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Question

Two waves of the same frequency and same amplitude are superimposed to produce a resultant disturbance wave of the same amplitude. What is the phase difference between the two original waves?

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Solution

Given that,
Frequency of first wave = Frequency of second wave.
Amplitude of first wave = Amplitude of second wave =A
Let ϕ is the phase difference between the two waves, then the resultant amplitude(AR) of the wave is given by
AR=A21+A22+2A1A2cosϕ
Substitute A1=A2=A
AR=A2+A2+2A2cosϕ
AR=A=2A2(1+cosϕ)
A=4A2cos2ϕ2
A=2Acosϕ2
cosϕ2=12
cosϕ2=cosπ3
ϕ=2π3
Why this question?

Bottom lines: Always remember that if two wave of same frequency and different amplitude is superpose then the resultant amplitude after superposition of wave is AR=A12+A22+2A1A2cosϕ where ϕ is phase difference between wave.

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