[Noisebridge-discuss] why a sine wave?

[Josh Myer]

On Tue, Jan 12, 2010 at 10:59 AM, Michael Shiloh <
michaelshiloh1010 at gmail.com> wrote:

> Why do we perceive a sine audio wave as a "pure" tone? Does it have to
> do with the mechanical vibrations in our ear? Does any non-sine wave
> introduce harmonics, vibrations other than the fundamental, which our
> brain perceives as non-pure?
>
> Regardless of mechanics, what is the perceptive reason a sine wave
> sounds pure?
>
>
That's a fun question; here's a Cliff's Notes version of the thorough reply.
 Note that it is just mechanics, though.

We perceive sound with hairs in a tube in your ear getting nudged by sound
waves.  Those vibrations are described most closely by a sine wave (but
they're probably not _perfectly_ sinusoidal, since the tube isn't perfectly
cylindrical, etc).  Because different sound waves stimulate different hairs,
everything you hear is being perceived as a set of sine waves, all laid on
top of each other.

http://health.howstuffworks.com/hearing.htm

Other wave shapes can be constructed as the sum of a bunch of different sine
waves on top of each other, via "superposition."  Here's some good
animations of the superposition principle in action:

http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

To see the voices in a typical synth constructed as sine waves, check out a
different page on that same site:

http://paws.kettering.edu/~drussell/Demos/Fourier/Fourier.html

So, you hear these other sounds as lots of sine waves laid on top of each
other via superposition.  We can get to those mathematically by the Fourier
transform (and by other ones, like the cosine transform, Goertzel algorithm,
the empirical mode transform, yadda yadda yadda).

To the question of: do non-sine waves generate harmonics?  Of course!  But
they generate harmonics of their component sine waves, which may or may not
go through destructive interference, nulling out the interesting
frequencies.

HtH,
-- 
Josh Myer 650.248.3796
josh at joshisanerd.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.noisebridge.net/pipermail/noisebridge-discuss/attachments/20100112/d76f3e1b/attachment-0003.html>