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JEE Main & Advanced AIEEE Solved Paper-2011

  • question_answer
    The transverse displacement \[y(x,t)\] of a wave on a string is given by \[y(x,t)={{e}^{-\left( a{{x}^{2}}+b{{t}^{2}}+2\sqrt{ab}xt \right)}}\] This represents a   AIEEE  Solved  Paper-2011

    A) Standing wave of frequency \[\frac{1}{\sqrt{b}}\]

    B) Wave moving in \[+x\] direction with speed \[\sqrt{\frac{a}{b}}\]

    C) Wave moving in \[-x\] direction with speed \[\sqrt{\frac{b}{a}}\]

    D) Standing wave of frequency \[\sqrt{b}\]

    Correct Answer: C

    Solution :

                 \[y(x,t)={{e}^{-{{(\sqrt{a}x+\sqrt{b}\,t)}^{2}}}}\] This is a wave travelling in \[-x\] direction with speed \[\frac{\sqrt{b}}{\sqrt{a}}\]


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