Waves from two sources superpose on each other at a particular point, amplitude and frequency of both the waves are equal. The ratio of intensities when both waves reach in the same phase and when they reach with the phase difference of $90^{\circ}$ will be

1 : 1

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\sqrt{2} : 1

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2 : 1

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4 : 1

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Solution

The correct option is C $2 : 1$
Let $I_{1}$ be the intensity when both waves of intensity $I$ reach in the same phase and $I_{2}$ be the intensity when both waves reach with the phase difference of $90^{\circ}$ .
Then, we have
$I_{1} = I + I + 2 \sqrt{I \times I} cos 0^{\circ} = 4 I$
and $I_{2} = I + I + 2 \sqrt{I \times I} cos 90^{\circ} = 2 I$
$\Rightarrow I_{1} : I_{2} = 2 : 1$

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