In the figure the intensity of waves arriving at D from two coherent sources S1 and S2 is I0. The wavelength of the wave is λ=4 m. Resultant intensity at D will be:

Question

In the figure the intensity of waves arriving at D from two coherent sources S1 and S2 is I0. The wavelength of the wave is λ=4 m. Resultant intensity at D will be: (A) 4 I0 (B) I0 (C) 2 I0 (D) zero

Tardigrade Admin · Accepted Answer

Path differences, Δ x=S2 D-S1 D=5-4=1 m ∴ The corresponding phase difference will be φ=(2 π/λ) Δ x=(2 π/4) ⋅ 1=(π/2) Using I=I1+I2+2 √I1 I2 cos φ I=I0+I0 +2 √I0 I0 cos (π/2)=2 I0

Q. 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:

$4 I_{0}$

$I_{0}$

$2 I_{0}$

zero

Path differences, $Δ x = S_{2} D - S_{1} D = 5 - 4 = 1 m$
$∴$ The corresponding phase difference will be
$ϕ = \frac{2 π}{λ} Δ x = \frac{2 π}{4} \cdot 1 = \frac{π}{2}$
Using $I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
$I = I_{0} + I_{0} + 2 I_{0} I_{0} cos \frac{π}{2} = 2 I_{0}$

Q. In the figure the intensity of waves arriving at D from two coherent sources S1​ and S2​ is I0​. The wavelength of the wave is λ=4m. Resultant intensity at D will be:

4I0​

I0​

2I0​