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I am comfortable with the electric and magnetic fields. I would like an explanation similar to the my intuition on the physical meaning of a sound wave (assuming it is correct):

A sound wave is the mathematical representation of air density disturbance.

(Magnitude vs Time) Plotting a sinusoidal sound wave as the density of the disturbed air vs time, the line y=0 would represent the normal density of the air, where peaks represent a higher density, and a valley represents a low density of air for a given value t.

I believe this gives definition provides good intuitions on what exactly a "sound wave" means. However I'm trying to grasp the concept of an EM wave in this manner. Specifically, what the actual wave form means.

Here is my attempt:

The wave is a graphical or mathematical representation of the changing electric and magnetic field at a point. Therefore, the peak of a wave should represent a higher magnitude of the fields at that point, and a valley represents a lower magnitude of the fields at that point.

While I don't know if this is even correct, I'm having a hard time figuring out what the base line y=0 of the graph means. Maybe the magnitude of the E and B fields before the EM wave passes through? That is, what is a negative points in the wave represent?

Also, how is this 'light'?

Can someone clarify things for me?