"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.



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.


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.


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.



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.