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JCECE Engineering JCECE Engineering Solved Paper-2008

  • 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

    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) \[\Rightarrow \]               \[\frac{3v}{4{{l}_{1}}}=\frac{4v}{2{{l}_{2}}}\]                   \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{3}{8}\]


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