Having a forcing term leads to the ability to continually pump energy into a system. However, if there is friction then any time there is motion energy is being pulled out of the system. The more friction there is, the more energy that gets pulled out. If you are looking at a place very close to the energy source then there is comparitively little friction, and the amplitude can be large. However, farther from the source the sound has had to propagate farther and interacted with more friction, and so more of the energy is lost and the amplitude drops. Thus, farther from the source the amplitude drops due to the friction.
A full mathematical description of this phenomenon is beyond the scope of this website, but it may be helpful to see what the solution to the pressure is for sound in a tube. If there is a loudspeaker at $x=0$ in a tube that extends to positive $x$, and the loudspeaker induces a pressure such that the pressure $p$ satisfies
$$p(0,t) = A\cos(2\pi f t),$$
where $A$ is the amplitude, $f$ is the frequency, and $t$ is the time, then we may write the pressure everywhere as
$$p(x,t)=Ae^{-\alpha x}\cos(2\pi f [t - x/c]),$$
where $\alpha$ is called the absorption coefficient, and is related to strength of the friction and the frequency of the signal. Also, $c$ here is the sound speed. Notice that the amplitude of the wave decreases exponentially with distance from the source. More complicated scenarios are, naturally, more complicated, but this basic principle remains true.
