JEE Main & Advanced Physics Wave Mechanics Question Bank Progressive Waves

  • question_answer
    The path difference between the two waves \[{{y}_{1}}={{a}_{1}}\sin \,\left( \omega t-\frac{2\pi x}{\lambda } \right)\] and \[{{y}_{2}}={{a}_{2}}\cos \,\left( \omega t-\frac{2\pi x}{\lambda }+\varphi  \right)\] is [MP PMT 1994]

    A)            \[\frac{\lambda }{2\pi }\varphi \]                                   

    B)            \[\frac{\lambda }{2\pi }\left( \varphi +\frac{\pi }{2} \right)\]

    C)            \[\frac{2\pi }{\lambda }\left( \varphi -\frac{\pi }{2} \right)\]             

    D)            \[\frac{2\pi }{\lambda }\varphi \]

    Correct Answer: B

    Solution :

               \[{{y}_{1}}={{a}_{1}}\sin \,\left( \omega \,t-\frac{2\pi x}{\lambda } \right)\]and \[{{y}_{2}}={{a}_{2}}\cos \,\left( \omega \,t-\frac{2\pi x}{\lambda }+\varphi  \right)\]\[={{a}_{2}}\sin \,\left( \omega \,t-\frac{2\pi x}{\lambda }+\varphi +\frac{\pi }{2} \right)\]            So phase difference =\[\varphi +\frac{\pi }{2}\] and D =\[\frac{\lambda }{2\pi }\left( \varphi +\frac{\pi }{2} \right)\]


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