MCQ
The fundamental frequency of a closed organ pipe of length $20\; cm$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is ...... $cm$
- A$100$
- ✓$120$
- C$140$
- D$80$
✓
Answer
Correct option: B.
$120$
b
Fundamental frequency of closed organ pipe $=\frac{ v }{4 \ell_{ c }}$
Fundamental frequency of closed organ pipe $=\frac{ v }{4 \ell_{ c }}$
$2^{nd}$ overtone frequency of open organ pipe $=\frac{3 v }{2 \ell_0}$
$\frac{ v }{4 \ell_{ c }}=\frac{3 v }{2 \ell_0}$
$\Rightarrow \ell_0=6 \ell_{ c }=6(20 cm )=120\; cm$
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