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JIPMER Jipmer Medical Solved Paper-2010

  • question_answer
    Two vibrating strings of the same material but lengths\[L\]and\[2L\]have radii\[2r\]and\[r\]respectively. They are stretched under the same tension.  Both the strings vibrate in their fundamental modes, the one of length \[L\] with frequency\[{{v}_{1}}\] and the other with frequency\[{{v}_{2}}.\]The ratio \[{{\text{v}}_{\text{1}}}\text{/}{{\text{v}}_{\text{2}}}\] is

    A)  2            

    B)                         4                            

    C)  8                            

    D)         1

    Correct Answer: D

    Solution :

    Fundamental frequency, \[v=\frac{1}{2l}\sqrt{\frac{T}{m}}=\frac{1}{2l}\sqrt{\frac{T}{\pi {{r}^{2}}\rho }}\] or            \[v\propto \frac{1}{lr}\] \[\therefore \]  \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{l}_{2}}{{r}_{2}}}{{{l}_{1}}{{r}_{1}}}=\frac{2L\times r}{L\times 2r}=1\]


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