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Principle of Superposition

Two sinusoida...

Question

Two sinusoidal plane waves of the same frequency having intensities $I_{0}$ and $4 I_{0}$ are travelling in the same direction. The resultant intensity at a point at which the waves meet with a phase difference of $\frac{π}{2}$ is

A

2 I_{0}

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B

5 I_{0}

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C

9 I_{0}

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D

3 I_{0}

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Solution

The correct option is B $5 I_{0}$
We know that resultant intensity at a point is given by,

$I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2} cos Δ ϕ}$

$\Rightarrow I = I_{0} + 4 I_{0} + 2 \sqrt{I_{0} \times 4 I_{o} cos \frac{π}{2}}$
$\Rightarrow I = 5 I_{0}$

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Principle of Superposition

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