TITLE: What is meant by a 'pure' wave?
QUESTION [6 upvotes]: What is meant by a 'pure' wave?
I know it might sound like a basic question, but I've never been taught this.
I saw that a sine wave is a pure wave. I tried Googling what a pure wave is, but all I get is links regarding Pure Wave Inverters for sale...which is not what I'm looking for.

REPLY [3 votes]: In electrical technology any periodic motion  can be expressed as a sum of the fundamental wave and several harmonics whose frequencies are multiple of the fundamental, expressible in Fourier series. If the wave is pure it means that amplitudes other than the fundamental are zero. The other harmonics are seen as "contaminating" the pure sine wave.
It is pure or aka simple harmonic, as is represented by the harmonic dynamic time differential function which strictly has a time period $T$ where $ \omega T = 2 \pi $ in:
$$ \ddot x +  \omega^2  x =0. $$ 
A square wave for example has several non-fundamental additives to the pure signal. It consistes of third, fifth,.. order harmonics:
Other Harmonics in Square Wave