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The Ghost
 
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Default Experimental Evidence for Dynamic Doppler Shift

THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source
moving at constant velocity also applies under dynamically changing
velocity conditions, one would expect the propagating sound, that is
produced by a high-frequency source moving dynamically at a low
frequency around a fixed position, to be frequency modulated. One
would further expect that the instantaneous frequency of the
propagating sound would reflect the dynamic low-frequency velocity the
source. If so, the waveform of the fm-demodulated high-frequency
propagating sound, should follow on an instantaneous basis, the
dynamic velocity of the low-frequency velocity of the source.


THE SETUP:
A small circular piezoelectric bimorph, having a resonant frequency of
approximately 10KHz was attached to the 10-lb armature/shaft of a
linear motor. The displacement of the armature/shaft was monitored
by a linear displacement transducer attached to the opposite end of
the armature/shaft. The linear displacement transducer also provided
feedback for the servo amplifier which was driving the linear motor.
Because the linear motor was in a servo loop, the displacement of the
motor followed with reasonable accuracy both sinusoidal and
non-sinusoidal command signals that were applied to the amplifier.
The piezoelectric sound source was driven by a low-distortion
oscillator at 10KHz. The sound emitted by the source was measured by a
microphone at a distance of approximately one foot. The output of the
microphone was amplified, high-pass filtered and applied to a
frequency-to-voltage converter. The output of the
frequency-to-voltage converter was low-pass filtered to reduce the
level of the residual 10KHz carrier, amplified and applied to a signal
averager. The signal averager was triggered by the command signal
that was applied to the linear motor. Averaging was used in order to
remove non-coherent 60Hz that was present in the output of the
demodulator.


THE MOTION OF THE SOUND SOURCE
A triangular command signal having a 50-msec period was applied to the
servo amplifier. A triangular command signal was used in order to
simplify interpretation of the measurement result and to avoid the
phase shift vs time delay ambiguity that would otherwise exist with
fixed frequency sinusoidal excitation. The output of the displacement
transducer was monitored on an oscilloscope and found to be triangular
with rounded corners. The rounding of the corners is due to the
limited closed-bandwidth of the servo. The velocity of the linear
motor was therefore trapezoidal with relatively flat and relatively
long plateaus and relatively short transitions.


THE MEASUREMENT RESULT
The propagating 10KHz signal emitted by the piezo bimorph was applied
to an FFT analyzer in zoom-analysis mode with a resolution bandwidth
of 0.1Hz. When the piezo bimorph was stationary, the propagating
signal picked up by the microphone showed only a single spectral peak
at 10KHz. When the piezo transducer was moving back and forth with a
triangular displacement provided by the linear motor, the propagating
signal received by the microphone contained numerous sidebands which
were indicative of FM modulation. Additionally, the output of the FM
demodulator was observed to be trapezoidal and followed on an
instantaneous basis the velocity of the linear motor and the attached
piezo transducer.


THE CHALLENGE
In science, theory usually follows experimental results. In this case
the experimental result shows that a 10KHz signal applied to a small
piezoelectric source moving back and forth around a fixed position
becomes frequency modulated by the back and forth motion of the
source. The measurement further shows that the received,
FM-demodulated signal follows the instantaneous velocity of the
source. This result is exactly what is expected on the basis of
Doppler frequency shift extrapolated from constant velocity to dynamic
velocity conditions. While some might argue that the observed
FM-like sidebands and the trapezoidal demodulated waveform are the
result of IM distortion, and not Doppler FM, the ball is in their
court. It is now up to them to provide an explanation/analysis
involving an IM producing mechanism in the present experimental setup
that accounts for the present experimental result. Finally, it must
be noted that the purpose of the present measurement was to
demonstrate fundamental phenomenological behavior. The 10KHz carrier
and the 50-msec peridiocity for the displacement of the linear motor
were chosen solely to accommodate the hardware on hand. There is
presently no reason to believe that the outcome of the present
measurement would be different if other carrier frequencies or other
source displacement periodicities or waveshapes were used.
  #2   Report Post  
Karl Uppiano
 
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"The Ghost" wrote in message
om...
THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source
moving at constant velocity also applies under dynamically changing
velocity conditions, one would expect the propagating sound, that is
produced by a high-frequency source moving dynamically at a low
frequency around a fixed position, to be frequency modulated. One
would further expect that the instantaneous frequency of the
propagating sound would reflect the dynamic low-frequency velocity the
source. If so, the waveform of the fm-demodulated high-frequency
propagating sound, should follow on an instantaneous basis, the
dynamic velocity of the low-frequency velocity of the source.


THE SETUP:
A small circular piezoelectric bimorph, having a resonant frequency of
approximately 10KHz was attached to the 10-lb armature/shaft of a
linear motor. The displacement of the armature/shaft was monitored
by a linear displacement transducer attached to the opposite end of
the armature/shaft. The linear displacement transducer also provided
feedback for the servo amplifier which was driving the linear motor.
Because the linear motor was in a servo loop, the displacement of the
motor followed with reasonable accuracy both sinusoidal and
non-sinusoidal command signals that were applied to the amplifier.
The piezoelectric sound source was driven by a low-distortion
oscillator at 10KHz. The sound emitted by the source was measured by a
microphone at a distance of approximately one foot. The output of the
microphone was amplified, high-pass filtered and applied to a
frequency-to-voltage converter. The output of the
frequency-to-voltage converter was low-pass filtered to reduce the
level of the residual 10KHz carrier, amplified and applied to a signal
averager. The signal averager was triggered by the command signal
that was applied to the linear motor. Averaging was used in order to
remove non-coherent 60Hz that was present in the output of the
demodulator.


THE MOTION OF THE SOUND SOURCE
A triangular command signal having a 50-msec period was applied to the
servo amplifier. A triangular command signal was used in order to
simplify interpretation of the measurement result and to avoid the
phase shift vs time delay ambiguity that would otherwise exist with
fixed frequency sinusoidal excitation. The output of the displacement
transducer was monitored on an oscilloscope and found to be triangular
with rounded corners. The rounding of the corners is due to the
limited closed-bandwidth of the servo. The velocity of the linear
motor was therefore trapezoidal with relatively flat and relatively
long plateaus and relatively short transitions.


THE MEASUREMENT RESULT
The propagating 10KHz signal emitted by the piezo bimorph was applied
to an FFT analyzer in zoom-analysis mode with a resolution bandwidth
of 0.1Hz. When the piezo bimorph was stationary, the propagating
signal picked up by the microphone showed only a single spectral peak
at 10KHz. When the piezo transducer was moving back and forth with a
triangular displacement provided by the linear motor, the propagating
signal received by the microphone contained numerous sidebands which
were indicative of FM modulation. Additionally, the output of the FM
demodulator was observed to be trapezoidal and followed on an
instantaneous basis the velocity of the linear motor and the attached
piezo transducer.


