Q144 / 180 · COMEDK 2013 · 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
    $\pi$
  • B
    zero
  • C
    $\pi / 3$
  • Correct answer
    D
    $2 \pi / 3$

Solution

The resultant amplitude after super position of two wave differing in phase by $\phi$ is given by $$ \begin{array}{ll} & A_{R}^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\ \Rightarrow & A_{1}=A_{2}=A_{R}=A \\ \Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi \\ \Rightarrow & \cos \phi=-\frac{1}{2} \\ \Rightarrow & \phi=\pi-\frac{\pi}{3}=\frac{2 \pi}{3} \end{array} $$

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

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