The Maxwell Equations contains four components. The first is about the electric field, the second is about the magnetic field, the third is about how the change electric field generates electricity, the last one is conversely, how the change of electric field or/and electric current generates magnetism.

Previously, classical Newtonian physicists have deduced the following equation to describe waves:

After applying the approximation of tanθ≈sinθ ,

By dividing dx on both sides of the above equation, one applies second differentiation and reach

They found this left part u/T square root is the reverse of the speed of light, hence

Replying on math manipulation

We can take vector times on below third equation of Maxwell Equations,

to get

This already looks quite similar to the wave equation (in three dimensions) as below

If we plug in μ0=4π×10^-7N/A²，ε0=8.854187818×10^ -12 (F/m)，we get the velocity of magnetism in vacuum is exact same as speed of light:

Same can be deduced from the fourth equation of the magnetism generated from the change of electricity, it also is a wave and runs at the speed of light.