THE CHALLENGE
In science, theory usually follows experimental results. In this case
the experimental result shows that a 10KHz signal applied to a small
piezoelectric source moving back and forth around a fixed position
becomes frequency modulated by the back and forth motion of the
source. The measurement further shows that the received,
FM-demodulated signal follows the instantaneous velocity of the
source. This result is exactly what is expected on the basis of
Doppler frequency shift extrapolated from constant velocity to dynamic
velocity conditions. While some might argue that the observed
FM-like sidebands and the trapezoidal demodulated waveform are the
result of IM distortion, and not Doppler FM, the ball is in their
court. It is now up to them to provide an explanation/analysis
involving an IM producing mechanism in the present experimental setup
that accounts for the present experimental result. Finally, it must
be noted that the purpose of the present measurement was to
demonstrate fundamental phenomenological behavior. The 10KHz carrier
and the 50-msec peridiocity for the displacement of the linear motor
were chosen solely to accommodate the hardware on hand. There is
presently no reason to believe that the outcome of the present
measurement would be different if other carrier frequencies or other
source displacement periodicities or waveshapes were used.


This experiment is very "pure", and in fact, pretty much *defines* the
Doppler effect and frequency modulation. To determine its relevance to audio
applications, someone now needs to add additional parameters. For example:

o It would be interesting to observe the results when the modulating
frequency and the carrier are close together in frequency, and the sidebands
significantly overlap the modulating frequency, as they would in a typical
loudspeaker.
o Is the Doppler effect of the same order of magnitude of other loudspeaker
nonlinearities, such as harmonic and intermodulation distortion? How
difficult is it to resolve these effects separately when occurring
simultaneously in the same loudspeaker?
o How much do multi-way speakers mitigate these effects? Are wide-range
drivers measurably worse in these effects? (My intuition predicts that they
will be, but some full range speakers manage to employ mechanical
crossovers -- but I would expect them to be ineffective in reducing Doppler
intermodulation distortion). For what it's worth, what we commonly refer to
as "intermodulation distortion" is "amplitude intermodulation distortion"
(AIM). Speakers are the only device that I'm aware of that would exhibit
measurable Doppler intermodulation distortion, or DIM.
o Are horn speakers (including low frequency horns, like Klipschorns) less
susceptible to DIM due to the fact that they're more efficient, and require
less diaphragm motion for a given SPL?


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ruffrecords
 
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The Ghost wrote:
THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source
moving at constant velocity also applies under dynamically changing
velocity conditions, one would expect the propagating sound, that is
produced by a high-frequency source moving dynamically at a low
frequency around a fixed position, to be frequency modulated. One
would further expect that the instantaneous frequency of the
propagating sound would reflect the dynamic low-frequency velocity the
source. If so, the waveform of the fm-demodulated high-frequency
propagating sound, should follow on an instantaneous basis, the
dynamic velocity of the low-frequency velocity of the source.



major snippage.

here we go again.

The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.

Ian
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Karl Uppiano
 
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The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single transducer.
it is not.


A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency as a
function motion of the diaphragm due to the lower frequency, assuming the
speed of sound in air remains constant under these conditions?


  #5   Report Post  
Paul Guy
 
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On 14 Aug 2004 16:49:59 -0700, (The Ghost)
wrote:



....Some stuff deleted........


THE CHALLENGE
In science, theory usually follows experimental results. In this case
the experimental result shows that a 10KHz signal applied to a small
piezoelectric source moving back and forth around a fixed position
becomes frequency modulated by the back and forth motion of the
source. The measurement further shows that the received,
FM-demodulated signal follows the instantaneous velocity of the
source. This result is exactly what is expected on the basis of
Doppler frequency shift extrapolated from constant velocity to dynamic
velocity conditions. While some might argue that the observed
FM-like sidebands and the trapezoidal demodulated waveform are the
result of IM distortion, and not Doppler FM, the ball is in their
court. It is now up to them to provide an explanation/analysis
involving an IM producing mechanism in the present experimental setup
that accounts for the present experimental result. Finally, it must
be noted that the purpose of the present measurement was to
demonstrate fundamental phenomenological behavior. The 10KHz carrier
and the 50-msec peridiocity for the displacement of the linear motor
were chosen solely to accommodate the hardware on hand. There is
presently no reason to believe that the outcome of the present
measurement would be different if other carrier frequencies or other
source displacement periodicities or waveshapes were used.


The only difference between AM (Intermodulation-IM) and FM or phase
modulation is the phase of the two sidebands. AM they are both in
phase (they add to the overall amplitude). In FM they are out of
phase, thus they have no effect on the amplitude. The individual
amplitudes are the same between AM and FM, assuming the FM is of small
deviation.

wc=carrier freq (rad/sec)
wm=modulating freq (rad/sec)
A=amplitude
M=FM modulation index
u=AM modulation factor
FM: A*cos(wc*t) + 1/2*M*A[ cos(wc + wm)*t - cos(wc - wm)*t]
AM: A*cos(wc*t) + 1/2*u*A[ cos(wc + wm)*t + cos(wc - wm)*t]

This applies to narrow band FM (M less than 0.3). Notice that the
sign of the lower sideband is the only difference. Because IM
distortion is a second or higher order effect, they increase in
amplitude more than FM sidebands as the signal increases.

The practical way to tell the difference is to look at the amplitude
of the microphone signal versus time. If there is a variation of
amplitude (AM modulation), you have IM distortion. Then take your
signal and "clip it" (square wave), then look for sidebands. These
sidebands will be from the FM or doppler distortion.
You must also make sure that your microphone is far enough away and
positioned such that the amplitude doesn't vary just because of its
POSITION. That would appear as IM distortion (and your ears would
percieve it as such).
In terms of psychoacoustics I don't know if the ear can tell the
difference between AM and narrow band FM (doppler) distortion. My
guess is that it can't, since the cochlea cannot determine phase,
unless both frequencies are very close (you'll hear "beating"), there
will be no way that the hearing system can determine the phase
relation.
What is most relevant to your discussion, is that in the presence of
a loud tone, there is considerable "masking" at frequencies close to
the main tone. Roughly speaking, for frequencies from the main tone to
about 20% lower, and from the main tone and about 50% higher, the
sidebands will not be heard if they are 20 db less than the main tone.
The relationship is complicated, in some cases its much less than the
20 db (after Wegal and Lane, 1924). What this really says, is that
NEARBY sidebands must be more than 10% before they can be heard in
any form. If this is truly the case, Doppler distortion is probably
there, but the ear cannot sense it.
If you check the sensitivity of the ear to multiple tones, you will
find that masking makes many of these forms of distortion into a
non-issue.
The ear has a deliberately poor dynamic range (about 20-30db) for
signals other than the predominant signal, unless the interfering
frequencies are much lower. Since distortions tend to be HIGHER
frequencies, you aren't that sensitive to them. The exception is
distortion that produces difference frequencies that are much lower in
pitch than the main dominant sounds.
In your case your modulating frequency (60Hz?)is MUCH lower than
your modulated frequency (10KHz). What happens when you have multiple
STRONG signals, that are not at opposite ends of the spectrum? First,
the formula above doesn't hold (modulating frequency is not small
compared to modulated frequency), instead you get a whole series of
sidebands. FM Doppler distortion can be one of the major sources of
distortion, and designers must control various parameters to minimize
cone velocity.
Doppler effects can be reduced by 3 way speaker systems, appropriate
crossovers, larger cones (less velocity for same sound pressure
level).
Some of the more knowledgeable people (like Dick Pierce) could give
you a better idea of what Doppler distortion issues there are in the
industry. Do a web search on Wolfgang Klippel, or Linkwitz Lab, they
cover a lot of the speaker design issues

