A sinusoidal progressive wave is generated in a string. It’s equation is given by $y = (2\,\, mm) sin (2\pi x - 100 \pi t + \pi /3)$. The time when particle at $x = 4$ $m$ first passes through mean position, will be
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$y=2 m m \sin \left(2 \pi x-100 \pi t+\frac{\pi}{3}\right)$
$\Rightarrow 0=2 \sin \left(2 \pi x-100 \pi t+\frac{\pi}{3}\right)$
$\Rightarrow n \pi=8 \pi-100 \pi t+\frac{\pi}{3}(n=0,1,2,3 \dots)$
$\Rightarrow t_{\min }=\frac{\frac{25 \pi}{3}-n \pi}{100 \pi}=\frac{\pi}{3} / 100 \pi=\frac{1}{300} s$
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