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