Rich Grise wrote:

On Wed, 11 Jul 2007 22:52:17 -0700, Jeff Liebermann wrote:

"NotMe" hath wroth:

(Please learn to trim quotations)

Actually the human ear can detect a beat note down to a few cycles.

No, you cannot. Figure on 20Hz to 20KHz for human hearing:
http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml

What happens when you zero beat something is that your brain is filling
in
the missing frequencies. As you tune across the frequency, and the beat
note goes down in frequency, most people overshoot to the other side, and
then compensate by splitting the different.

No, you've got it all wrong. The beat note happens because, when the
signals are close to 180 degrees out of phase, they cancel out such that
there is, in fact, no sound. This is what your ear detects. Now, if
you're zero-beating, say, 400 Hz against 401 Hz, I don't know if the
801 Hz component is audible or if it's even really there, but
mathematically, it kinda has to, doesn't it?

Thanks,
Rich

No, It doesn't have to be there (the 801 Hz frequency). If your method
of 'beating' two signals together is by adding them, then there is no 801
Hz tone, only the 400 and 401 Hz tones.

With two function generators and a spectrum analyzer you can see this.

With a scope, you can see that the zero crossings in the summation occur at
a 400.5 Hz rate.

This is exactly what the trig identity earlier in the thread indicates.

If your method of beating is via multiplication, then there will be 0, 400,
401 and 801 Hz signals present (assuming the mixer is not balanced).

When you are discussing 'beating' two signals together you need to indicate
whether you are adding or multiplying the signals. The results are
different.

If you are multiplying two signals to find a zero beat with your ear, that
is difficult as you will be trying to hear tones less than 20 Hz.

If you are adding two signals to find a zero beat, that is easy because you
are listening to a tone that is at the average frequency. In the above
example, at 400.5 Hz.