The wave property that increases as the number of vibrations producing the wave increases is amplitude.

Here's why:

* Amplitude is the maximum displacement of a wave from its rest position.

* When more vibrations contribute to a wave, they essentially "add up" their individual displacements. This results in a larger overall displacement, leading to a greater amplitude.

Imagine dropping a pebble into a still pond. A single ripple has a small amplitude. Now, imagine dropping several pebbles simultaneously. The combined ripples will have a larger amplitude because they are all adding to the overall disturbance of the water.

Important Note: While amplitude increases with more vibrations, other properties like frequency and wavelength might not change. Frequency is determined by the rate of vibrations, and wavelength is determined by the speed of the wave and its frequency.