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MGIMS WARDHA MGIMS WARDHA Solved Paper-2008

  • question_answer
    The equation of a simple harmonic wave is given by y = 5 sin                                                                                                             \[\frac{\pi }{2}\] (100 t - x), where x and y are in metre and time is in second. The period of the wave in second will be

    A)  0.04                                      

    B) 0.01

    C) 1                                             

    D) 5

    Correct Answer: A

    Solution :

    The given equation is                                                                                             \[y=5\sin \frac{\pi }{2}(100t-x)\]                         ...(i) Comparing Eq. (i) with standard wave equation, given by                                                                                                   \[y=A\sin (\omega t-kx)\]                            ...(ii) we have                                                                                         \[\omega =\frac{100\pi }{2}=50\pi\]                                                                                                              \[\Rightarrow\]                                                                                                     \[\frac{2\pi }{T}=50\pi\]                                                                                                              \[\Rightarrow\]                                                                                           \[T=\frac{2\pi }{50\,\pi }=0.04\,s\]


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