Questions to be pondered:

 Since music is made up of combinations of sine waves, what instrument do you think can produce a graph that is the closest to the standard f(x)=sin(x)? (Another way to think about it: What instrument produces the purest tone?)

 What instrument do you think would produce the most complex sine waves?

 Since music is made up of combinations of sine waves, what instrument do you think can produce a graph the closest to the standard f(x)=sin(x)? (Another way to think about it: What instrument produces the purest tone?

The instrument that produces the purest tone (a wave closest to the standard sine wave) is the flute!

Here's a zoom-in so you can see what's really going on!

Note: If you consider the range of instruments used in Hillbilly music...... then the bottle really gives the purest tone! Check it out!

 (Please ignore the fact that this picture says "flute" - It's really a bottle!)

If we zoom-in, we can see what a perfect sine wave blowing into a bottle can produce!

 What instrument do you think would produce the most complex sine waves?

The instrument that produces the most complex sine wave is the cymbal! (Or the human voice, if you don't consider a cymbal an instrument.)

Look how messy this zoom-in is!