The Outcome of Maxwell's Equations

The outcome is the establishment of electromagnetic wave and later it has been proved that Light is an EM wave.
Now we get E(x,t) = E(x - ct) . It is a function of  x,t. As natural continuous functions are Fourier transformable so can find Fourier transform of this wave w.r.t time and space.

E(x,t) = E(x) ∫f(w) e^iwt dw

Now if we assume that only one frequency 'n' is there so we get  :-
E(x,t) = E_s(x) e^2iπnt ~ E_s(x) cos(2πnt) [In real domain]

So, we get a frequency relation.

Now we want to determine the frequency velocity relationship.

We can further write that E(x,t) = Σ E₀ cos(2π(x/λ - n.t)) by taking Fourier transform about both x,t .

Now for a specific bi-periodic wave E(x,t) = E₀ cos(2π(x/λ - n.t)) we get that c = nλ .