Waves Ques 2
2. 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
[2018]
(a) $13.2$ $ \mathrm{cm}$
(b) $8 $ $\mathrm{cm}$
(c) $16 $ $\mathrm{cm}$
(d) $12.5$ $ \mathrm{cm}$
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Answer:
Correct Answer: 2.(a)
Solution: (a) For closed organ pipe, third harmonic
$ n=\frac{(2 N-1) V}{4 \ell}=\frac{3 V}{4 \ell} \quad (\because \mathrm{N}=2) $
For open organ pipe, fundamental frequenty
$ n=\frac{N V}{2 \ell}=\frac{V}{2 \ell^{\prime}} \quad (\because \mathrm{N}=1) $
According to question, $\frac{3 V}{4 \ell}=\frac{V}{2 \ell^{\prime}}$
$ \Rightarrow \quad \ell^{\prime}=\frac{4 \ell}{3 \times 2}=\frac{2 \ell}{3}=\frac{2 \times 20}{3}=13.33$ $ \mathrm{cm} $
BETA
