CLOSED organ pipe \[{{n}_{1}}=\frac{3V}{4{{l}_{1}}}\] Third overtone of open organ pipe \[{{n}_{2}}=\frac{4V}{2{{L}_{2}}}\] \[{{n}_{1}}={{n}_{2}}\] (GIVEN) \[\Rightarrow \]\[\frac{3v}{4{{L}_{1}}}=\frac{4v}{2{{L}_{2}}}\Rightarrow \]\[\frac{{{L}_{1}}}{{{L}_{2}}}=\frac{3}{8}\]

"> CLOSED organ pipe \[{{n}_{1}}=\frac{3V}{4{{l}_{1}}}\] Third overtone of open organ pipe \[{{n}_{2}}=\frac{4V}{2{{L}_{2}}}\] \[{{n}_{1}}={{n}_{2}}\] (GIVEN) \[\Rightarrow \]\[\frac{3v}{4{{L}_{1}}}=\frac{4v}{2{{L}_{2}}}\Rightarrow \]\[\frac{{{L}_{1}}}{{{L}_{2}}}=\frac{3}{8}\]

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An organ pipe \[{{P}_{1}}\] closed at one end vibrating in its first overtone and another pipe \[{{P}_{2}}\] open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of \[{{P}_{1}}\] and \[{{P}_{2}}\] is [EAMCET 1997; MH CET 1999; AFMC 2001]

Joint Entrance Exam - Main (JEE Main) Physics in Joint Entrance Exam - Main (JEE Main) . 8 months ago

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First overtone of CLOSED organ pipe \[{{n}_{1}}=\frac{3V}{4{{l}_{1}}}\] Third overtone of open organ pipe \[{{n}_{2}}=\frac{4V}{2{{L}_{2}}}\] \[{{n}_{1}}={{n}_{2}}\] (GIVEN) \[\Rightarrow \]\[\frac{3v}{4{{L}_{1}}}=\frac{4v}{2{{L}_{2}}}\Rightarrow \]\[\frac{{{L}_{1}}}{{{L}_{2}}}=\frac{3}{8}\]

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