A) \[10\text{ }cm\]
B) \[8\text{ }cm\]
C) \[12\,\,cm\]
D) \[5\,\,cm\]
Correct Answer: D
Solution :
Third overtone of an open organ pipe \[{{n}_{1}}=\frac{4v}{2{{l}_{1}}}\] Second overtone of closed pipe \[{{n}_{2}}=\frac{5v}{4{{l}_{2}}}\] As \[{{n}_{1}}\] and \[{{n}_{2}}\] are in resonance. \[{{n}_{1}}={{n}_{2}}=n\] \[\frac{4v}{2{{l}_{1}}}=\frac{5v}{4{{l}_{2}}}\] \[\frac{4v}{2\times 8}=\frac{5v}{4{{l}_{2}}}\] \[\Rightarrow \] \[{{l}_{2}}=5\,cm\]
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