Re: Doppler Distortion - A Question In Classical Physics
From: Edward Green (spamspamspam3_at_netzero.com)
Date: 08/19/04
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Date: 18 Aug 2004 17:37:14 -0700
I'm cutting the ng back to sci.physics, because I don't feel quite up
to the august level of s.p.r..
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message news:<cflk9j$rmn$1@titan.btinternet.com>...
> "Bob Cain" <arcane@arcanemethods.com> wrote in message
> news:cfkfio01mj2@enews3.newsguy.com...
> >
> >
> > The simple argument I've been using to disprove the
> > phenomenon boils down to whether or not the principle of
> > reciprocity applies to acoustic systems,
>
> Your simple argument is, alas, incorrect.
>
> > whether the motion
> > of an ideal test piston (zero mechanical impedence) in an
> > infinite waveguide, a tube, with a plane wave traveling in
> > it will be the same motion as that of a piston creating that
> > wave but with a delay. Seems obvious to me and I think, but
> > am not sure, that this reciprocity can be proved by an
> > appeal to the conservation of energy.
>
> This is essentially where you are quite wrong.
> The radiation impedance of a piston in a tube of the same diameter is
> identical with the acoustic impedance of a sound wave propagated in
> the tube. Such a piston will not cause a high frequency to be
> modulated by a low frequency vibration of the source.
Ok. I assume all that conceptually charged language means that if our
speaker were a piston in a semi-infinite tube -- and a massless piston
to boot -- that in fact the the effect of concern would be
non-existent?
I still have some problem understanding unambiguously what that means
-- in particular, just what is the input signal, and how is that ideal
piston supposed to be responding to it? Assume again for simplicity
the input is a linear superposition of two pure tones. Is our ideal
piston then supposed to be executing a displacement as a function of
time which is then simply a sum of two sinusoidal displacements?
I assume this is what is intended, and that you are both in agreement
that under these conditions, some measure of the sound wave down the
tube will yield an undistorted superposition of sinusoidal frequencies
at the same frequencies, with no distortion. "Some measure" indicates
additional confusion/ambiguity on my part, since I don't know if we
are suppose to measure the pressure, the velocity, or the displacement
of the medium. Maybe it doesn't matter.
Now, you make this assertion in view of sophisticated concepts like
acoustic impedance and radiation impedence, which may be correctly
applied, but seem unlikely to speak to somebody who understands the
so-called vernacular argument, is not on your level, and doesn't
understand how the vernacular argument is wrong on more immediate
physical terms.
Ed: Does this argument make it clear to you where you were led astray
by that old sophist Richard Herring? ;-)
Ed: Nooo???
One thing both of you gentleman have made fast and loose with is
infinite tubes. I don't see any infinite tubes when I listen to my
stereo. Maybe this makes a difference? In fact, it seems rather
likely it will, just as restricting our solution space to variation in
one dimension vs. three makes a big difference in the character of
electrostatic solution -- your monotonous constant electric field
between the infinite capacitor plates vs. the radially decaying field
of point source. Some things may happen in the tube which do not
happen in the far acoustic field of the speaker, where it looks more
like a point source.
Let me in my lame-brained way try to understand how it could possibly
be that Herring's sophistical specious fest could _possibly_ be wrong
in any context, and let's again go to a conveniently extreme case:
say, an ideal piston in the mythical tube excite by a linear
combination of 1000hz and 10^-9 hz. Now, this is an ideal system, is
it not? I didn't hear anything about approximations for
for-sufficiently-large's or small's, so your claims ought to work even
here -- and I'm not saying they don't either, only that the method by
which they achieve this prodigy may be educational.
The piston moving at 10^-9 hz has been in unidirectional motion for a
long time! It seems likely in fact that it has been in motion at
essentially constant velocity for such a long time that for any local
effects in time and space we can just completely ignore the distant
past and future when it will be in some other state of motion. And
what does this mean? It means our eonic-low-frequency excitation
essentially makes the piston into a pump, moving all the air ahead of
it at constant velocity (assuming the amplitude of this very-very long
period vibration is large enought to make the velocity interesting).
Now, are you going to tell me, if I have a piston moving to the right,
say, at 10m/s, and that it has been moving at this velocity since
before your mother was born, and that the piston is also buzzing at
1000hz, and I drop a transducer in the tube at some location ahead of
the moving piston, that I will _not_ detect an appropriate doppler
shift for the 10m/s motion!?
Don't be silly.
However, I don't necessarily conclude that your claims are wrong, just
that, if right, they may need some careful interpretation. For there
is still clearly one auditor for whom the 1000hz signal will still be
an unshifted 1000hz signal, just as you claim -- and that is clearly
one co-moving with the medium ahead of the piston at 10m/s. So I
tentatively conclude that for your claim to be valid it may apply in
general to a local observer co-moving with local gas velocity, and
not to an observer stationary in the frame in which piston movement is
defined.
This unease without even stepping outside the ideal tube!
> On the other hand, the radiation impedance of a piston,
I take it you meant to add "in unconfined space"?
> either free or
> mounted in a baffle, is strongly frequency-dependant. In particular,
> this results in the circumstance that the piston has to vibrate with a
> much larger velocity at a low frequency than at a high frequency, if
> equal sound pressures are to be produced at a large distance from the
> piston. In a freely propagating plane wave, these two velocities are
> identical. The nett effect is that when, on this piston, a high
> frequency vibration is superimposed on a low frequency one, it
> effectively finds itself produced by a source moving at a velocity
> larger than that required by the superposition principle, which in
> turn will then produce a frequency-modulated output.
I'm not sure I 100% buy that -- I still want to make hay out of the
fact that if speakers are not always operated strictly in the far
field in our living rooms, neither are they strictly in the near
field: and the far field case looks very much like the moving train --
which, for what it's worth, produces frequency distortion of mounted
sources no matter what the relative magnitude of train motion
"required by the superposition principle".
But I know enough to know that this problem is merely a little tag
which says "pull me", and thereby leads to a complete study of all
aspects of acoustics and signal processing, so that in the end it
didn't even matter where we started, and in the meantime can lead to
infinite blather and time wasting: but I don't know enough to stop
before I start.
> The effect is quantitatively calculable. It turns out to be
> negligibly small for all except determined audiophiles in the case of
> speakers operating in normal listening conditions.
I think I mentioned already seen super-woofers at discos whose total
travel at the center may have been 5cm. I guess that is not "normal
listening conditions", and anyway, distortion was not the issue --
except of the listener's viscera!
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