The property of a mechanical wave that measures the amount of particle vibration is amplitude.

Here's why:

* Amplitude is the maximum displacement of a particle from its rest position as the wave passes through.

* The larger the amplitude, the greater the distance the particles move back and forth, indicating a stronger vibration.

* Think of a rope: a large amplitude wave creates a big, noticeable up and down motion, while a small amplitude wave has a less pronounced, smaller movement.

Let me know if you'd like more details about wave properties!