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WB JEE Medical WB JEE Medical Solved Paper-2006

  • 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 \[{{v}_{1}}/{{v}_{2}}\]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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