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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • 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

    A)  \[{{n}_{A}}={{n}_{B}}\]

    B)  \[{{n}_{A}}>{{n}_{B}}\]

    C)  \[{{n}_{A}}<{{n}_{B}}\]

    D)  Either  or  depending on the ratio of their diameters

    Correct Answer: C

    Solution :

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


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