Roofing felt is something of a misnomer. It is made from paper fibers or spun polyester, saturated with asphalt and pressed into thin, flat sheets. It doesn't feel fibrous and is not soft to the touch like felt. Roofing felt does not insulate and is not truly weather tight.
Roofing felt -- or roofing paper -- is applied to the substrate of a roof before installing shingles or metal roofing. The felt forms an adequately tight envelope that keeps weather out of the house before the permanent roof is installed. Once the shingles are nailed to the roof, the felt is riddled with nail holes and does not serve as a last resort to stop rain that gets past the shingles.
Roofing felt will do little to dampen outside noises from coming through the roof.
The true solution to noise is adequate insulation in the attic, either in the floorboards or on the underside of the roof itself. The best noise dampening for a roof is the use of closed-cell polyurethane foam insulation, which wards off cold, moisture and noise.
If you install insulation on both the underside of the roof and in the attic floor boards, you should have significant noise reduction. Insulating exterior walls helps to further dampen noise. New, double-glazed windows are often used as a solution to excessive noise in houses near airports and military installations.