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Well, let's start with the definition of a wave:  a wave is any disturbance that transmits energy through matter or space.  Now, that being said, there are two types of waves, mechanical waves and electromagnetic waves.  The one you asked about is a type of wave that has to have...

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Well, let's start with the definition of a wave:  a wave is any disturbance that transmits energy through matter or space.  Now, that being said, there are two types of waves, mechanical waves and electromagnetic waves.  The one you asked about is a type of wave that has to have a medium through which to travel.  A medium is a substance through which the wave can work.  Sound waves are great examples of mechanical waves.  Did you realize that if we didn't have air as a medium for sound we could talk all we wanted, and no one would be able to hear anything?  Sound waves don't work at all in a vacuum, where there is no air.  The other type, electromagnetic waves, don't require a medium through which to travel.  As a matter of fact, they work better without a medium.  Visible light from the sun is a good example of an electromagnetic wave.  Light from the sun travels all the way from the sun to the Earth in only 8.3 minutes.  That's through the void of space, with no air present!

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