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AMU Medical AMU Solved Paper-2014

  • question_answer
    A 70 cm long sonometer wire is in unison with a tuning fork. If the length of the wire is decreased by 1.0 cm, it produces 4 beats per second with the same tuning fork. The frequency of the tuning fork is

    A)  186 Hz                 

    B)  220 Hz

    C)  276 Hz

    D)  312 Hz

    Correct Answer: C

    Solution :

                     Let the frequency of the fork be n. In the first case, the length of the wire is 70cm. Therefore,                 \[n=\frac{1}{2\times 70}\sqrt{\frac{T}{m}}\]                                       ?. (i) On decreasing the length of the wire, its frequency will increase. Hence, in the second case when the length is 69cm, then                 \[n+4=\frac{1}{2\times 69}\sqrt{\frac{T}{m}}\]                  .... (ii) Dividing Eqs. (i) by (ii), we get                 \[\frac{n}{n+4}=\frac{1/70}{1/69}\] \[\Rightarrow \]               \[\frac{n}{n+4}=\frac{69}{70}\]                 \[70n-69\,n=69\times 4\]                                 \[n=276\,Hz\]


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