There are two basic types of waves-transverse waves and longitudinal waves. Transverse waves may be polarized and longitudinal waves may not. Electromagnetic waves-including light, radio waves, television waves, and microwaves-are transverse waves. Sound is certainly the most important example of a longitudinal wave.
Water waves are very common and very pretty. Small waves on the surface of the water seem to be transverse waves. But water waves really involve more a complex structure that just what we see on the surface. As water waves come into the shore and begin to interact with the bottom surface of a beach this more complex structure may cause some of the waves to break over-causing the white water of breakers that is so pretty to watch.
Sound waves-like waves on a string-require a medium to move. It is fun to listen to a ringing electric bell inside a glass bell jar as the air is pumped out. As the air is evacuated from the jar, the sound of the bell becomes fainter and fainter. When there is no air, we do not hear the bell at all. The crash and thunder and explosive sounds we hear is science fiction movies of battles in the vacuum of space may generate excitement and sweaty palms or clinched fists, but those sounds would not be heard in a real battle in the vacuum of space for there is no air to carry the sound waves.
But we can still see the silenced ringing bell in the evacuated
bell jar. No medium is needed for light waves. This seems reasonable
now but about a hundred years ago it was not as clear. The search
for such a medium at that time is an interesting and exciting
story in its own right.
Our Earth itself supports or carries waves-both longitudinal and
transverse waves. Geologists can determine characteristics of
the Earth by measuring the wave speeds of the waves. They can
use this to help locate deposits of oil or minerals. Earthquakes
are waves at Earth's surface caused by movement of material deeper
below the surface.