A) \[2:1\]
B) \[1:2\]
C) \[1:3\]
D) \[3:1\]
Correct Answer: A
Solution :
: Frequency of the second overtone (i.e. third harmonic) of the open pipe is \[\upsilon =\frac{3V}{2{{L}_{O}}}\] ???(i) where v is the speed of sound in air and \[{{L}_{O}}\] is the length of the open pipe. Frequency of the first overtone (i.e. third harmonics of the closed pipe is \[\upsilon =\frac{3V}{4{{L}_{C}}}\] ??.(ii) As per question, \[\upsilon =\upsilon \] \[\therefore \] \[\frac{3\upsilon }{2{{L}_{O}}}=\frac{3\upsilon }{4{{L}_{C}}}\] or \[\frac{{{L}_{O}}}{{{L}_{C}}}=\frac{2}{1}\]
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