at the temporal coordinates: 10/31/01 2:14 PM, the entity known as Michael
J. Hu=DFmann at michael_at_michael-hussmann.de conveyed the following:
> Eric L. Strobel (fyzycyst_at_home.com) wrote:
>=20
>> Well, picture this -- you are pushing a child on a swing. You can push
>> every time the kid comes back to you, or you can push every OTHER time, =
or
>> every THIRD time. With the latter two, you're forcing the system at a
>> harmonic frequency below the base (swing's) frequency.
>=20
> In this case, one system (me) oscillating at a frequency f is causing
> another system (the swing) to oscillate at 2f or 3f. Nothing mysterious
> about that, but I fail to see how this analogy relates to harmonics
> (_components_ of a _single_ oscillation) at all. At any case, calling the
> pushing frequency the harmonic (rather than the frequency of the swing,
> which to me at least would make slightly more sense) seems to be arbitrar=
y.
OK, let's try differently. A _single_ (or pure) oscillation, in isolation,
would have no other components. All other components (harmonics) are from
resonant modes of the system producing the sound (string vibrating, a closed
ended or open ended pipe, a membrane, etc.). Now, if the frequency of the
oscillation is higher than the fundamental mode of the resonating structure,
then LOWER harmonics _of the fundamental mode_ can get excited. I believe
this is what is being referred to.
Now, I'm having a hard time thinking of a system where the *efficiency* of
this coupling to lower harmonics is very great. But in the example given,
namely where the primary tone is inaudible, in principle one could be able
to detect the lower harmonics.
Not that it matters much to me anyway. I'm a married man, so I *know* I
can't hear properly. ;-)
- Eric.
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