Which property is unique to electromagnetic waves?

They can be controlled by the pull of gravity.

They can travel on the surface of water.

They can travel in a vacuum.

They can shake structures on Earth.

Well, electromagnetic waves definitely know how to shake things up on Earth, but I'm going to have to say that the unique property you're looking for is actually that they can travel in a vacuum. It's like they've got their own little cosmic bungee cords, allowing them to journey through space without any pesky mediums getting in their way. Pretty impressive, right?

The property that is unique to electromagnetic waves is that they can travel in a vacuum.