Many objects in nature can be thought of as "mass-spring-systems" because they are composed of objects which have inertial mass as well as a spring like stiffness. It is natural for mass spring systems to enter into sinusoidal oscillation. These oscillations may create vibrations of the surrounding air (i.e. periodic sounds), as described under "sound propagation" below.
This figure is an animated version of Figure 1-1 of "Auditory Neuroscience"
The thing to take away from this are the following:
Whenever you have objects that have "springiness" and "heaviness" (and a lot of objects do), then, due to some relatively simple laws of physics, these objects will "want to vibrate sinusoidally". This makes them potential sound sources.
Also, because of the same laws of physics, lighter objects will vibrate faster - at higher frequencies - than heavier ones.
Even if your mathematical brain doesn't know how to solve the physical equations that prove this last point, your auditory brain still appreciates this intuitively. Listen to the sounds made by two different mystery objects here below, "object A" and "object B". You can't see the objects of lift them, but you still can easily tell which one is heavier. It's obvious, isn't it?