Two waves y1=Asin(ωt−kx) and y2=Asin(ωt−kx+ϕ) are superimposed such that the resultant amplitude of oscillation is √2A, then the value of ϕ is
A
π2
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B
π4
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C
π3
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D
π6
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Solution
The correct option is Aπ2 The resultant amplitude of oscillation is given by, Ar=√A21+A22+2A1A2cos Δϕ
where Δϕ=ϕ is the phase difference between given waves.
Given: Ar=√2A ⇒√2A=√A2+A2+2A2cos Δϕ ⇒2A2=2A2(1+cos ϕ) ⇒1+cos ϕ=1 ⇒cos ϕ=0 ⇒ϕ=π2or3π2 ∴Option (a) is correct.