Track decay rate (TDR), meaning the rate of attenuation of bending waves through the rail, is the most important indicator of a track’s dynamic characteristic impacting the rail noise emission. TDR depends on various parameters related to the construction of the track, and it can be increased using rail dampers. These are mechanical devices working on the principle of dynamic absorbers and are attached to the rail. This paper addresses the track with light rails needing improvements to reduce the rail noise emission using a particular rail damper with a mixed damping system (rubber–oil). The bending waves that propagate through the rail, the frequency response function of the rail, and TDR are investigated considering different scenarios regarding the parameters of the track: soft/stiff rail pad, tampered/settled ballast, and sleeper bay. To this end, an analytic model of the track featuring rail dampers consisting of an infinite Timoshenko beam with discrete attached oscillators is used. Numerical results show the possibility to increase TDR of railway track with light rails for both soft/stiff rail pads from 4 to 500 Hz up to 1250–1600 Hz using rail dampers with a mixed damping system.