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KVPY Sample Paper KVPY Stream-SX Model Paper-18

  • question_answer
    When a tuning fork of frequency \[f\]is excited and held near me end of a straight pipe of length L open at both ends, the air column in the pipe vibrates in its fundamental mode and is in resonance with the tuning fork. The pipe is now kept vertical in a jar containing water so that half the length of the pipe is inside water. What should be the frequency of the tuning fork to be used to make the air column vibrate in its fundamental mode in resonance with the tuning fork now?

    A) \[f\]

    B) \[2f\]  

    C) \[f/2~\] 

    D) \[f/4\]

    Correct Answer: A

    Solution :

    In the fundamental mode the air column in the open pipe (pipe open at both ends) vibrates with consecutive antinodes at its ends so that the length L of the pipe is equal to \[\lambda /2\] where \[\lambda \] is the wave length of sound in air. Therefore\[\lambda =2L.\] The air column in the closed pipe (pipe closed at one end) on the other hand vibrates in its fundamental mode, with a mode at the closed end (at the water surface inside the pipe) and the neighbouring antinode at the open end so that \[L/2=\lambda /4.\] Again we obtain\[\lambda =2L.\] The frequencies in the two cases are same.


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