The particles in the interactive are not behaving as they would in the real world. They do not collide, and they do not jitter. You can, however, think of them as if they are interacting with one another using some kind of force field.

You can visually verify the wave equation $$\frac{\partial^2 \chi}{\partial x^2} = \frac{1}{c^2_s} \frac{\partial^2 \chi}{\partial t^2}.$$ The bottom coordinate system contains two plots: a blue one that illustrates $\frac{\partial^2 \chi}{\partial x^2}$, and a red one that illustrates $\frac{\partial^2 \chi}{\partial t^2}$. Notice that they have the same shape and the same roots (points where their value is zero). They only differ by a constant scaling factor, $c^2_s$. Try setting $c_s$ to $1 \text{ m/s}$ and observe that the two plots are now exactly the same.