Empty egg trays are generally not used “professionally” as acoustic dampers.
“egg crate foam” is a style of foam construction used to “cheaply” deaden sound.
The pro ones are generally more pointy: http://www.foambymail.com/soundproofing.html
And actual anechoic chambers look really scary: http://www.ta.chalmers.se/images/CRAG/hemi_anech.jpg
For typical building acoustics, they don’t bother with foam, usually 2” duct liner is just tacked up behind visual screens to absorb extra reflections