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

 

Answers (1)

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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