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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(d)
$y=0.2 \sin 0.8 x \cos 3000 t$
The distance between any two points of minimum or maximum displacement is simply wavelength $\left(\frac{\lambda}{4}\right)$ of the wave.
$k=\frac{2 \pi}{\lambda}=0.8$
$\text { or } \lambda=\frac{2 \pi}{0.8}$
$\therefore \lambda=\frac{5 \pi}{2} m \Rightarrow \frac{\lambda}{4}=\frac{5 \pi}{8} \,m$
Hence answer must be $(d)$.
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