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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • 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 \[{{v}_{1}}\]. The ratio \[{{v}_{1}}/{{v}_{2}}\]

    A)  \[2:1\]                                      

    B)  \[4:1\]

    C)  \[8:1\]                                      

    D)  \[1:1\]

    Correct Answer: D

    Solution :

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


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