-Paul
.................................................. .............
Paul Guy
Somewhere in the Nova Scotia fog


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Randy Yates
 
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Paul Guy writes:
[...]
This applies to narrow band FM (M less than 0.3).


How do you know the type of FM here is narrowband? The
deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.

Doppler effects can be reduced by 3 way speaker systems, appropriate
crossovers, larger cones (less velocity for same sound pressure
level).


A real-life example of Doppler distortion in woofers in
direct-radiator systems can be heard in Emerson, Lake and Palmer's
"Trilogy" album (circa 1974?) in which a hellatious low synth bass
note is sustained simultaneously with notes from some type of
bell(s). The key is that the bell notes have fundamentals that aren't
that high - probably under 1 kHz - so they fall within the woofer's
range. Most direct-radiator systems produce this passage horribly,
especially with any volume. The Klipschorns do a marvelous job.
--
% Randy Yates % "So now it's getting late,
%% Fuquay-Varina, NC % and those who hesitate
%%% 919-577-9882 % got no one..."
%%%% % 'Waterfall', *Face The Music*, ELO
http://home.earthlink.net/~yatescr
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Arny Krueger
 
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"Paul Guy" wrote in message


snip mostly agreeable lead-up comments

This applies to narrow band FM (M less than 0.3). Notice that the
sign of the lower sideband is the only difference. Because IM
distortion is a second or higher order effect, they increase in
amplitude more than FM sidebands as the signal increases.


The practical way to tell the difference is to look at the amplitude
of the microphone signal versus time.


Not much help when the modulation indices are low and the measurement
environment is noisy, as it always seems to be for speakers.

If there is a variation of
amplitude (AM modulation), you have IM distortion. Then take your
signal and "clip it" (square wave), then look for sidebands. These
sidebands will be from the FM or Doppler distortion.


A bit more than that. You have to narrowband bandpass filter it before
clipping in order to avoid intermodulation. After clipping you either filter
it again, or just ignore the out-of band distortion product.

In terms of psychoacoustics I don't know if the ear can tell the
difference between AM and narrow band FM (Doppler) distortion. My
guess is that it can't, since the cochlea cannot determine phase,
unless both frequencies are very close (you'll hear "beating"), there
will be no way that the hearing system can determine the phase
relation.


Do tremolo and vibrato sound different?

What is most relevant to your discussion, is that in the presence of
a loud tone, there is considerable "masking" at frequencies close to
the main tone. Roughly speaking, for frequencies from the main tone to
about 20% lower, and from the main tone and about 50% higher, the
sidebands will not be heard if they are 20 db less than the main tone.
The relationship is complicated, in some cases its much less than the
20 db (after Wegal and Lane, 1924). What this really says, is that
NEARBY sidebands must be more than 10% before they can be heard in
any form. If this is truly the case, Doppler distortion is probably
there, but the ear cannot sense it.


A bit more than that. If nearby sidebands were that hard to hear, we'd never
hear tremolo and vibrato when the modulating frequency is low.

There are two modes of perception of modulation. If the sidebands are close
to the carrier, and they are audible, they are audible as roughness. If they
are distant from the carrier, then they are audible as separate tones,
subject to the kind of spectral masking shown above.

If you check the sensitivity of the ear to multiple tones, you will
find that masking makes many of these forms of distortion into a
non-issue.


See previous comments about low frequency modulation.

snip mostly agreeable other comments


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Arny Krueger
 
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"Randy Yates" wrote in message

Paul Guy writes:
[...]
This applies to narrow band FM (M less than 0.3).


How do you know the type of FM here is narrowband?


Look at the sidebands. If there is a simple structure and/or they are small,
then the modulation index is probably low.

The deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.


Yes, note that our experiments cover a range of 40 dB.

Doppler effects can be reduced by 3 way speaker systems,
appropriate crossovers, larger cones (less velocity for same sound
pressure level).


A real-life example of Doppler distortion in woofers in
direct-radiator systems can be heard in Emerson, Lake and Palmer's
"Trilogy" album (circa 1974?) in which a hellatious low synth bass
note is sustained simultaneously with notes from some type of
bell(s). The key is that the bell notes have fundamentals that aren't
that high - probably under 1 kHz - so they fall within the woofer's
range. Most direct-radiator systems produce this passage horribly,
especially with any volume. The Klipschorns do a marvelous job.


How do you know that this isn't just plain old AM distortion?


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Randy Yates
 
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"Arny Krueger" writes:
[...]
How do you know that this isn't just plain old AM distortion?


It sounds like the bell tones are warbling, i.e., varying in frequency.

As a listener, it really doesn't matter, distortion is distortion -
the sound is MUCH better with it removed.
--
% Randy Yates % "My Shangri-la has gone away, fading like
%% Fuquay-Varina, NC % the Beatles on 'Hey Jude'"
%%% 919-577-9882 %
%%%% % 'Shangri-La', *A New World Record*, ELO
http://home.earthlink.net/~yatescr
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Randy Yates
 
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"Arny Krueger" writes:
"Randy Yates" wrote in message

[...]
The deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.


Yes, note that our experiments cover a range of 40 dB.


40 dB? What exactly is 40 dB?
--
% Randy Yates % "Bird, on the wing,
%% Fuquay-Varina, NC % goes floating by
%%% 919-577-9882 % but there's a teardrop in his eye..."
%%%% % 'One Summer Dream', *Face The Music*, ELO
http://home.earthlink.net/~yatescr


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Arny Krueger
 
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"Randy Yates" wrote in message

"Arny Krueger" writes:
"Randy Yates" wrote in message

[...]
The deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.


Yes, note that our experiments cover a range of 40 dB.


40 dB? What exactly is 40 dB?


