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YDSE Problems I

In the figure...

Question

In the figure, the intensity of waves arriving at D from two coherent sources $s_{1}$ and $s_{2}$ is $I_{0}$ . The wavelength of the wave is $λ = 4 m$ . Resultant intensity at D will be

$4 I_{0}$

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$I_{0}$

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$2 I_{0}$

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Zero

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Solution

The correct option is C
$2 I_{0}$

Path difference

$Δ x = s_{2} D - s_{1} D = 5 - 4 = 1 m$

$∴$ The corresponding phase difference will be

$ϕ = \frac{2 π}{λ} Δ x = (\frac{2 π}{4}) (1) = \frac{π}{2}$

Using $I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} c o s ϕ$

$I = I_{0} + I_{0} + 2 \sqrt{I_{0} I_{0}} c o s \frac{π}{2} = 2 I_{0}$

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