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Question

A wave is represented by y1=10cos(5x+25t)
where, x is measured in metres and t in seconds. A second wave for which y2=20cos(5x+25t+π3)
interferes with the first wave. Deduce the amplitude and phase of the resultant wave.

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Solution

y1=10cos(5x+25t)
y2=20cos(5x+25t+π3)
Resultant wave will be (S=π3)
y=y1+y2=Acos(5x+25t+α)
Where,
A=A12+A22+2A1A2cosδ
=(10)2+(20)2+2(200)cosπ3
A=26.46cm
tanα=A2sinδA1+A2cosδα=0.714rad.

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