MCQ
Two waves having equations
$ x_1=a \sin \left(\omega t+\phi_1\right), x_2=a \sin \left(\omega t+\phi_2\right)$
If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is
  • A
    $\frac{\pi}{6}$
  • $\frac{2 \pi}{3}$
  • C
    $\frac{\pi}{4}$
  • D
    $\frac{\pi}{3}$

Answer

Correct option: B.
$\frac{2 \pi}{3}$
(b) Superposition of waves does not alter the frequency of resultant wave and resultant amplitude
$\Rightarrow a^2=a^2+a^2+2a^2\cos\phi=2a^2(1+\cos\phi)$
$\Rightarrow \cos \phi=-1 / 2=\cos 2 \pi / 3 $
$\therefore \phi=2 \pi / 3$

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