"The Ghost" wrote in message
om...
"Karl Uppiano" wrote in message
...

"The Ghost" wrote in message
om...
THE HYPOTHESIS:
Assuming that the.....
THE SETUP:
A small circular piezoelectric bimorph.......
THE MOTION OF THE SOUND SOURCE
A triangular command signal.........
THE MEASUREMENT RESULT
The propagating 10KHz signal.......
THE CHALLENGE
In science, theory usually follows.........



1. I believe this experiment is relevant in that we should be able to
mathematically predict and experimentally measure frequency modulation
due
to Doppler shifts with a good degree of agreement within the constraints
this setup (i.e., a linear motor pushing a peizo radiator back and
forth).
It is not clear whether the OP was able to correlate the experimental
results with the mathematical predictions, or merely *detected
something*.
There may be some more work required here.

You are correct. You should be able to mathematically model the
experiment and predict the experimental result, but I am not going to
do it for you. Also, the measurement didn't just merely detect
"something." The measurement demonstrated that motional information
about the periodic trapezoidal velocity the peizo element exists in
the FM sidebands of the 10KHz propagating carrier and that the FM
demodulated signal had the same trapezoidal shape as the velocity of
the shaft of the linear motor. This result is exactly what is
predicted qualitatively by a phenomenological model of dynamic Doppler
shift. This experimental result is difficult, if not impossible, to
explain on the basis of IM distortion because there is no readily
identifiable nonlinear mechanism that is common to both the
low-frequency motion of the shaft and the high frequency motion of the
piezo element. The measurement results provide a very strong
counter-argument against those claiming that dynamic Doppler shift
does not exist. That was the sole purpose of measurement. If you or
anyone else wishes to carry it to the next "quantative" level, please
be my guest.


That's why my initial reaction to your experiment was positive. My mistake
(and others also) was in jumping to the conclusion that your results could
be applied directly to Doppler FM in a loudspeaker. It cannot, and you never
claimed they could, which is a "Good Thing".

2. This experiment *cannot* be generalized to mathematically predict and
experimentally measure frequency modulation due to Doppler shifts
*through a
loudspeaker*. Note that the experiment doesn't mention this
generalization;
it does not discuss loudspeakers at all.

That is correct, unless you can find a loudspeaker that produces
negligible IM distortion so that the propagating energy in the
sidebands is predominantly the result of dynamic Doppler shift and not
the result of IM in the actual cone vibration itself.

Unfortunately, that's true. AM and FM sidebands look fairly similar at low
FM modulation indices. They might be hard to distinguish, although IIRC,
upper and lower FM sidebands are opposite in phase.

The linear motor does *not* radiate
the low frequency as sound waves, as a loudspeaker does. This completely
changes the dynamics of the situation in terms of the motion of the
radiators and the transfer of energy into the surrounding air.

That is incorrect. The surface of the piezo element radiates the low
frequency motion of the motor shaft, but that radiation is very low
because the frequency is low and because the surface area of the piezo
element is small. Furthermore, the amount of low-frequency sound that
is radiated is irrelevent to the issue of the production of dynamic
Doppler shift.

The low frequency radiation is much less efficient for the reasons you
state. A loudspeaker, on the other hand, radiates all frequencies in its
usable frequency range with nominally equal efficiency. That is not the case
with your experimental setup, as you point out.

I not only believe that it is not only relevant, *but crucial* whether the
low frequency component is radiated, to the issue of dynamic Doppler shift.
The entire energy equation changes. Instead of a high frequency sound source
moving back and forth in free air, we are instead summing two acoustic
waves. It's entirely different.

3. To have any relevance to audio reproduction through loudspeakers, this
experiment needs to be repeated to mathematically predict, and then,
*using
a loudspeaker*, experimentally measure frequency modulation due to
Doppler
shifts.

Because of the existence of IM, the mathematical model will have to
take into account both the radiation of IM products as well as the
dynamic Doppler shift, since both contribute sideband energy at the
same frequencies. If you are prepared to take on that task, all I can
do is wish you luck.

I'm afraid I don't have the time or the equipment. I'm just suggesting the
need for further research if anyone is really interested in proving or
disproving the existence of Doppler FM in loudspeakers. This is where a
prediction from a mathematical model is important. It isn't sufficient to
get a louspeaker to produce something that "smells like Doppler FM". You
need a model that predicts how much, at what freqencies, in what phase,
etc., and then you need to get good experimental agreement with your
prediction. Otherwise, you could be measuring anything -- other forms of
distortion, environmental noise, sampling errors, etc. In the end, it must
all be accounted for if it's the *truth* you're looking for. Unsubstantiated
claims are much less demanding :-)

4. For either experiment, it is not sufficient to simply *detect* FM
sidebands. The frequencies, amplitudes and phases obtained experimentally
must agree closely with the values predicted mathematically.

Amplitudes and phase information needs to be preserved, but in the
case of my experiment, no mathematical prediction is necessary. I
used a trapezoidal instead of sinusoidal velocity of the shaft linear
motor specifically to get around the need for a mathematical
prediction. Because the velocity of the linear motor was
non-sinusoidal, the information in the sidebands needs to be accurate
only in terms of relative amplitude and relative phase. The
non-sinusoidal velocity information will be preserved in the
sidebands, and appear at the output of the FM demodulator, only if the
relative ampliude and relative phase information is correctly
preserved in the sidebands of the radiated signal.

I believe prediction *is* necessary. You did predict some things, and you
were able to experimentally bear out your predictions. But if you had
predicted trapezoidal FM with a slope x, and you measured sinusoidal FM with
a maximum slope of -2x, I'd say your predictions, or your measurements were
off. You haven't proved anything until you have a high degree of agreement
between your prediction and your measured results, and you can account for
any remaining errors to the satisfaction of all reviewers. That's what's
meant by "reproducible results".