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BCECE Medical BCECE Medical Solved Papers-2005

  • question_answer
    A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of:

    A)  125 m/s      

    B)  250 m/s

    C)  500 m/s      

    D)  1000 m/s

    Correct Answer: C

    Solution :

    A normal mode of an oscillating system is a motion in which all particles of the system move sinusoidally with the same frequency. In general, pth mode of a string fixed at ends has frequency                 \[n=\frac{p\,v}{2\,l}\] p = 1, 2, 3, ? where v is velocity of wave and \[l\] is length of string. In fourth normal mode, \[p=4\] \[\therefore \] \[n=\frac{4v}{2\,l}\] Given,   \[n=500\,Hz,\,l=2\,m\] Hence, \[500=\frac{4\,v}{2\times 2}\] or \[v=\frac{500\times 4}{4}=500\,m/s\]


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