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JEE Main & Advanced Physics Wave Mechanics Question Bank Critical Thinking

  • question_answer
    The displacement due to a wave moving in the positive x-direction is given by \[y=\frac{1}{(1+{{x}^{2}})}\] at time \[t=0\] and by \[y=\frac{1}{[1+{{(x-1)}^{2}}]}\] at \[t=2\] seconds, where x and y are in metres. The velocity of the wave in m/s is

    A)            0.5 

    B)            1

    C)            2    

    D)            4

    Correct Answer: A

    Solution :

               In a wave equation, x and t must be related in the form \[(x-v\,t)\]. We rewrite the given equations \[y=\frac{1}{1+{{(x-v\,t)}^{2}}}\] For \[t=0,\] this becomes \[y=\frac{1}{(1+{{x}^{2}})}\], as given For \[t=2,\] this becomes \[y=\frac{1}{[1+{{(x-2v)}^{2}}]}=\frac{1}{[1+{{(x-1)}^{2}}]}\] Þ \[2v=1\] or \[v=0.5m/s\].


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