Resultant amplitude of two interfering waves

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SUMMARY

The resultant amplitude of two interfering waves can be calculated using two distinct equations: A_r = √(A_1² + A_2² + 2 A_1 A_2 cos(φ)) and 2A cos(δ/2) sin(kx - ωt + δ/2). The first equation focuses solely on amplitude, while the second encompasses the entire wavefunction. In the second equation, the amplitude is represented as 2A cos(δ/2), assuming A1 and A2 are equal (A1 = A2 = A). The phase difference φ in the first equation corresponds to δ in the second, indicating a direct relationship between the two formulations.

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Maxo
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How do you calculate the resultant amplitude of two interfering waves, at any given point?

I found two different equations:
[tex]A_r = \sqrt{A_1^2 + A_2^2 + 2 A_1 A_2 \cos{\varphi}}[/tex]
but also
[tex]2A cos(\delta/2)sin(kx-\omega t+\delta/2)[/tex]

How are these two equations related?
 
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To compare the two equations you must understand that the 1st equation shows just the amplitude while the 2nd equation shows the whole wavefunction. The amplitude in the 2nd equation is just 2Acos(δ/2). Also the second equation assumes A1 and A2 are identical A1=A2=A. Finally, the ø of the first equation and the δ of the second are the same thing under different names. May be now you can find how they are related?
 
Thanks.
 
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