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The fundamental frequency of open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 21 cm, the length of the open pipe is

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12.5 cm

16 cm

14 cm

8 cm

answer is A.

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Detailed Solution

$f_{0} = \frac{v}{2 l_{1}}$

Fundamental frequency of open organ pipe, $f_{0} = \frac{v}{2 l_{1}}$

third harmonic of a closed organ pipe, $f_{3} = \frac{3 v}{4 l_{2}}$

It is given $f_{0} = f_{3}$

$\frac{v}{2 l_{1}} = \frac{3 v}{4 l_{2}}$

or, $I_{1} = \frac{2}{3} l_{2} = \frac{2 \times 21}{3} cm = 14 cm$

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