Sound level intensity. I think the actual SPLs were 78, 88, 98 and 108 dB,
more or less @ 1 meter. RS SPL meter so its not excactly NBS tracable,


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Randy Yates
 
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"Arny Krueger" writes:

"Randy Yates" wrote in message

"Arny Krueger" writes:
"Randy Yates" wrote in message

[...]
The deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.

Yes, note that our experiments cover a range of 40 dB.


40 dB? What exactly is 40 dB?


Sound level intensity. I think the actual SPLs were 78, 88, 98 and 108 dB,
more or less @ 1 meter. RS SPL meter so its not excactly NBS tracable,


What level was the first plot on your site (the one with the simple 4000 + 50
Hz signal) made at? (Approximate is fine.)

Also, as I asked in a personal email, if cone motion does not account
for the AM, then how would you account for it?
--
% Randy Yates % "The dreamer, the unwoken fool -
%% Fuquay-Varina, NC % in dreams, no pain will kiss the brow..."
%%% 919-577-9882 %
%%%% % 'Eldorado Overture', *Eldorado*, ELO
http://home.earthlink.net/~yatescr
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ruffrecords
 
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Karl Uppiano wrote:
The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single transducer.
it is not.



A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency as a
function motion of the diaphragm due to the lower frequency, assuming the
speed of sound in air remains constant under these conditions?




Go look in a good text book for the words 'linear' and 'sum'

Ian
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Karl Uppiano
 
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"ruffrecords" wrote in message
...
Karl Uppiano wrote:
The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.



A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency as
a function motion of the diaphragm due to the lower frequency, assuming
the speed of sound in air remains constant under these conditions?




Go look in a good text book for the words 'linear' and 'sum'


Why don't you just answer my question, and forego the superior attitude? I'm
sure you can figure out what I meant.


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Arny Krueger
 
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"Randy Yates" wrote in message

"Arny Krueger" writes:

"Randy Yates" wrote in message

"Arny Krueger" writes:
"Randy Yates" wrote in message

[...]
The deviation is dependent on the throw of the cone and the
modulating frequency (higher frequencies have a higher
first derivative, thus the associated Doppler will be higher)
These effects are highly implementation- and signal-specific.

Yes, note that our experiments cover a range of 40 dB.

40 dB? What exactly is 40 dB?


Sound level intensity. I think the actual SPLs were 78, 88, 98 and
108 dB, more or less @ 1 meter. RS SPL meter so its not excactly NBS
tracable,


What level was the first plot on your site (the one with the simple
4000 + 50 Hz signal) made at? (Approximate is fine.)


About 90 dN at one meter.

Also, as I asked in a personal email, if cone motion does not account
for the AM, then how would you account for it?


Speakers being speakers! ;-)




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ruffrecords
 
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Karl Uppiano wrote:
"ruffrecords" wrote in message
...

Karl Uppiano wrote:

The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.


A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency as
a function motion of the diaphragm due to the lower frequency, assuming
the speed of sound in air remains constant under these conditions?




Go look in a good text book for the words 'linear' and 'sum'



Why don't you just answer my question, and forego the superior attitude? I'm
sure you can figure out what I meant.



OK. No, otherwise it would not be a linear sum. Hence my reading
suggestion.

Ian
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Karl Uppiano
 
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"ruffrecords" wrote in message
...
Karl Uppiano wrote:
"ruffrecords" wrote in message
...

Karl Uppiano wrote:

The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.


A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency
as a function motion of the diaphragm due to the lower frequency,
assuming the speed of sound in air remains constant under these
conditions?




Go look in a good text book for the words 'linear' and 'sum'



Why don't you just answer my question, and forego the superior attitude?
I'm sure you can figure out what I meant.


OK. No, otherwise it would not be a linear sum. Hence my reading
suggestion.


I understand what "linear" and "sum" mean. When modulated by two sinusoids,
the x position of the diaphragm as a function of time is defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

Where A and B are the amplitudes of the two frequencies, and w2 and w2 are
the frequencies in radians per second of the two frequencies. Let's call w1
the low frequency and w2 the high frequency. There are no non-linear terms
in this equation, so we won't get harmonic or IM distortion. I understand
that.

Since Doppler shift is based on the velocity, not the position of the
diaphragm, we must differentiate this equation. The velocity of the
diaphragm as a function of time is then

v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )

The formula for Doppler shift is

ls = lo ( 1 - ( vs / c ) )

where

ls = the resulting wavelength (lambda shifted)

lo = the original wavelength of the higher frequency (lambda original)

vs = the velocity of the source (diaphragm velocity)

c = is the speed of sound in air

therefore, substituting v(t) for vs,

ls( t ) = lo ( 1 - ( ( w1 A cos( w1 t ) + w2 B cos( w2 t ) ) / c ) )

which appears to my eye as a time-varying wavelength based on the diaphragm
velocity. What am I doing wrong?


  #18   Report Post  
Karl Uppiano
 
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"ruffrecords" wrote in message
...
Karl Uppiano wrote:
"ruffrecords" wrote in message
...

Karl Uppiano wrote:

The flaw in this argument is that this set up assumes it is the same as
the linear superposition of the of the two signals in a single
transducer. it is not.


A single loudspeaker reproducing the linear sum of two different
frequencies. The higher frequency "riding" back and forth on the lower
frequency. Will that not affect the wavelength of the higher frequency
as a function motion of the diaphragm due to the lower frequency,
assuming the speed of sound in air remains constant under these
conditions?




Go look in a good text book for the words 'linear' and 'sum'



Why don't you just answer my question, and forego the superior attitude?
I'm sure you can figure out what I meant.


OK. No, otherwise it would not be a linear sum. Hence my reading
suggestion.


Reposting this, since it didn't appear to "take" last time:

I understand what "linear" and "sum" mean. When modulated by two sinusoids,
the x position of the diaphragm as a function of time is defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

Where A and B are the amplitudes of the two frequencies, and w2 and w2 are
the frequencies in radians per second of the two frequencies. Let's call w1
the low frequency and w2 the high frequency. There are no non-linear terms
in this equation, so we won't get harmonic or IM distortion. I understand
that.

Since Doppler shift is based on the velocity, not the position of the
diaphragm, we must differentiate this equation. The velocity of the
diaphragm as a function of time is then

v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )

The formula for Doppler shift is

ls = lo ( 1 - ( vs / c ) )

where

ls = the resulting wavelength (lambda shifted)

lo = the original wavelength of the higher frequency (lambda original)

vs = the velocity of the source (diaphragm velocity)

c = is the speed of sound in air

therefore, substituting v(t) for vs,

ls( t ) = lo ( 1 - ( ( w1 A cos( w1 t ) + w2 B cos( w2 t ) ) / c ) )

which appears to my eye as a time-varying wavelength based on the diaphragm
velocity. What am I doing wrong?



