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

  • 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 n1 and the other with frequency n2. The ratio n1/n2 is given by [IIT-JEE (Screening) 2000]

    A)            2    

    B)            4 

    C)            8    

    D)            1

    Correct Answer: D

    Solution :

                         Fundamental frequency \[n=\frac{1}{2l}\sqrt{\frac{T}{\pi {{r}^{2}}\rho }}\]  where m = Mass per unit length of wire Þ\[n\propto =\frac{1}{lr}\Rightarrow \frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{r}_{2}}}{{{r}_{1}}}\times \frac{{{l}_{2}}}{{{l}_{1}}}=\frac{r}{2r}\times \frac{2L}{L}=\frac{1}{1}\]


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