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JEE Main & Advanced Physics Wave Mechanics Question Bank Vibration of String

  • question_answer
    In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to \[\frac{3}{4}\]th of the original length and the tension is changed. The factor by which the tension is to be changed, is                    [EAMCET 2001]

    A)            \[\frac{3}{8}\]                      

    B)            \[\frac{2}{3}\]

    C)            \[\frac{8}{9}\]                      

    D)            \[\frac{9}{4}\]

    Correct Answer: D

    Solution :

                         \[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\Rightarrow n\propto \frac{\sqrt{T}}{l}\]                    Þ \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)}^{2}}{{\left( \frac{{{l}_{2}}}{{{l}_{1}}} \right)}^{2}}={{(2)}^{2}}{{\left( \frac{3}{4} \right)}^{2}}=\frac{9}{4}\]


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