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JEE Main & Advanced Physics Wave Mechanics Question Bank Interference and Superposition of Waves

  • question_answer
    Out of the given four waves (1), (2), (3) and (4)                    \[y=a\sin (kx+\omega t)\]                                                                        ......(1)                    \[y=a\sin (\omega t-kx)\]                                                                         ......(2)                    \[y=a\cos (kx+\omega t)\]                                                                       ......(3)                    \[y=a\cos (\omega t-kx)\]                                                                        ......(4) emitted by four different sources \[{{S}_{1}},\,{{S}_{2}},\,{{S}_{3}}\] and \[{{S}_{4}}\] respectively, interference phenomena would be observed in space under appropriate conditions when    [CPMT 1988]

    A)            Source \[{{S}_{1}}\] emits wave (1) and \[{{S}_{2}}\] emits wave (2)

    B)            Source \[{{S}_{3}}\] emits wave (3) and \[{{S}_{4}}\] emits wave (4)

    C)            Source \[{{S}_{2}}\] emits wave (2) and \[{{S}_{4}}\] emits wave (4)

    D)            \[{{S}_{4}}\] emits waves (4) and \[{{S}_{3}}\] emits waves (3)

    Correct Answer: C

    Solution :

               For interference, two waves must have a constant phase relation ship. Equation ?1? and ?3? and ?2? and ?4? have a constant phase relationship of \[\frac{\pi }{2}\] out of two choices. Only one S2 emitting ?2? and S4 emitting ?4? is given so only  option is correct.


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