  #19   Report Post  
Bob Cain
 
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Karl Uppiano wrote:


I understand what "linear" and "sum" mean. When modulated by two sinusoids,
the x position of the diaphragm as a function of time is defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )


It is the piston velocity v(t) that follows this for equal
sound pressure at all frequencies.


Where A and B are the amplitudes of the two frequencies, and w2 and w2 are
the frequencies in radians per second of the two frequencies. Let's call w1
the low frequency and w2 the high frequency. There are no non-linear terms
in this equation, so we won't get harmonic or IM distortion. I understand
that.

Since Doppler shift is based on the velocity, not the position of the
diaphragm, we must differentiate this equation. The velocity of the
diaphragm as a function of time is then

v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )


That would be the acceleration a(t) which has no acoustic
consequences.

I'm too tired right now to follow those corrections all the
way through the rest of your welcome attempt to quantify
this but would you consider working them through to the
conclusion you can reach?


Thanks,

Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
  #20   Report Post  
Karl Uppiano
 
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"Bob Cain" wrote in message
...


Karl Uppiano wrote:


I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )


It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.


Hmmm... what is the equation for x( t ) then?


Where A and B are the amplitudes of the two frequencies, and w2 and w2
are the frequencies in radians per second of the two frequencies. Let's
call w1 the low frequency and w2 the high frequency. There are no
non-linear terms in this equation, so we won't get harmonic or IM
distortion. I understand that.

Since Doppler shift is based on the velocity, not the position of the
diaphragm, we must differentiate this equation. The velocity of the
diaphragm as a function of time is then

v( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )


That would be the acceleration a(t) which has no acoustic consequences.


Isn't velocity the first derivative of position? Isn't acceleration the
first derivative of velocity? It seems that acceleration (if we cared about
it) would be

a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) )

However, all three equations only differ by a constant. So I believe you
could get the same physical consequences by simply adjusting A and B
accordingly.

I'm too tired right now to follow those corrections all the way through
the rest of your welcome attempt to quantify this but would you consider
working them through to the conclusion you can reach?


My end result would differ by a constant (i.e., it would have a different
magnitude), as I mentioned above, but I believe the phenomenon would be the
same.

Thanks,

Bob
--

"Things should be described as simply as possible, but no simpler."

A. Einstein





  #21   Report Post  
Bob Cain
 
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Karl Uppiano wrote:

"Bob Cain" wrote in message
...


Karl Uppiano wrote:



I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )


It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.



Hmmm... what is the equation for x( t ) then?


x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t )

Isn't velocity the first derivative of position? Isn't acceleration the
first derivative of velocity? It seems that acceleration (if we cared about
it) would be

a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) )


Try

a( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )


However, all three equations only differ by a constant. So I believe you
could get the same physical consequences by simply adjusting A and B
accordingly.


And phase. The adjustment to A and B is a constant if W is.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
  #22   Report Post  
Karl Uppiano
 
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"Bob Cain" wrote in message
...


Karl Uppiano wrote:

"Bob Cain" wrote in message
...


Karl Uppiano wrote:



I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.



Hmmm... what is the equation for x( t ) then?


x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t )


....which I assume you arrived at by integrating my original equation. Is
there a derivation of this somewhere that I can look up?

Isn't velocity the first derivative of position? Isn't acceleration the
first derivative of velocity? It seems that acceleration (if we cared
about it) would be

a( t ) = - ( w1^2 A sin( w1 t ) + w2^2 B sin( w2 t ) )


Try

a( t ) = w1 A cos( w1 t ) + w2 B cos( w2 t )


However, all three equations only differ by a constant. So I believe you
could get the same physical consequences by simply adjusting A and B
accordingly.


And phase. The adjustment to A and B is a constant if W is.


Right. Bottom line, though, it seems that the wavelength is still a
time-varying function of the diaphragm velocity. Now, I need to understand
how the diaphragm motion is converted into sound. I will accept the
possibility that somehow the motion is irrelevant to the wavelength, but I
need to see the physics.


  #23   Report Post  
Bob Cain
 
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Karl Uppiano wrote:

"Bob Cain" wrote in message
...


Karl Uppiano wrote:


"Bob Cain" wrote in message
...


Karl Uppiano wrote:




I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

It is the piston velocity v(t) that follows this for equal sound pressure
at all frequencies.


Hmmm... what is the equation for x( t ) then?


x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t )



...which I assume you arrived at by integrating my original equation. Is
there a derivation of this somewhere that I can look up?


Yes. I just noted that for frequency independant operation
it is the velocity that should have been modeled with your
equation, not the position. x( t ) and a( t ) follow by
differentiation and integration respectively.



And phase. The adjustment to A and B is a constant if W is.



Right. Bottom line, though, it seems that the wavelength is still a
time-varying function of the diaphragm velocity.


Why would the wavelength vary over time? If you drive the
piston with a fixed magnitude sinusoid, its wavelength is
fixed and so is that of the acoustic wave it puts out unless
it moves with constant velocity relative to the air. If
driven with any periodic function, the period is determined
by the lowest Fourier component.

The velocity of that piston is converted into an acoustic
wave with the same shape as that of the piston's velocity
function.

If it is in constant linear translation, the wave function
will be an expanded or contracted version of the piston's
velocity function. That's Doppler shift.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
  #24   Report Post  
Karl Uppiano
 
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"Bob Cain" wrote in message
...


Karl Uppiano wrote:

"Bob Cain" wrote in message
...


Karl Uppiano wrote:


"Bob Cain" wrote in message
...


Karl Uppiano wrote:




I understand what "linear" and "sum" mean. When modulated by two
sinusoids, the x position of the diaphragm as a function of time is
defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )

It is the piston velocity v(t) that follows this for equal sound
pressure at all frequencies.


Hmmm... what is the equation for x( t ) then?

x( t ) = -(A/w1) cos( w1 t ) - (B/w2) cos( w2 t )



...which I assume you arrived at by integrating my original equation. Is
there a derivation of this somewhere that I can look up?


Yes. I just noted that for frequency independant operation it is the
velocity that should have been modeled with your equation, not the
position. x( t ) and a( t ) follow by differentiation and integration
respectively.



And phase. The adjustment to A and B is a constant if W is.



Right. Bottom line, though, it seems that the wavelength is still a
time-varying function of the diaphragm velocity.


Why would the wavelength vary over time? If you drive the piston with a
fixed magnitude sinusoid, its wavelength is fixed and so is that of the
acoustic wave it puts out unless it moves with constant velocity relative
to the air. If driven with any periodic function, the period is
determined by the lowest Fourier component.

The velocity of that piston is converted into an acoustic wave with the
same shape as that of the piston's velocity function.

If it is in constant linear translation, the wave function will be an
expanded or contracted version of the piston's velocity function. That's
Doppler shift.


