Two waves have equations x1=asin(kx−ωt+ϕ1) and x2=asin(kx−ωt+ϕ2). If in the resultant wave the frequency and amplitude remain equal to amplitude and frequency of each superimposing waves, the phase difference between them is
A
π6
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B
2π3
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C
π4
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D
π3
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Solution
The correct option is B2π3 Given, x1=asin(kx−ωt+ϕ1) x2=asin(kx−ωt+ϕ2)
Resultant, x′=x1+x2
x′=a[sin(kx−ωt+ϕ1)+sin(kx−ωt+ϕ2)]
Using , sinC+sinD=2sin(C+D2)cos(C−D2)
x′=2asin(kx−ωt+ϕ1+ϕ22)cos(ϕ1−ϕ22)
From the data given in the question, we can say that,