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, \[{{n}_{1}}={{n}_{2}}\] So, \[\frac{v}{{{\lambda }_{1}}}=\frac{v}{{{\lambda }_{2}}}\] Or \[\frac{v}{4{{l}_{1}}}=\frac{v}{{{l}_{2}}}\] Therefore, \[{{l}_{1}}:{{l}_{2}}=1:2\]
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