Vibrations and waves are closely related. However, there is a difference between vibration and wave.
What is a vibration?
A wiggle in time is a vibration. What do we mean though by a wiggle in time?
A wiggle could be described as a back and forth movement. Therefore, a wiggle in time or what we call vibration is the time it takes an object to go to another location and back to its original location.
Notice that you have to give the object time to go back where it started. Everytime the object goes back to its original location, the object has completed 1 cycle.
If the object is able to go back to its original position twice in 1 second, the object has completed 2 cycles or 2 vibrations in 1 second.
What is a wave?
A wiggle in space and time is a wave. A wave cannot exist in just one place. It has to move from one place to another. For example, light and sound move though space as waves.
An illustration that shows how sound can go from one place to another is explained below.
Sometimes, you are in your car waiting at the traffic light.Then, all of a sudden, a car stops next to you with a very loud music.
As a result of the loud music, you feel that your body vibrates and you are annoyed and upset.
Why does your body vibrate even though you were not the one playing the loud music?
This is the result of the wave sound that moved from the person's car to yours.
The transmitting antenna of a radio station does the exact same thing.
Electrons in the antenna vibrates about 1 million times each second.
This in turn produces radio waves that can reach far away the radio in your car or in your house so you can listen to your favorite music.
In conclusion, keep in mind that the source of all waves is something that vibrates.
Waves can travel from one location to another. Vibrations cannot travel.