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Question

x1=Asin(ωt0.1x) and x2=Asin(ωt0.1xϕ2). Resultant amplitude of combined wave is

A
2Acosϕ4
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B
A2cosϕ/2
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C
2Acosϕ2
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D
A2(1+cosϕ4)
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Solution

The correct option is A 2Acosϕ4
x1=Asin(ωt0.1x)
x2=Asin(ωt0.1xϕ2)
x1+x2=A[sin(ωt0.1x)+sin(ωt0.1xϕ2)]
=A⎢ ⎢ ⎢2sin⎜ ⎜ ⎜ωt0.1x+ωt0.1xϕ22⎟ ⎟ ⎟.cos⎜ ⎜ ⎜ωt0.1xωt+0.1x+ϕ22⎟ ⎟ ⎟⎥ ⎥ ⎥
=2Acosϕ4.sin(ωt0.1xϕ4)
So, amplitude will be =2Acosϕ4

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