Resultant amplitude of two interfering waves

[Maxo]

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

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

How are these two equations related?

 

[dauto]

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?

 

[Maxo]

Thanks.