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BHU PMT BHU PMT (Screening) Solved Paper-2008

  • question_answer
    The displacement of a particle executing periodic motion is given by \[y=4{{\cos }^{2}}(t/2)\sin (1000t)\] This expression may be considered to be a result of superposition of

    A)  two waves       

    B)  three waves

    C)  four waves      

    D)  five waves

    Correct Answer: B

    Solution :

                     \[y=4{{\cos }^{2}}(t/2)\sin (1000t)\] \[=2[2{{\cos }^{2}}(t/2)\sin (1000t)]\] \[=2(1+\cos t)\sin (1000t)\] \[=2\sin (1000t)+2\sin (1000t)\cos t\] \[=2\sin (1000t)+\sin (1001t)+\sin (999t)\] Thus, given wave represents the superposition of three waves.


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