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

  • question_answer
    The fundamental frequency of a sonometre wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be                                          [BCECE 2005]

    A)            n    

    B)            \[\frac{n}{\sqrt{2}}\]

    C)            \[\frac{n}{2}\]                     

    D)            \[\frac{n}{2\sqrt{2}}\]

    Correct Answer: D

    Solution :

                         \[n=\frac{1}{2l}\sqrt{\frac{T}{\pi {{r}^{2}}\rho }}\]Þ \[n\propto \frac{\sqrt{T}}{r}\] Þ \[\frac{{{n}_{2}}}{{{n}_{1}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\sqrt{\frac{{{T}_{2}}}{{{T}_{1}}}}\]\[=\frac{1}{2}\times \sqrt{\frac{1}{2}}\]=\[\frac{1}{2\sqrt{2}}\]


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