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