Is there a web site that would describe the physics, mathematically, of how
diaphragm motion is converted to sound? And more specifically, with two
frequencies, how the time-varying velocity of the lower frequency would not
Doppler-shift the higher one? I just want to understand the physics of this,
and get at the truth of the matter.


  #25   Report Post  
Bob Cain
 
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Karl Uppiano wrote:

Is there a web site that would describe the physics, mathematically, of how
diaphragm motion is converted to sound?


If you are up to it:

http://www.silcom.com/~aludwig/Physi..._of_sound.html

I haven't printed it off and holed up with it yet and I've
got to do that.

And more specifically, with two
frequencies, how the time-varying velocity of the lower frequency would not
Doppler-shift the higher one? I just want to understand the physics of this,
and get at the truth of the matter.


The piston doesn't know from two frequencies. It knows and
transfers its instantaneous velocity to the correct position
of the outward propegating wave. It doesn't care what was
mixed to get that velocity and it doesn't care what came
before or after that instant.

If you can make the piston move the way you want you can get
it to produce the acoustic wave you want.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein


  #26   Report Post  
Goofball_star_dot_etal
 
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On Tue, 17 Aug 2004 00:21:59 -0700, Bob Cain
wrote:



Karl Uppiano wrote:


I understand what "linear" and "sum" mean. When modulated by two sinusoids,
the x position of the diaphragm as a function of time is defined by

x( t ) = A sin( w1 t ) + B sin( w2 t )


It is the piston velocity v(t) that follows this for equal
sound pressure at all frequencies.


Oops a daisy!
  #27   Report Post  
Karl Uppiano
 
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"The Ghost" wrote in message
om...
THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source
moving at constant velocity also applies under dynamically changing
velocity conditions, one would expect the propagating sound, that is
produced by a high-frequency source moving dynamically at a low
frequency around a fixed position, to be frequency modulated. One
would further expect that the instantaneous frequency of the
propagating sound would reflect the dynamic low-frequency velocity the
source. If so, the waveform of the fm-demodulated high-frequency
propagating sound, should follow on an instantaneous basis, the
dynamic velocity of the low-frequency velocity of the source.


THE SETUP:
A small circular piezoelectric bimorph, having a resonant frequency of
approximately 10KHz was attached to the 10-lb armature/shaft of a
linear motor. The displacement of the armature/shaft was monitored
by a linear displacement transducer attached to the opposite end of
the armature/shaft. The linear displacement transducer also provided
feedback for the servo amplifier which was driving the linear motor.
Because the linear motor was in a servo loop, the displacement of the
motor followed with reasonable accuracy both sinusoidal and
non-sinusoidal command signals that were applied to the amplifier.
The piezoelectric sound source was driven by a low-distortion
oscillator at 10KHz. The sound emitted by the source was measured by a
microphone at a distance of approximately one foot. The output of the
microphone was amplified, high-pass filtered and applied to a
frequency-to-voltage converter. The output of the
frequency-to-voltage converter was low-pass filtered to reduce the
level of the residual 10KHz carrier, amplified and applied to a signal
averager. The signal averager was triggered by the command signal
that was applied to the linear motor. Averaging was used in order to
remove non-coherent 60Hz that was present in the output of the
demodulator.


THE MOTION OF THE SOUND SOURCE
A triangular command signal having a 50-msec period was applied to the
servo amplifier. A triangular command signal was used in order to
simplify interpretation of the measurement result and to avoid the
phase shift vs time delay ambiguity that would otherwise exist with
fixed frequency sinusoidal excitation. The output of the displacement
transducer was monitored on an oscilloscope and found to be triangular
with rounded corners. The rounding of the corners is due to the
limited closed-bandwidth of the servo. The velocity of the linear
motor was therefore trapezoidal with relatively flat and relatively
long plateaus and relatively short transitions.


THE MEASUREMENT RESULT
The propagating 10KHz signal emitted by the piezo bimorph was applied
to an FFT analyzer in zoom-analysis mode with a resolution bandwidth
of 0.1Hz. When the piezo bimorph was stationary, the propagating
signal picked up by the microphone showed only a single spectral peak
at 10KHz. When the piezo transducer was moving back and forth with a
triangular displacement provided by the linear motor, the propagating
signal received by the microphone contained numerous sidebands which
were indicative of FM modulation. Additionally, the output of the FM
demodulator was observed to be trapezoidal and followed on an
instantaneous basis the velocity of the linear motor and the attached
piezo transducer.


THE CHALLENGE
In science, theory usually follows experimental results. In this case
the experimental result shows that a 10KHz signal applied to a small
piezoelectric source moving back and forth around a fixed position
becomes frequency modulated by the back and forth motion of the
source. The measurement further shows that the received,
FM-demodulated signal follows the instantaneous velocity of the
source. This result is exactly what is expected on the basis of
Doppler frequency shift extrapolated from constant velocity to dynamic
velocity conditions. While some might argue that the observed
FM-like sidebands and the trapezoidal demodulated waveform are the
result of IM distortion, and not Doppler FM, the ball is in their
court. It is now up to them to provide an explanation/analysis
involving an IM producing mechanism in the present experimental setup
that accounts for the present experimental result. Finally, it must
be noted that the purpose of the present measurement was to
demonstrate fundamental phenomenological behavior. The 10KHz carrier
and the 50-msec peridiocity for the displacement of the linear motor
were chosen solely to accommodate the hardware on hand. There is
presently no reason to believe that the outcome of the present
measurement would be different if other carrier frequencies or other
source displacement periodicities or waveshapes were used.


Since this thread was started, it has meandered here and there, and I just
realized that we may have jumped to some invalid conclusions. Here are some
important points to consider:

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.

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. 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.

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.

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.



  #28   Report Post  
The Ghost
 
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"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.
  #29   Report Post  
Karl Uppiano
 
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"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".


  #30   Report Post  
Bob Cain
 
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The Ghost wrote:


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.


He was correct and you are not. It is entirely a matter of
the frequency dependant coupling.

I know, I know. You could prove otherwise but won't.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein


  #31   Report Post  
The Ghost
 
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"Karl Uppiano" wrote in message .. .


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".


My measurement results can be applied to a loudspeaker but only to the
extent that they demonstrate that dynamic Doppler shift can be
produced by a loudspeaker. Whether or not Doppler shift produced by a
loudspeaker can be measured is another issue. That is going to depend
on the relative amount of intermodulation distortion that the
loudspeaker also produces because the Doppler FM components and the
intermodulation distortion components are at the same frequencies.
Personally, I wouldn't waste my time trying to separate the two.


................... 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 FM demodulator that I used was a precision frequency-to-voltage
converter which operates on zero crossings and, as such, is completely
insensitive to amplitude variations of the signal being demodulated.


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.


