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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \mathrm{~cm}$, the length of the open organ pipe is(1) $12.5 \mathrm{~cm}$(2) $8 \mathrm{~cm}$(3) $13.2 \mathrm{~cm}$(4) $16 \mathrm{~cm}$
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \mathrm{~cm}$, the length of the open organ pipe is
(1) $12.5 \mathrm{~cm}$
(2) $8 \mathrm{~cm}$
(3) $13.2 \mathrm{~cm}$
(4) $16 \mathrm{~cm}$
Physics
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \mathrm{~cm}$, the length of the open organ pipe is
(1) $12.5 \mathrm{~cm}$
(2) $8 \mathrm{~cm}$
(3) $13.2 \mathrm{~cm}$
(4) $16 \mathrm{~cm}$

Answer is (3)

For closed organ pipe, third harmonic will be $\frac{3 v}{4 l}$

For open organ pipe, fundamental frequency will be$\frac{v}{2 l^{\prime}}$

Given,

$\frac{3 v}{4 l}=\frac{v}{2 l^{\prime}}$

$\Rightarrow \quad l^{\prime}=\frac{4 l}{3 \times 2}=\frac{2 l}{3}$

$=\frac{2 \times 20}{3}=13.33 \mathrm{~cm}$

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