How can sine waves represent both AC and sound waves?

There are several parameters that can be used to represent the sound wave. The most common is acoustic pressure. This is the change in pressure above and below the equilibrium pressure. So zero acoustic pressure means equilibrium pressure which may be just atmospheric pressure for sound waves in open air.

Look at this animation showing a sound wave propagating from right to left.

_{(animation from Dennis Lindwall - Marine Seismic Surveys with Vector Acoustic Sensors)}

In real sound waves the oscillation is not as slow as in this animation, but much faster (between $20$ and $20000$ oscillations per second).

You see there are several kinds of oscillations occurring:

• Every single particle oscillates between a left-most and a right-most position (see the red arrow). So its position as a function of time can be described by a sine function.
• The density at every place oscillates between higher and lower density (see the blue marks). So the density as a function of time can be described by a sine function.

Silence (i.e. no sound) means, all particles are sitting still and also the density is constant all over the place.