The wave in which particles of the medium vibrate in an up and down motion is called a transverse wave.

Here's why:

* Transverse waves are characterized by the fact that the particles of the medium vibrate perpendicular to the direction the wave travels. Imagine shaking a rope up and down. The rope itself moves horizontally, but the individual segments of the rope move vertically.

* Longitudinal waves, on the other hand, have particles that vibrate parallel to the direction of wave propagation. A good example is a sound wave, where air molecules compress and expand in the same direction the sound travels.

Let me know if you'd like to know more about transverse or longitudinal waves!