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

  • question_answer
    Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is ?a? and the phase of A is ahead by \[\frac{\pi }{3}\] than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter                  [BVP 2003]

    A)            2a  

    B)            \[a\sqrt{3}\]

    C)            \[a\sqrt{2}\]                         

    D)            a

    Correct Answer: D

    Solution :

               Path difference \[(\Delta x)\] \[=50\,cm\,=\frac{1}{2}m\]                    \[\therefore \] Phase difference \[\Delta \varphi =\frac{2\pi }{\lambda }\times \]\[\Delta x\Rightarrow \varphi =\frac{2\pi }{1}\times \frac{1}{2}=\pi \]                    Total phase difference = \[\pi -\frac{\pi }{3}=\frac{2\pi }{3}\]                    Þ \[A=\sqrt{{{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\cos (2\pi /3)}=a\]


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