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

  • question_answer
    In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m3. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become (take g = 10 ms?2)  [KCET 2001]

    A)            240 Hz                                     

    B)            230 Hz

    C)            220 Hz                                     

    D)            200 Hz

    Correct Answer: A

    Solution :

                         \[n=\frac{p}{2l}\sqrt{\frac{T}{m}}\propto \sqrt{T}\]Þ \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\]            Þ\[\frac{260}{{{n}_{2}}}=\sqrt{\frac{50.7g}{(50.7-0.0075\times {{10}^{3}})g}}\]Þ\[{{n}_{2}}\approx 240\]


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