The wavelength of the waves arriving at P from two coherent sources S1 and S2 is 4 m, while intensity of each wave is I0. The resultant intensity at P is 2I0 Find the minimum value of S2 P.

I=I0+I0+2I0⋅I0cos⁡ϕ=2I0 (given)So cos⁡ϕ=0 ϕ=nπ2=π2 n=1 for S2P to be minimum ϕ=2πλΔx=2π4Δx=π2 Δx=1m Δx=S2P−S1P=1 S2P=S1P+1=(x+1) metre

The wavelength of the waves arriving at P from two coherent sources S1 and S2 is 4 m, while intensity of each wave is I0. The resultant intensity at P is 2I0 Find the minimum value of S2 P.

I=I0+I0+2I0⋅I0cos⁡ϕ=2I0 (given)So cos⁡ϕ=0 ϕ=nπ2=π2 n=1 for S2P to be minimum ϕ=2πλΔx=2π4Δx=π2 Δx=1m Δx=S2P−S1P=1 S2P=S1P+1=(x+1) metre

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The wavelength of the waves arriving at P from two coherent sources S₁ and S₂ is 4 m, while intensity of each wave is I₀. The resultant intensity at P is 2I₀ Find the minimum value of S₂ P.

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$\frac{x \sqrt{5}}{2}$

$2 x$

$(x + 1)$

$(x + \sqrt{2})$

answer is C.

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Detailed Solution

$I = I_{0} + I_{0} + 2 \sqrt{I_{0} \cdot I_{0}} \cos ϕ = 2 I_{0} (given)$

$\begin{array}{l} So \cos ϕ = 0 \\ ϕ = \frac{nπ}{2} = \frac{π}{2} (n = 1 for S_{2} P to be minimum) \\ ϕ = (\frac{2 π}{λ}) Δx = (\frac{2 π}{4}) Δx = \frac{π}{2} \\ Δx = 1 m \\ Δx = S_{2} P - S_{1} P = 1 \\ S_{2} P = S_{1} P + 1 = (x + 1) metre \end{array}$