Hein ten Horn wrote:

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.
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.

Under the stated conditions there is no sine wave oscillating at 222
Hz. The wave has a complex shape and contains spectral components at
two distinct frequencies (neither of which is 222Hz).

It might be correct to say that matter is vibrating at an
average, or effective frequency of 222 Hz.


No, it is correct. A particle cannot follow two different
harmonic oscillations (220 Hz and 224 Hz) at the same
time.

The particle also does not average the two frequencies. The waveform
which results from the sum of two pure sine waves is not a pure sine
wave, and therefore cannot be accurately described at any single
frequency.

Obviously. It's a very simple matter to verify this by experiment.


Indeed, it is. But watch out for misinterpretations of
the measuring results! For example, if a spectrum
analyzer, being fed with the 222 Hz signal, shows
that the signal can be composed from a 220 Hz and
a 224 Hz signal, then that won't mean the matter is
actually vibrating at those frequencies.

:-) Matter would move in the same way the sound pressure wave does,
the amplitude of which is easily plotted versus time using
Mathematica, Mathcad, Sigma Plot, and even Excel. I think you should
still give that a try.

jk