Sound reduction must be balanced with other factors in my opinion. Carpeting is excellent from the many times I've seen it used at portable train show displays. Unfortunately, it is difficult to erect signs, trees, and other landscaping without heavy glue or screws. I am not sure about its flamibility depending on the materials used and whether your train has sparking. Homasote, the ubiquitous material for sound deadening on layouts, is almost like foam, but suffers from the same thing as carpeting for the stable placement of items and fixing down track. Although a smoother surface than carpeting, You can't use screws well and have to use glue to hold things down. The screws won't hold well. My preference is first to increase mass by cutting a piece of drywall to the size of your platform. The platform can be 1/2" to 3/4" plywood or any other wood (like particle board) you want to use (I don't use particle board because of the formaldehyde binder used in its formulation--but it is definitely firmer than plywood). The combination of drywall and wood platform gives you the mass almost like running your train on a cement floor with very little vibration. Keep in mind that vibration is what makes sound. The next thing is to either use a roadbed made from foam or cork for your track or else line the entire platform with cork which is what I did. You can use sheets or cut the cork from rolls in the size to cover your platform. This cuts down on surface vibration and also holds screws much better than foam when fixing down your tracks. By using cork over the entire platform also cuts down surface vibration from operating accessories on your layout. I have also placed blue sill plate foam under switches to further reduce that noise and done the same with some operating accessories, like the Lionel gateman. In screwing in the track ties, I put a dab of non-hardening caulk between the screw heads and ties. The screw itself never penetrates beneath the cork. All the ties have foam strips cut from a roll that is normally used as weatherstripping. I do not use many screws, just enough, especially at curves, to keep the track stable and a couple along the straight runs. Too many screws, if they penetrate into the platform can cause vibration to be transmitted; however with the drywall underneath, probably will not to amount to much noise from that vibration. That is the good thing about increasing mass. Recently, I ballasted my 0 gauge tubular with gravel stones used in fish tanks, with some glue and double-faced tape at the bottom to stabilize the stones. I think this also reduced vibration along the tracks, stabilized the tracks, and made for less noise. Perhaps this was due to another increase in mass along the tracks because the surface noise of the cars going on the track now is not as great and the track seems more solid on its surface with all the stones inside and out along the edges of the track. I incorporated another suggestion which I think is more theoretical than practical: I used pillow fluff inside all my boxcars and covered hoppers to minimize any vibration from the wheels and trucks that could be transmitted to the body of the car and amplified by the hollowness of the car. Again, I did not notice any apparent difference in noise level, but it may be more minor than significant. Finally, make sure you have close bracing of benchwork, especially on large boards without drywall underneath. Insufficient bracing can introduce vibration of the platform creating a drum head effect. I also have my layout on a carpeted floor which helps minimize sound emanating from under the platform that bounces to the floor. Hardwood floors can bounce the sound around creating an echo sometimes. I run eight trains and a trolley on my layout simultaneously, using separate loops; so you can understand why I am somewhat interested in this topic. Originally, before I revamped my layout, no one could even hear each other talk from the noise level.
