"Hein ten Horn" wrote in message
...
Jim Kelley wrote:
Hein ten Horn wrote:
Hein ten Horn wrote:

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

From the example: there's no 222 Hz tone in the air.

That one I'd like to take back.
Obviously the superposition didn't cross my mind.
The matter is actually vibrating at the frequency
of 222 Hz. Not at 220 Hz or 224 Hz.

You were correct before.

That's a misunderstanding.
A vibrating element here (such as a cubic micrometre
of matter) experiences different changing forces. Yet
the element cannot follow all of them at the same time.

It does. Not identically but it does follow all of them.

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

You have looked at a segment of the waveform
and judged "frequency" based on a few peaks.
Your method is incomplete and cannot be applied
generally.

snip