.............. 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 :-)


Not surprisingly, we again mostly disagree. In the early stages of
research, where the issue is whether or not a phenomenon exists, the
first order of business is to demonstrate experimentally the existence
of the phenomenon. After the existence of the phenomenon has been
demonstrated, model development and quantative predictions follow.
For whatever reason, you seem to refuse to distinguish between the
existence of a phenomenon and the accurate quantitative description of
a phenomenon. The absence of a quantitative description of a
phenomenon is not a justifiable excuse for denying its existence. In
the history of science, there are many phenomena that were
demonstrated first and quantified later.


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".


If you believe that, then you have a lot to learn. It has been my
experience over many years that models go up in flames, more often
than not, becasue of fundamental phenomenological
inconsistencies/inadequacies rather than because they did not produce
a sufficiently high degree of agreement between prediction and
measured results.
  #32   Report Post  
Bob Cain
 
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The Ghost wrote:

Not surprisingly, we again mostly disagree. In the early stages of
research, where the issue is whether or not a phenomenon exists, the
first order of business is to demonstrate experimentally the existence
of the phenomenon. After the existence of the phenomenon has been
demonstrated, model development and quantative predictions follow.
For whatever reason, you seem to refuse to distinguish between the
existence of a phenomenon and the accurate quantitative description of
a phenomenon. The absence of a quantitative description of a
phenomenon is not a justifiable excuse for denying its existence. In
the history of science, there are many phenomena that were
demonstrated first and quantified later.


Evidence for existence of a phenomenon requires elimination
of spurious causes one way or another, either by
experimental setup or by having a _good_ characterization of
the spurious phenomena so that their effect can be removed
from the test data. How does your "experiment" do either so
that what remains can be legitimately regarded as evidence
of Doppler distortion?

And even if it satisfied that requirement, the phenomenon in
question now is not simply Doppler distortion but the
mechanism that produces it so a predictive model is
absolutely required. Why, if the mechanism is as simple as
is described, has no such model been forthcoming?

This is basic stuff and should not have to be spoon fed to
anyone who claims to be an experimental scientist.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
  #33   Report Post  
Ben Bradley
 
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Deleting alt.sci.physics.acoustics from the crosspost.

In
alt.music.home-studio,rec.audio.tech,rec.audio.pro,alt.sci.physic s.acoustics
On Mon, 23 Aug 2004 18:55:28 -0700, Bob Cain
wrote:



The Ghost wrote:

Not surprisingly, we again mostly disagree. In the early stages of
research, where the issue is whether or not a phenomenon exists, the
first order of business is to demonstrate experimentally the existence
of the phenomenon. After the existence of the phenomenon has been
demonstrated, model development and quantative predictions follow.
For whatever reason, you seem to refuse to distinguish between the
existence of a phenomenon and the accurate quantitative description of
a phenomenon. The absence of a quantitative description of a
phenomenon is not a justifiable excuse for denying its existence. In
the history of science, there are many phenomena that were
demonstrated first and quantified later.


Evidence for existence of a phenomenon requires elimination
of spurious causes one way or another, either by
experimental setup or by having a _good_ characterization of
the spurious phenomena so that their effect can be removed
from the test data.


How would something cause the doppler effect? By emitting sound and
moving relative to a receiver. What is moving (and emitting sound) in
the systems we have been describing? Voice coil, cone, spider,
surround. Of these, perhaps the surround could cause spurious doppler
effect (because it's moving, but "on average" it moves only half as
fast and half as far as the cone). It also has much less radiating
area than the cone. I'm not even considering the spider and voice
coil, because not only do they not offer much surface area, they're
not facing forward and aren't 'visible' through the cone. There's also
the dust cap, but it is considered part of the cone.
You could argue the speaker frame moves in response to the cone's
movement (Newton's Nth law of motion, I forget what N is), but that
can be reduced substantially by securely mounting the driver on a
large concrete block, effectively increasing its mass and lowering its
movement.

How does your "experiment" do either so
that what remains can be legitimately regarded as evidence
of Doppler distortion?

And even if it satisfied that requirement, the phenomenon in
question now is not simply Doppler distortion but the
mechanism that produces it so a predictive model is
absolutely required. Why, if the mechanism is as simple as
is described, has no such model been forthcoming?

This is basic stuff and should not have to be spoon fed to
anyone who claims to be an experimental scientist.


Yes, Bob, it IS basic stuff.

The speed of sound at sea level is about 1116 feet per second
(google). A 1kHz tone has a wavelenth of 1.116 feet (or 1 foot, 1.32
inches). Run a 1kHz tone from a signal generator into both an
oscilloscope (channel 1, trigger on channel 1) and an audio amplifier
that drives a speaker. Put a microphone a couple of feet from the
speaker, run its output through a preamp (or directly) to channel 2 of
the oscilloscope. Adjust vertical gains appropriately to get a good
vertical displacement of each sine wave. You should be able, by
changing the distance from the microphone to the speaker, put these
two sine waves in phase. If you increase the distance between the mic
and speaker, the bottom (channel 2) trace should go through a whole
cycle when the distance changes by 1 foot and 1.32 inches.
Mount the speaker on a shaker table, and program it to do various
movements (changing the distance between it and the mic) at various
speeds. Observe the scope traces while this is happening. The bottom
trace shows a phase change that corresponds exactly and instantly
(less a small amount of latency caused by the speed of sound) to the
motion of the speaker, or more specifically, the distance between it
and the mic.
Mix (in the audio, additive sense, not the radio/RF,
multiplicative/nonlinear sense) a low-frequency (0.1 Hz to 50 Hz)
signal with the 1kHz tone so that they both are amplified and drive
the speaker. This causes cone motion (assuming it stays within the
linear range of the driver), but the 1kHz signal is still emitted from
the speaker. Observe the trace on channel 2, it will show a small
amount of phase shift that directly follows the cone motion. Assuming
1/2 inch peak-to-peak cone excursion, the shift in degrees will be
360*(0.5/12)/1.116=13 degrees. This is not a lot, but you should be
able to increase both the trace speed (shorter timebase) and the
vertical gain for channel 2, and see a diagonal line (if not visible,
move the mic until itiis) that moves back and forth with the speaker
cone. This movement directly follows the cone motion (which in this
case is caused by the low-frequency driving signal), just as it did
when the speaker was on the shaker table.
Bob, I expect you believe the shaker table description, so you
shouldn't have to actually do it. But I would hope you do the
description in the last paragraph. I presume you have the equipment to
do it and know how to wire it up. You should be able to see the phase
change of the 1kHz signal, and IIRC the derivative of the phase change
is frequency change. So if the cone moves (actually accelerates or
decelerates) a visible distance, it will happen. It doesn't matter if
it's below (the cone's free-air) resonance or above resonance, if it
moves visibly, it's enough to cause measurable phase shift and thus
frequency modulation.

