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JEE Main & Advanced Physics Wave Mechanics Question Bank Organ Pipe (Vibration of Air Column)

  • question_answer
    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]

    A)            1 : 2                                          

    B)            1 : 3

    C)            3 : 8                                          

    D)            3 : 4

    Correct Answer: C

    Solution :

               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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