A) 0.95m
B) 0.85 m
C) 0.75 m
D) 0.67 m
Correct Answer: D
Solution :
The given, \[{{n}_{2}}-{{n}_{1}}=5\,Hz\] .... (i) (If the speed of sound in air is 330 m/s) \[\frac{v}{2{{l}_{2}}}-\frac{v}{2{{l}_{1}}}=5\] [For open organ pipe, \[n=\frac{v}{2l}\]] \[\frac{v}{2}\left[ \frac{1}{0.66}-\frac{1}{{{l}_{1}}} \right]=5\] \[\frac{330}{2}\left[ \frac{100}{66}-\frac{1}{{{l}_{1}}} \right]=5\] \[33\left[ \frac{50}{33}-\frac{1}{{{l}_{1}}} \right]=1\] \[=\frac{50}{33}-\frac{1}{{{l}_{1}}}=\frac{1}{33}\] \[\frac{1}{{{l}_{1}}}=\frac{50}{33}-\frac{1}{33}\Rightarrow \frac{1}{{{l}_{1}}}=\frac{49}{33}\] \[{{l}_{1}}=0.67\,m\]
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