A string is clamed at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units)
JEE MAIN 2019, Medium
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$4^{\text {th }}$ harmonic
$4 \frac{\lambda}{2}=\ell \quad ; 2 \lambda=\ell$
From equation $\frac{2 \pi}{\lambda}=0.157$
$\lambda=40 ; \quad \ell=2 \lambda=80 \mathrm{m}$
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