What is the main difference between a longitudinal wave and a transverse wave?

The main difference between a longitudinal wave and a transverse wave is that a transverse wave is characterized by particles moving perpendicular to the direction of the wave's motion. Therefore, the correct statement among the options given is:

**A transverse wave is made of particles that move perpendicular to the motion of the wave.**

Here's a brief explanation of the other statements:

- **A longitudinal wave always travels faster than a transverse wave.**: This is not necessarily true; the speed of waves depends on the medium and other conditions, not solely on the type of wave.

- **A longitudinal wave does not need a medium to travel through.**: This is incorrect; both longitudinal and transverse waves typically require a medium to propagate. Exceptions exist, such as electromagnetic waves (which are transverse), that can travel through a vacuum.

- **A transverse wave always carries more energy so that it can travel through empty space.**: This is not accurate; energy carried by a wave depends on factors like amplitude and frequency, not strictly on the wave type or its ability to travel through space.

Therefore, the primary distinction is in the direction of particle movement relative to wave propagation, with transverse waves exhibiting perpendicular movement.