Two waves of equal amplitude and frequency interfere with each other. The ratio of intensity when the two waves arrive in phase to that when they arrive $90^{\circ}$ out of phase is:

  • A
    $1 : 1$
  • B
    $\sqrt{2} : 1$
  • C
    $2 : 1$
  • D
    $4 : 1$

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The displacement equations of two interfering waves are given by
$y_1 = 10 \sin \left(\omega t + \frac{\pi}{3}\right) \text{ cm}$
$y_2 = 5[\sin (\omega t) + \sqrt{3} \cos \omega t] \text{ cm}$ respectively.
The amplitude of the resultant wave is $............. \text{ cm}$.

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