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JEE Main & Advanced Physics Wave Mechanics JEE PYQ-Wave Mechanics

  • question_answer
    Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats and frequency \[5\,Hz.\] The tension of the string B is slightly increased and the beat frequency is found to decrease by\[3\,Hz.\]If the frequency of is , the original frequency of A is 425 Hz, the original frequency of B is

    A)  430 Hz

    B)  428 Hz

    C)  422 Hz            

    D)  420 Hz

    Correct Answer: A

    Solution :

    [a] the difference in frequency is known as the number of beats.
    Here, frequency of \[A\,{{f}_{A}}=324\,Hz\]
    We know,
    Frequency of \[B\,{{f}_{B}}={{f}_{A}}\,\pm \]beat frequency
    \[=425\pm 5\]
    \[=420Hz\text{ }or\text{ }430Hz\]
    Now, if tension in string slightly reduced then its frequency also reduce from\[{{f}_{B}}\]
    Now, if tension in the string is slightly reduced its frequency will also reduce from 324 Hz.
    Now, if
    \[{{f}_{B}}=420\]reduces, then beat frequency should increase which is not the case but if
    \[{{f}_{B}}=430\,Hz\]then beat frequency should decrease, which is the case
    hence =430 Hz.
    \[{{f}_{B}}=430\,Hz.\]
    Let the frequency of string
    \[B=\]
    \[{{f}_{B}}\]and frequency of string
    Initially beat frequency =\[=5Hz\]
    Now the tension in string B is increased so frequency b will decrease as frequency is inversely proportional to tension.
    \[{{f}_{A}}=425\,HZ\]
    \[{{f}_{B}}\]can be either 430HZ or 420HZ
    But when tension is increased frequency\[{{f}_{B}}\] will decrease and it is given that it produces beat frequency\[=3HZ\]
    Which is only possible when\[fB=230Hz\]
    \[{{F}_{B}}=430HZ\]   


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