Is there such thing in physics as, a wave traveling on top of another wave..?

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Richard

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A smaller wave traveling on top of a bigger wave.
If i made a large waveform then instantly started emitting smaller faster wave frequency would the smaller faster waveform catch up with the first wave ad travel across it.
 
Yes, the larger wave is known as the carrier wave,and is Modulated by the smaller one.
In telecommunications, the carrier wave is received by the receiver, and the voice/music is modulating the carrier wave, The receiver then filers out the carrier wave, and so you just hear the music.
 
yes, happens all the time.

Except the part about "catching up" as they would travel at the same speed.

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