A) \[\frac{n+1}{(2n+1)}\]
B) \[\frac{2(n+1)}{(2n+1)}\]
C) \[\frac{n}{(2n+1)}\]
D) \[\frac{(n+1)}{2n}\]
Correct Answer: B
Solution :
Let\[\ell \]be the length of the pipes and v the speed of sound. Then frequency of open organ pipe of overtone is \[{{f}_{1}}=(n+1)\frac{v}{2\ell }\]and frequency. Of closed organ pipe of nth overtone is \[{{f}_{2}}=(2n+1)\frac{v}{4\ell }\] Hence, the correction option is [b].
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