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NEET Sample Paper NEET Sample Test Paper-17

  • question_answer
    Equations of two progressive waves at a certain point in a medium are given by \[{{y}_{1}}=a\sin (\omega t+{{\phi }_{1}}),\]and\[{{y}_{2}}=a\sin (\omega t+{{\phi }_{2}}).\]If amplitude and time period of resultant wave formed by the superposition of two waves is same as that of both the waves, then\[({{\phi }_{1}}-{{\phi }_{2}})\]is:

    A) \[\frac{\pi }{3}\]                                 

    B) \[\frac{2\pi }{3}\]                               

    C) \[\frac{\pi }{6}\]                                 

    D) \[\frac{\pi }{4}\]   

    Correct Answer: B

    Solution :

    \[{{A}^{2}}=a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos \phi \] Here, \[\phi ={{\phi }_{1}}-{{\phi }_{2}},A={{a}_{1}}={{a}_{2}}=a\] Putting there values, \[\cos \phi =-\frac{1}{2}\]or \[\phi =2\pi /3.\] Hence, the correction option is [b].


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