A) 1 : 2
B) 2 : 1
C) 2 : 3
D) 4 : 3
Correct Answer: A
Solution :
Avoiding end correction, the length of closed organ pipe is \[{{l}_{1}}=\frac{{{\lambda }_{1}}}{4}\] or \[{{\lambda }_{1}}=4{{l}_{1}}\] The length of open organ pipe is \[{{l}_{2}}=\frac{{{\lambda }_{2}}}{2}\] or \[{{\lambda }_{2}}=2{{l}_{2}}\] Here, \[{{n}_{1}}={{n}_{2}}\] \[\Rightarrow \] \[\frac{v}{{{\lambda }_{1}}}=\frac{v}{{{\lambda }_{2}}}\] or \[\frac{v}{4{{l}_{1}}}=\frac{v}{4{{l}_{2}}}\] Therefore,\[{{l}_{1}}:{{l}_{2}}=1:2\]
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