A) 1 : 2
B) 4 : 1
C) 8 : 3
D) 3 : 8
Correct Answer: A
Solution :
In first overtone of organ pipe open at one end, end, \[{{n}_{c}}=\frac{3v}{4{{l}_{c}}}\] .....(i) Third harmonic or second overtone of organ pipe open at both end, \[{{n}_{0}}=\frac{3v}{2{{l}_{0}}}\] .....(ii) given \[{{n}_{c}}={{n}_{o}}\]\[\Rightarrow \,\,\,\,\frac{3v}{4{{l}_{c}}}=\frac{3{{v}_{0}}}{2{{l}_{0}}}\,\,\,\Rightarrow \,\,\frac{{{l}_{c}}}{{{l}_{o}}}=\frac{1}{2}.\]
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