Q131 / 180 · COMEDK 2019 · Physics

If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude the waves differ in phase by

  • A
    $\pi / 3$
  • Correct answer
    B
    $2 \pi / 3$
  • C
    $\pi$
  • D
    zero

Solution

Given that, amplitude and frequency of two waves are same. Hence, resultant amplitude due to superposition of two waves with phase difference $\phi$ is given by $$ \begin{aligned} A^{2} &=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\ \Rightarrow A^{2} &=A^{2}+A^{2}+2 A^{2} \cos \phi \\ \Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi \end{aligned} $$ $\begin{aligned} \Rightarrow & & \cos \phi &=\frac{-1}{2} \\ \Rightarrow & & \phi &=\frac{2 \pi}{3} \end{aligned}$

Hence, the correct answer is option: 'B'.

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