The resultant intensity for two identical waves of intensity I with a phase difference of $π / 3$ is

R = 2 \sqrt{3 I}

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R = \sqrt{3 I}

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R = 4 \sqrt{3 I}

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R = 3 \sqrt{3 I}

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Solution

The correct option is B $R = \sqrt{3 I}$
The resultant of two waves is given by $R^{2} = A^{2} + B^{2} + 2 A B c o s θ; θ$ is the phase difference and A and B are the amplitudes of the individual waves.
Since both the waves are identical, their amplitudes are equal

Thus, $R^{2} = A^{2} + A^{2} + A^{2} = 3 A^{2} ⟹ R = \sqrt{3} A$
Since intensity is proportional to $\sqrt{A}$ , we can write the resultant amplitude $R = \sqrt{3 I}$
The correct option is (b)

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