Jeff Liebermann wrote:


As I stated earlier in this thread
(though more towards its tail)...

quote
We hear the average of two frequencies if both frequencies
are indistinguishably close, say with a difference of some few
hertz. For example, the combination of a 220 Hz signal and
a 224 Hz signal with the same amplitude will be perceived as
a 4 Hz beat of a 222 Hz tone.
unquote

Let me use this example to take away
some possible misinterpretations.

"An audible beat tone is produced by the constructive and
destructive interference between two sound waves in air."

The statement above is true if you leave out the word "tone".
From the example: there's no 222 Hz tone in the air.
In our perception however the 222 Hz tone 'exists'
and that's why we don't have to leave out the word "audible".
Yet, I'd preferred this one:
A beat is produced by the constructive and destructive
interference between two sound waves in air.
To be complete, using the word "tone" referring to 4 Hz
would make the statement misleading because we do not
hear frequences as low as 4 Hz.


I did manage to find a nifty Java applet that shows the effects of
acoustic interference:
http://falstad.com/interference/
It appears to refer to variations in amplitude across the area where
both tones are present. What's missing is any reference to any beat
note.

Well, try this one.
http://www.ngsir.netfirms.com/englishhtm/Beats.htm


I'll make it easy. The difference of the two tones are in the audible
range. For example, 25 kHz and 26 kHz to produce a 1 kHz beat note.

We can hear beat frequencies up to say 15 Hz.
Our auditory organ is not able to follow faster amplitude
variations.
So take another example: 25000 Hz and 25006 Hz.
Again, constructive and destructive interference produce 6 Hz
amplitude variations in the air.
But, as we can't hear ultrasonic frequencies, we will not produce
a 25003 Hz perception in our brain. So ther's nothing to hear,
no tone and consequently, no beat.

And with two very different frequencies within the audible
range, for instance 220 Hz and 880 Hz, we here only these
two frequencies. No average frequency and no beat.

HTH

gr, Hein