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

  • question_answer
    Two waves are represented by \[{{y}_{1}}=a\sin \left( \omega \,t+\frac{\pi }{6} \right)\] and \[{{y}_{2}}=a\cos \omega \,t\]. What will be their resultant amplitude [RPMT 1996]

    A)            a    

    B)            \[\sqrt{2}\,a\]

    C)            \[\sqrt{3}\,a\]                     

    D)            2a

    Correct Answer: C

    Solution :

               \[A=\sqrt{(a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos \varphi )}\]            Putting \[{{a}_{1}}={{a}_{2}}=a\] and \[\varphi =\frac{\pi }{3}\], we get \[A=\sqrt{3}a\]


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