Originally Posted by hellosailor
The lead/vinyl absorbs energy just because it is so dense. The foam decouples that vibration from the engine compartment walls, and in theory you get less noise.
The lead/vinyl for the most part doesn't absorb the energy. Its purpose is to create a density change which reflects sound back into the engine compartment. Both density transitions (air to lead/vinyl, and lead/vinyl to foam) reflect sound. The foam also creates a third density change (foam to fiberglass) which causes an additional reflection. The foam does absorb energy as you explain, but its primary purpose is to create additional density changes and thus additional reflections. Each reflection means less sound that's leaking out of the compartment.
Reflection and Transmission
This is also the reason that certain fish without swim bladders (e.g. tuna) don't show up well on fishfinders. Muscle is almost the same density as water, so without much of a density change there isn't much echo for the sonar to pick up. A swim bladder OTOH (muscle to air to muscle) creates a big echo.