A) \[1:2\]
B) \[2:1\]
C) \[3:4\]
D) \[4:3\]
Correct Answer: A
Solution :
Neglecting and correction, the length of closed organ pipe is given by, \[{{\lambda }_{1}}=4{{l}_{1}}\] or \[{{l}_{2}}=\frac{{{\lambda }_{1}}}{4}\] ?..(i) The length of open organ pipe is, \[{{\lambda }_{2}}=2{{l}_{2}}\] or \[{{l}_{2}}=\frac{{{\lambda }_{2}}}{2}\] ?..(ii) Here, \[{{n}_{1}}={{n}_{2}}\] \[\frac{V}{{{\lambda }_{1}}}=\frac{V}{{{\lambda }_{2}}}\] From equations (i) and (ii), we obtain, \[\frac{V}{4{{l}_{1}}}=\frac{V}{2{{l}_{2}}}\] or \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{2}{4}=\frac{1}{2}\] Hence, \[{{l}_{1}}:{{l}_{2}}=1:2\]
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