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The fundamental frequency of an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is(A) 12.5cm(B) 13.2cm(C) 16cm(D) 8cm

Last updated date: 16th Sep 2024
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Hint We should know that by the term fundamental frequency we mean the lowest frequency at which a medium will oscillate freely. Based on this concept we have to solve this question.

We know that the fundamental frequency for an open organ pipe is $\dfrac{{\text{V}}}{{{\text{2l}}}}$
Also, we can therefore derive the frequency of third harmonic for closed organ pipe as $\dfrac{{{\text{3V}}}}{{{\text{4}}{{\text{l}}_1}}}$
$\dfrac{{\text{V}}}{{{\text{2l}}}} = \dfrac{{{\text{3V}}}}{{{\text{4}}{{\text{l}}_1}}}$
$\Rightarrow {\text{l = }}\dfrac{{{\text{2}}{{\text{l}}_1}}}{3}$
$\Rightarrow {\text{l = }}\dfrac{{2 \times 20}}{3}$
$\therefore {\text{l = 13}}{\text{.2cm}}$