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JCECE Medical JCECE Medical Solved Paper-2008

  • question_answer
    An organ pipe \[{{\text{P}}_{\text{1}}}\]closed at one end vibrating in its first overtone and another pipe \[{{\text{P}}_{2}}\]open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of \[{{\text{P}}_{\text{1}}}\]and\[{{\text{P}}_{2}}\] is

    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 \[{{n}_{2}}=\frac{4v}{2{{l}_{2}}}\] \[{{n}_{1}}={{n}_{2}}\,\text{(given)}\] \[\Rightarrow \] \[\frac{3v}{4{{l}_{1}}}=\frac{4v}{2{{l}_{2}}}\] \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{3}{8}\]


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