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Question

Two waves represented by equation,
y1=2sin(πt0.1x) and y2=2sin(πt0.1x+ϕ) are superimposed. If the resultant wave has a maximum amplitude equal to 4 cm, the value of ϕ is :

A
π
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B
2π
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C
π2
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D
3π2
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Solution

The correct option is B 2π
The phase difference between the given waves is,
Δϕ=(πt0.1x+ϕ)(πt0.1x)
Δϕ=ϕ
Here, we can see that the maximum amplitude of resultant wave:
Amax=A1+A2
The maximum amplitude of resultant wave suggests that the waves have interfered constructively.
Δϕ=2nπ
The phase difference between waves is an integral multiple of 2π
For n=1,
Δϕ=ϕ=2π

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