On Thu, 05 Jul 2007 00:06:02 -0700, isw wrote:

In article ,
John Fields wrote:

On Wed, 04 Jul 2007 09:11:58 -0700, isw wrote:

In article ,
"Ron Baker, Pluralitas!" wrote:

You win.

When I conceived the problem I was thinking
cosines actually. In which case there are no
phase shifts to worry about in the result.

I also forgot the half amplitude factor.

While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation; there is no
non-linear process involved (i.e. no multiplication).

---
That's not true.

The human ear has a logarithmic amplitude response and the beat note
(the difference frequency) is generated there. The sum frequency is
too, but when unison is achieved it'll be at precisely twice the
frequency of either fundamental and won't be noticed.

Now you get to explain why the beat is measurable with instrumentation,
and can can be viewed in the waveform of a high-quality recording.

---
Simple. The process isn't totally linear, starting with the musical
instrument itself, so some heterodyning will inevitably occur which
will be detected by the measuring instrumentation.
---

Then go on to show why all other multi-frequency-component signals (e.g.
a full orchestra) don't produce similar intermodulation effects in ears
under normal conditions.

---
They do, and why don't you try being a little less of a pompous ass?


--
JF