The characteristic of a wave that describes the greatest distance it vibrates from its resting position is called amplitude.

Here's why:

* Amplitude is the maximum displacement of a point on a wave from its equilibrium position. It's essentially the "height" of the wave.

* Frequency refers to how many wave cycles pass a point in a given time.

* Wavelength is the distance between two corresponding points on successive waves, like the distance between two crests or two troughs.

* Speed is how fast the wave travels through a medium.

So, the greater the amplitude, the further the wave vibrates from its resting position.