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

  • question_answer
    Two waves having equations                    \[{{x}_{1}}=a\sin (\omega \,t+{{\varphi }_{1}})\], \[{{x}_{2}}=a\sin \,(\omega \,t+{{\varphi }_{2}})\] If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is                              [CBSE PMT 2001]

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

    B)            \[\frac{2\pi }{3}\]

    C)            \[\frac{\pi }{4}\]                 

    D)            \[\frac{\pi }{3}\]

    Correct Answer: B

    Solution :

               Superposition of waves does not alter the frequency of resultant wave and resultant amplitude                    Þ \[{{a}^{2}}={{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\cos \varphi =2{{a}^{2}}(1+\cos \varphi )\]                          Þ \[\cos \varphi =-1/2=\cos 2\pi /3\]\\[\varphi =2\pi /3\]


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