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JEE Main & Advanced Physics Wave Mechanics Question Bank Organ Pipe (Vibration of Air Column)

  • question_answer
    A cylindrical tube, open at both ends, has a fundamental frequency \[{{f}_{0}}\] in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is [RPET 1999; RPMT 1998, 2000; J & K CET 2000; KCET  2002; BHU 2002; BCECE 2003]

    A)            \[3{{f}_{0}}/4\]                   

    B)            \[{{f}_{0}}\]

    C)            \[{{f}_{0}}/2\]                      

    D)            \[2{{f}_{0}}\]

    Correct Answer: B

    Solution :

               \[{{n}_{\text{open}}}=\frac{v}{2{{l}_{\text{open}}}}\]            \[{{n}_{\text{closed}}}=\frac{v}{4{{l}_{\text{closed}}}}=\frac{v}{4{{l}_{\text{open}}}/2}=\frac{v}{2{{l}_{\text{open}}}}\]                    \[\left( As\ {{l}_{closed}}=\frac{{{l}_{open}}}{2} \right)\], i.e. frequency remains unchanged.


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