The type of waves that travel perpendicularly to the direction of their motion are transverse waves.

Here's why:

* Transverse waves involve oscillations that are perpendicular to the direction the wave travels. Imagine shaking a rope up and down. The wave will travel horizontally, but the rope itself moves vertically.

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

Let me know if you'd like more examples!