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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Waves

  • question_answer
      Two sources of sound placed close to each other are emitting progressive waves given by\[{{y}_{1}}=4\sin 600\pi t\] and\[{{y}_{2}}=5\sin 608\pi t\]. An observer located near these two sources of sound will hear:

    A)  4 beats per second with intensity ratio 25 : 16 between waxing and waning.

    B)  8 beats per second with intensity ratio 25 : 16 between waxing and waning

    C) 8 beats per second with intensity ratio 81: 1 between waxing and waning

    D) 4 beats per second with intensity ratio 81 : 1 between waxing and waning

    Correct Answer: D

    Solution :

    [d] \[2\pi {{f}_{1}}=600\pi \] \[{{f}_{1}}=300\]                          ... (i) \[2\pi {{f}_{2}}=608\pi \]                          \[{{f}_{2}}=304\]           ...(ii) \[\left| {{f}_{1}}-{{f}_{2}} \right|=4\,beats\] \[\frac{{{I}_{\max }}}{{{I}_{\operatorname{m}.n.}}}=\frac{{{({{A}_{1}}+{{A}_{2}})}^{2}}}{{{({{A}_{1}}+{{A}_{2}})}^{2}}}=\frac{{{(5+4)}^{2}}}{{{(5-4)}^{2}}}=\frac{81}{1}\] where\[{{A}_{1}}\],\[{{A}_{2}}\] are amplitudes of given two sound wave.


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