The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is $100 H z$ . The frequency of the third harmonic of the closed pipe is:

100 H z

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200 H z

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300 H z

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150 H z

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Solution

The correct option is D $300 H z$
Let the length of closed pipe be $L^{'}$ .
Thus length of open pipe $L = 2 L^{'}$
Fundamental frequency in open pipe $f_{o} = \frac{v}{2 L} = \frac{v}{4 L^{'}} = 100 H z$
Frequency of third harmonic in closed pipe $f_{3} = \frac{3 v}{4 L^{'}}$
$⟹$ $f_{3} = 3 \times 100 = 300 H z$

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The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is 100 Hz. The frequency of the third harmonic of the closed pipe is:

The correct option is D 300 HzLet the length of closed pipe be L′.Thus length of open pipe L=2L′Fundamental frequency in open pipe fo=v2L=v4L′=100 HzFrequency of third harmonic in closed pipe f3=3v4L′⟹ f3=3×100=300 Hz

The length of an open organ pipe is twice the length of another closed organ pipe. The fundamental frequency of the open pipe is $100 H z$ . The frequency of the third harmonic of the closed pipe is: