How do electromagnetic waves travel in a vacuum?

Hint: Electromagnetic waves are produced by an accelerating electric charge which emits radiation. Waves are the disturbances created in the medium that carries energy from one place to another. Sound waves which we hear are a type of mechanical wave that needs medium to travel and transfer energy from one place to another. But electromagnetic waves do not need a medium to carry energy from one place to another.

Complete answer:
Electromagnetic waves are transverse in nature. They do not need any medium to propagate because the propagation of electromagnetic waves is due to the mutual changes between magnetic and electric fields. The electromagnetic wave is produced by an oscillating electric charge where a variable magnetic field produces an electric field and a variable electric field produces the magnetic field. This variation in the electric and magnetic fields leads to the propagation of the energy carried by the electromagnetic wave.
Hence, in this way, electromagnetic waves travel through a vacuum without the presence of a material medium.

Note:
Electromagnetic waves travel in a vacuum and air with speed $3 \times {10^8}m/s$.
In our daily life examples, the sound wave is the mechanical energy that needs a material medium to travel from one place to another, it means in a vacuum we cannot hear each other’s voice. Similarly, light is an example of an electromagnetic wave that does not need a material medium to travel.
The direction of propagation, the direction of the electric field, and the direction of the magnetic field are perpendicular to each other.