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

  • question_answer
    Two travelling waves \[{{y}_{1}}=A\sin [k(x-ct)]\] and\[{{y}_{2}}=A\sin [k(x+ct)]\]are superimposed on string. The distance between adjacent nodes is

    A)  \[ct/\pi \]          

    B)  \[ct/2\pi \]

    C) \[\pi /2k\]          

    D) \[\pi /k\]

    Correct Answer: D

    Solution :

    [d] \[y=A\sin (kx-kct)+A\sin (kx+kct)\] \[=2\,A\,\sin \] \[\left( \frac{kx-kct+kx+kct}{2} \right).\cos \left( \frac{kx-kct-kx-kct}{2} \right)\] \[=2\,A\,\sin (kct).cos\,kx.\] Thus\[\frac{2\pi }{\lambda }=k\],   \[\therefore \lambda =\frac{2\pi }{k}\] The distance between adjacent nodes \[=\frac{\lambda }{2}=\frac{\pi }{k}\]


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