Re: Doppler Distortion - Fact or Fiction?
From: Edward Green (spamspamspam3_at_netzero.com)
Date: 08/21/04
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Date: 20 Aug 2004 17:51:31 -0700
Bob Cain <arcane@arcanemethods.com> wrote in message news:<cg1ibl0266t@enews4.newsguy.com>...
> Here's what I've come up with after fending off a lot of
> flack and considering a bunch of hypothetical situations in
> a couple of other groups:
>
> Let's look at the simplest toy system that would exhibit the
> Doppler distortion phenomenon if the usual argument
> employing summed sinusoidal velocities were true, i.e. that
> one modulates the other in the output because of a Doppler
> shift that varies with time.
>
> If the piston contains no constant velocity component then
> the propegating wave will be a faithful reproduction of the
> velocity of the piston because its position is always in
> proper correspondence to the velocity it is imparting to the
> wave so as to impart no error. I.e., it is _in_ the wave it
> is generating and thus always at the proper position within
> it to impart the commanded velocity. The usual intuitive
> rationalization for Doppler distortion is just wrong. The
> process is linear and real in this case. There is no
> modulation of anything by anything else
>
> However, my belief that in the tube a piston of constant
> velocity imparts no constant velocity to the wave was wrong
> as shown here:
>
> http://www.silcom.com/~aludwig/Physics/Piston_collisions.htm
>
> The upshot is that there is no Doppler distortion in an
> infinite tube with a driving piston in it for any signal
> (until the piston smacks into the receiver if moving toward
> it. :-)
>
> In all other configurations, no Doppler distortion will
> occur among components within the portion of its passband
> that is fairly flat. It is the difference in the coupling
> between the piston and the air at different frequencies that
> produces Doppler distortion in the far field because there
> is then an error in the instantaneous position of the piston
> compared to where it would be if it coupled equally at all
> frequencies. For constant velocity motion, a speaker on a
> train, that error comprises the usual Doppler shift because
> the piston cannot impart to the air the constant component
> of its velocity relative to it.
>
> Yes, a speaker swinging back and forth on a rope will
> evidence Doppler distortion because the low frequence swing
> does not couple to the air signifigantly. This means that
> the piston's position is never appropriate to the
> superimposed velocities of the speaker signal and the swing
> given it, so a Doppler shift that varies with the lower
> frequency velocity will occur.
>
> A Doppler distortion will occur for any two frequencies that
> couple differently to the air but in the region of fairly
> flat transduction, there will be none.
>
> Whatcha think?
That this problem will generate the same evanescent and fruitless
illusion that I am about to develop a serious and sustained interest
in acoustics that other problems have created for fluid dynamics? But
enough of that. :-/ There is a lot going on here, but I think
Richard Herring gave us a powerful simplying key: concentrate on the
kinematics.
Consider any source you like, real or ideal, in a tube, in a large
anechoic space, mounted on a train, swinging from a tree. Excite the
source linearly, as the sum of two sinusoids, high frequency and low.
The displacement is the linear sum of two sinusoids, the velocity is
the linear sum of two sinusoids. Linear, linear, linear.
Now, consider an observer stationary wrt the mean of the sinusoidal
displacements. In short, stationary. Let him monitor any aspect of
the wave you like: displacement, pressure, dynamic pressure, velocity.
You name it. Forget dynamics. We don't know about no stinkin'
dynamics: all we known is, that the source produces a train of crests
associated with the high frequency oscillation: ping, ping, ping,
ping, ping.
Now, as Richard Herring points out, the pings produced when the source
is on the observer side of the mean position have a shorter distance
to travel than those produced on the far side. Therefore, we have
exactly two possibilities: either the points of constant phase will
_not_ arrive at the location of the observer with the proper constant
period -- i.e., we have frequency distortion -- or, a mechanism must
to found to alter the mean velocity of the pings between source and
observer proportional to the low frequency displacement of the source:
those produced nearer the observer traveling slower, those farther
away, faster, to just compensate for their varying travel distances
and arrive in the correct timing.
Well, which is it? Can you make an argument for such a mechanism in
any conceivable arrangement of source and observer? Your best bet
would seem to be the idealized piston in the tube, though I don't
think it works even there.
Does it?
I begin to think that in the range of motion which would make this
effect significant, that what we call sound, even in a semi-infinite
tube, becomes a sufficiently complicated non-linear mish-mash (because
of the finite vs. infinitesimal motion of the medium) that it may be
necessary to abandon much of the friendly linear machinery of
acoustics which you and Franz Heymann seem conversant with, and all
bets are off, etc. Like most contentious problems, progress would
require very careful operational definition of all terms, and...
I don't know. :-)
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