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BCECE Engineering BCECE Engineering Solved Paper-2006

  • question_answer
    Two closed organ pipes A and B have the same length. A is wider than B. They resonate in the fundamental mode at frequencies \[{{n}_{A}}\] and \[{{n}_{B}}\] respectively, then:

    A)  \[{{n}_{A}}={{n}_{B}}\]

    B)         \[{{n}_{A}}>{{n}_{B}}\]

    C)         \[{{n}_{A}}<{{n}_{B}}\]

    D)         either (b) or (c) depending on the ratio of their diameters

    Correct Answer: C

    Solution :

    In the fundamental mode of vibration \[\frac{\lambda }{4}=(l+0.3d)\] where 0.3 d is the necessary end correction.  Frequency of vibration,\[n=\frac{v}{\lambda }=\frac{v}{4(l+0.3d)}\] As \[l\]is same for both pipes, wider pipe (A) will resonate at a lower frequency i.e., \[{{n}_{A}}<{{n}_{B}}.\]


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