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MGIMS WARDHA MGIMS WARDHA Solved Paper-2008

  • question_answer
    When the length of the vibrating segment of a sonometer wire is increased by 1%, the percentage change in its frequency is

    A) 100/101                               

    B) 99/100

    C) 1                                             

    D) 2

    Correct Answer: C

    Solution :

    The frequency of sonometer wire is                                                                                          \[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\] Taking logarithm and differentiate, we get                           \[\frac{\Delta n}{n}=\frac{\Delta l}{l}+\frac{1}{2}\frac{\Delta T}{T}+\frac{1}{2}\frac{\Delta m}{m}\]                                                                                                               \[\therefore\]                                                                             \[\frac{\Delta n}{n}=\frac{\Delta l}{l}+0+0=1%\] Hence, frequency will increase by 1%.


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