I wanted to add, the sound is similar to what a fluorescent lightbulb might sound like.

Your son is correct... it is the low voltage transformer making the noise.

Normel- is that Normal? Or is it indicative of a bad transformer?

It is quite normal.
The transformer is probably not "buzzing", I would guess that it is attcahed to some metal duct work and the vibration of the transformer is causing the buzz.
Have someone move the transformer or remount it with some kind of vibration isolation and the noise will probably disappear or significantly diminish.

not to shoot down the transformer idea making the noise, but is your furnace by chance electric?
I myself have an electric furnace in one of my houses that makes a buzzing noise. It comes from one of the double pole breakers in the furnace unit. Some breakers just make a buzzing noise.
I haven't tired replacing the breaker because I don't care that much since the noise isn't that loud and there's no harm from it buzzing at all.