The 3 main types of waves are mechanical waves, electromagnetic waves, and matter waves.
A mechanical wave is a wave that can only exist within a material medium such as air, water, or rock. We encounter mechanical waves almost constantly, so we should be familiar with them.
Examples of mechanical waves include slinky waves, sound waves, water waves, and seismic waves.
Mechanical waves can either be transverse or longitudinal.
With transverse waves, the vibrations are perpendicular to the direction of motion. In other words, while the particles move up and down, the wave travels to the right or to the left.
With longitudinal waves, the vibrations are paralllel to the direction in which the wave travels. For instance, while the particles vibrates from left to right, the wave travels to the right.
This website has an animation that shows the difference between tranverse and longitudinal waves.
Unlike mechanical waves, electromagnetic waves do not require a material medium to exist. Instead they travel through a vacuum at the speed of light.
Examples of electromagnetic waves include radio and television waves, microwaves, x rays, radar waves, and light waves from stars.
You are much less familiar with this type of wave. It is mostly used in modern technology.
This type of wave is associated with particles, atoms, and molecules.
It got its name from the fact that matter is made of lots of atoms, particles, or molecules.