A) 1 : 2
B) 2 : 1
C) 2 : 3
D) 4 : 3
Correct Answer: A
Solution :
Let \[{{l}_{1}}\] and \[{{l}_{2}}\] be the length?s of closed and open pipes respectively. (Neglecting end correction) \[{{l}_{1}}=\frac{{{\lambda }_{1}}}{4}\Rightarrow {{\lambda }_{1}}=4{{l}_{1}}\] and \[{{l}_{2}}=\frac{{{\lambda }_{2}}}{2}\Rightarrow {{\lambda }_{2}}=2{{l}_{2}}\] Given \[{{n}_{1}}={{n}_{2}}\] so \[\frac{v}{{{\lambda }_{1}}}=\frac{v}{{{\lambda }_{2}}}\Rightarrow \frac{v}{4{{l}_{1}}}=\frac{v}{2{{l}_{2}}}=\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{1}{2}\]
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