I have some experience in this. My first layout was built using 5/8" GIS ply in three full slabs mated along their sides to form a huge layout. Yeah, I know, but I wanted exactly that, and didn't have much in the way of problems. Everything ran well, and I used EZ-Track to boot...with 3.8% grades.
I stacked and layered 1.5" carved expanses of foam to create a vast mountain. I carved out the grade on the edge of this mountain. It was a lot of of work. I had a timber scale trestle, scratchbuilt, and another German bridge. The most obviously quiet places on the whole layout were when trains crossed either bridge. You'll find that to be the case. The air surrounding the components of the bridge structure doesn't transmit vibrations well at the frequencies you'll hear from the rest of the 'terrain' you build.
Foam is very noisy. If you support it with joists, stay with 1X4 stood up on edge and wedged between parallel frame stringers, and use PL-300 (safe for foam) to keep it from squirming around on you, you'll find it quite a bit more quiet. Pl-300 eventually dries hard, so the noise will increase. Early on, it stays somewhat malleable, so it will be more quiet.
If you use hardened glue, like many do, say white or yellow glue (they'll both work fine when dry), it will be somewhat noisier because of the hardened glue. If you use a rubbery caulk, it will be quiet. If you have cork or more foam for roadbed to raise the tracks realistically, and use white or yellow, it will be noisy. If you use very thinly spread PL-300, it will eventually become noisy, as I explained above.
So, over/through the surrounding air, as on a bridge, all you can hear is the drive mechanism or the sound system built into the locomotive. Over foam, largely a single expanse, no support, it will be noisy. If you support it, even with a thin sheet of plywood glued below it for either support, or to protect the nether surface , or because you want to mount switch motors and want a harder and more durable surface, it will be more quiet, especially if you use gobs of acrylic caulking.
General rule for acoustics: sounds travel well through single materials. Through composites, not so well. Through two or more monolithic materials sandwiched, very poorly. The idea, if you want to minimize both vibrations AND sound, is to place two different densities of material against each other, flush. Celestron, the telescope manufacturer, used to sell vibration dampening 'shoes', large hockey puck-like things, to place under the legs of their heavy tripods. Users complained that, when they touched the focuser, or even tried to move the scope, it would oscillate or vibrate for many long seconds afterwards, spoiling the view. So, their engineers designed and built these dual-density polymer cups/pucks on which the customer was expected to mount the tripod. It worked surprisingly well. And the same idea applies to sound deadening on the layout. Use different materials, foam and plywood, but soft DAP Alex Plus with Silicone as a fixative between them. Gobs of it, spread a bit, then let the two adhere with some boxes placed atop the foam until the DAP sets.
Lastly, 2" foam, while expensive, will support itself over 6' expanses easily and not sag appreciably over time. If you placed a full paint can in the very middle, all 12 pounds of it, and left it, yeah, that would probably not be so great after a few days, but your structures and trains won't cause that type of deflection.