.02 \ m) \sin (5 \pi x - 20 t)$.Comparing this with the standard wave equation $y = A \sin (kx - \omega t)$, we

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$0.2$

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(D) The given wave equation is $y = (0.02 \ m) \sin (5 \pi x - 20 t)$.Comparing this with the standard wave equation $y = A \sin (kx - \omega t)$, we get the wave number $k = 5 \pi \ m^{-1}$.The wavelength $\lambda$ is given by $k = \frac{2 \pi}{\lambda}$, so $\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{5 \pi} = 0.4 \ m$.Particles in a wave have the same speed if they are separated by a distance equal to half the wavelength $(\frac{\lambda}{2})$ or an integer multiple of the wavelength. The minimum distance between two particles having the same speed is $\frac{\lambda}{2}$.Therefore, the minimum distance $= \frac{0.4 \ m}{2} = 0.2 \ m$.

$A$ wave is represented by the equation $y = (0.02 \ m) \sin (5 \pi x - 20 t)$. The minimum distance between two particles always having the same speed is: (Assume $x$ and $t$ are in $SI$ units) (in $m$)

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