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

  • question_answer
    A string is rigidly tied at two ends and its equation of vibration is given by \[y=\cos 2\pi \,t\sin \sin \pi x.\] Then minimum length of string is                                                           [RPMT 2001]

    A)            1 m                                           

    B)            \[\frac{1}{2}m\]

    C)            5 m                                           

    D)            2pm

    Correct Answer: B

    Solution :

                         Given equation of stationary wave is                    \[y=\sin 2\pi x\cos 2\pi t\], comparing it with standard equation \[y=2A\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi x}{\lambda }\]                    We have \[\frac{2\pi x}{\lambda }=2\pi x\] Þ \[\lambda =1m\]            Minimum distance of string (first mode)\[{{L}_{\min }}\,=\frac{\lambda }{2}=\frac{1}{2}m\]


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