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

  • question_answer
    Calculate the frequency of the second harmonic formed on a string of length 0.5 m and mass 2 ´ 10?4 kg when stretched with a tension of 20 N                                        [BHU (Med.) 2000]

    A)            274.4 Hz                                 

    B)            744.2 Hz

    C)            44.72 Hz                                 

    D)            447.2 Hz

    Correct Answer: D

    Solution :

                         Mass per unit length \[m=\frac{2\times {{10}^{-4}}}{0.5}kg/m\]\[=4\times {{10}^{-4}}kg/m\]                    Frequency of 2nd harmonic \[{{n}_{2}}=2{{n}_{1}}\]            \[=2\times \frac{1}{2l}\sqrt{\frac{T}{m}}\]\[=\frac{1}{0.5}\sqrt{\frac{20}{4\times {{10}^{-4}}}}=447.2Hz\]


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