Why does cos(phi1- phi 2 +kX)=cos(kx)?

[thegirl]

In the case of two fields interfering with each other when calculating the total electric field, cos (phi1-phi2 + kx) = cos( kx) where kx is the path difference between the two fields.

How does cos (phi1-phi2 +kx)=cos(kx) Isit just algebra?

 

[blue_leaf77]

Is it said anything about ##\phi_1-\phi_2##? Those equality can be true if ##\phi_1-\phi_2## is a multiple of ##2\pi##.

 

[thegirl]

Earlier on a general interference between two waves is obtained and it is assumed that they have the same phase velocity and so phi1=phi2, and the function collapses. Perhaps this is the case here?

 

[blue_leaf77]

Is ##\phi = \omega t ##?

 

[thegirl]

I don't think it is, as wt is mentioned seperately when phi is mentioned. Phi is mentioned when defining the amplitude of the wave Eo= |Eo|e^iphi{Eo}, where {Eo} is the unit vector.

 

[vanhees71]

I've no clue, what's discussed here. Do you have two plane waves interfering, i.e., something like
$$\phi=A_0 \cos(\omega t-k x+\phi_1)+A_1 \cos(\omega t-k x+\phi_2)?$$