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Haryana PMT Haryana PMT Solved Paper-2010

  • question_answer
    The fundamental frequency of a closed pipe is 220 Hz. If \[\frac{1}{4}\] of the pipe is filled with water, the frequency of the first overtone of the pipe now is

    A)  220 Hz                                 

    B)  440 Hz

    C)  880 Hz                                 

    D)  1760 Hz

    Correct Answer: C

    Solution :

                    Fundamental frequency of closed pipe \[n=\frac{v}{4l}=220Hz\]                 \[\Rightarrow \]               \[v=220\times 4l\] If \[\frac{1}{4}\] of the pipe is filled with water then remaining length of air column is \[\frac{3l}{4}\]. Now, fundamental frequency \[=\frac{v}{4\left( \frac{3l}{4} \right)}=\frac{v}{3l}\] and  First overtone \[=3\times \]fundamental  frequency.                                 \[=3\times \frac{v}{3L}=\frac{3\times 220\times 4l}{3l}\]                                 \[=880Hz\]


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