The wave that does not require a medium but can travel through empty space is an electromagnetic wave.

Here's why:

* Electromagnetic waves are made up of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.

* These waves do not need a medium to travel, unlike sound waves or water waves, which require a material to vibrate through.

* Examples of electromagnetic waves include light, radio waves, microwaves, X-rays, and gamma rays.

Let me know if you'd like to learn more about electromagnetic waves!