Re: fallacious filtered white noise

["John S. Denker" <jsd@MONMOUTH.COM>]

At 03:54 PM 12/8/00 -0600, Gary Karshner wrote:
>  Resonance frequencies of an oscillator are the frequencies at which they
> naturally oscillate.

That's narrowly true, if  we take "naturally" to mean something like "in
the aftermath of a limited-duration excitation".

>  Whether they oscillate or not depends on the driving force. If
> the driving force contains components of those natural resonance
> frequencies, it will cause the device to oscillate.

That's true enough as written, but the obvious implication is that if the
driving force is off-resonance, the device will not oscillate.  The
implication is false.

In the linear regime, when driving a resonator with an off-resonance
signal, it _always_ responds at the frequency of the driving force, _never_
at its resonant frequency or any other frequency.  The magnitude of the
response depends on frequency.  For any finite Q and for any finite
frequency, there will always be some response.

> They work by you generating a source of "white noise" like
> blowing across the top of the pop bottle. The bottle then selects out the
> components of the noise that correspond to its natural resonance
> frequencies.

I've never studied whistles, so I'll be careful and just say that if that's
how a whistle works, I'm surprised.  It's certainly not how a flute works.

> String instruments are not plucked or bowed at the center but off to one
> side to
> excite not only the fundamental frequency but their harmonics as well.

I am quite sure that a violin does not work by producing white noise and
then resonantly filtering it.  You can verify what I'm saying with a
microphone and an oscilloscope, in less time than it takes to tell about
it.  Observe that a steady violin note produces a steady waveform.  All the
complicated features are (within reason) repeated, trace after trace,
indicating that the higher harmonics are phase locked to the
fundamental.  As I said earlier today, there is no way you could explain
that using the filtered-noise model.