# A string is clamped at both the ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y=0.3\: sin\left ( 0.157x \right )cos\left ( 200\pi t \right ).$The length of the string is : (All quantities are in $SI$ units.) Option 1) $20\: m$ Option 2) $80\: m$ Option 3) $40\: m$ Option 4) $60\: m$

$y=0.3\; sin\left ( 0.157x \right )cos\left ( 200\pi t \right )$

$y=2A sin \left ( kx \right )cos\left ( wt \right )$

$k=\frac{2\pi}{\lambda }$

$\lambda =\frac{2\pi }{K}$

$4\left ( \frac{\lambda }{2} \right )=l$

$l\Rightarrow 2\times \lambda$

$l\Rightarrow 2\times \frac{2\pi }{K}$

$=2\times \frac{2\times 3.14}{\cdot 157}$

$=80\; m$

Option 1)

$20\: m$

Option 2)

$80\: m$

Option 3)

$40\: m$

Option 4)

$60\: m$

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