Bob


I can suggest some sauce for your hat, it's Mezzetta's Habanero
sauce with the appropriate words "Twist and Shout" on the label. It's
definitely up there on the heat scale, but not as concentrated as the
"Hell Hot" sauce which seems to have a lot of radioactive byproducts.
Mezzetta's has a touch of sweet (?) taste along with the hot flavor,
while others of just have the hot flavor piled on top of the hot
flavor. Putting a teaspoon or two on the edge of your plate and adding
a small bit to each bite can add that extra flavor to even the
toughest dishes.

-----
http://mindspring.com/~benbradley
  #34   Report Post  
Bob Cain
 
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Ben Bradley wrote:


Bob, I expect you believe the shaker table description, so you
shouldn't have to actually do it.


Ben, you may not have seen it in my posts for the last week
or so but I am no longer disputing that a Doppler distortion
phenomeon exists and that your experiment would show it even
with ideal speakers. It's patently obvious from the thought
experiment of a speaker on a long swing emitting a tone.
Where I remain in divergence from the mainstream is the
cause of it. I do not believe that if you were to do the
two tone experiment with a clean piston in a tube such that
the boundry conditions enforce the creation of a plane wave,
that you would see any Doppler distortion. Mainstream
thinking says you would. The reason it doesn't is that the
coupling of speaker to a distant receiver is a constant,
frequency independant function in that case. I say that
mixing does not occur at the piston/air interface but
further out in the radiated field instead.

What I am disputing at this point is the mechanism. It does
not occur because of little fast waves riding on big slow
ones in the cone but rather under circumstances where the
coupling from speaker to detector is frequency dependant. A
speaker in a box has a very frequency dependant coupling
to the far field and will evidence Doppler distortion.

An ESL in a push-pull configuration is a very low distortion
emitter and has the advantage that the diapragm motion can
be very accurately measured by incuding the capacitance
between the diaphragm an one of the push-pull plates in a
tuned RF modulator. An FM detector on that RF signal will
quite accurately tell what the diaphragm is actually doing
so as to provide a reference signal for any experiment.

I predict that such a system will show no Doppler distortion
in a tube if one can be constructed. The requisite
terminations at the ends is probably too difficult, however.
If it is too difficult, the ESL can be used free standing
for a different experiment. If the principle of my theory
of what causes Doppler distortion is correct, the amount of
it will increase relative to the signal as you distance
yourself from the speaker if the low frequency used in the
experiment is low enough that its coupling to the receiver
decreases much more rapidly with distance than the high
frequency one. The principle I am trying to refute would
make the amount of distortion relative to the signal
independant of the receiver position in space.


I can suggest some sauce for your hat, it's Mezzetta's Habanero
sauce with the appropriate words "Twist and Shout" on the label. It's
definitely up there on the heat scale, but not as concentrated as the
"Hell Hot" sauce which seems to have a lot of radioactive byproducts.
Mezzetta's has a touch of sweet (?) taste along with the hot flavor,
while others of just have the hot flavor piled on top of the hot
flavor. Putting a teaspoon or two on the edge of your plate and adding
a small bit to each bite can add that extra flavor to even the
toughest dishes.


I will definitely save that recipe should either solid
experiment or theory refute the principle on which I think
an accurate theory can be based. :-)

Without a full development of either, I've shown how the
predictions of mine and the popular one will differ with a
fairly easy experiment to set up and do (as experiments go.)
Wish I could do it myself but I have neither the resources
nor the available time.

I still haven't seen any attempt at all to refute the
argument which says it can't exist with a piston in a tube
because of the principle of reciprocity. Several have
hollered that reciprocity doesn't apply to pistons driving
air but without a single detailed reason why not without
appeal to sound pressures that yield a signifigantly
non-linear relationship between pressure and velocity.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
  #35   Report Post  
Porky
 
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"The Ghost" wrote in message
om...
THE HYPOTHESIS:
Assuming that the equation for the Doppler frequency shift of a source
moving at constant velocity also applies under dynamically changing
velocity conditions, one would expect the propagating sound, that is
produced by a high-frequency source moving dynamically at a low
frequency around a fixed position, to be frequency modulated. One
would further expect that the instantaneous frequency of the
propagating sound would reflect the dynamic low-frequency velocity the
source. If so, the waveform of the fm-demodulated high-frequency
propagating sound, should follow on an instantaneous basis, the
dynamic velocity of the low-frequency velocity of the source.


THE SETUP:
A small circular piezoelectric bimorph, having a resonant frequency of
approximately 10KHz was attached to the 10-lb armature/shaft of a
linear motor. The displacement of the armature/shaft was monitored
by a linear displacement transducer attached to the opposite end of
the armature/shaft. The linear displacement transducer also provided
feedback for the servo amplifier which was driving the linear motor.
Because the linear motor was in a servo loop, the displacement of the
motor followed with reasonable accuracy both sinusoidal and
non-sinusoidal command signals that were applied to the amplifier.
The piezoelectric sound source was driven by a low-distortion
oscillator at 10KHz. The sound emitted by the source was measured by a
microphone at a distance of approximately one foot. The output of the
microphone was amplified, high-pass filtered and applied to a
frequency-to-voltage converter. The output of the
frequency-to-voltage converter was low-pass filtered to reduce the
level of the residual 10KHz carrier, amplified and applied to a signal
averager. The signal averager was triggered by the command signal
that was applied to the linear motor. Averaging was used in order to
remove non-coherent 60Hz that was present in the output of the
demodulator.


THE MOTION OF THE SOUND SOURCE
A triangular command signal having a 50-msec period was applied to the
servo amplifier. A triangular command signal was used in order to
simplify interpretation of the measurement result and to avoid the
phase shift vs time delay ambiguity that would otherwise exist with
fixed frequency sinusoidal excitation. The output of the displacement
transducer was monitored on an oscilloscope and found to be triangular
with rounded corners. The rounding of the corners is due to the
limited closed-bandwidth of the servo. The velocity of the linear
motor was therefore trapezoidal with relatively flat and relatively
long plateaus and relatively short transitions.


THE MEASUREMENT RESULT
The propagating 10KHz signal emitted by the piezo bimorph was applied
to an FFT analyzer in zoom-analysis mode with a resolution bandwidth
of 0.1Hz. When the piezo bimorph was stationary, the propagating
signal picked up by the microphone showed only a single spectral peak
at 10KHz. When the piezo transducer was moving back and forth with a
triangular displacement provided by the linear motor, the propagating
signal received by the microphone contained numerous sidebands which
were indicative of FM modulation. Additionally, the output of the FM
demodulator was observed to be trapezoidal and followed on an
instantaneous basis the velocity of the linear motor and the attached
piezo transducer.


THE CHALLENGE
In science, theory usually follows experimental results. In this case
the experimental result shows that a 10KHz signal applied to a small
piezoelectric source moving back and forth around a fixed position
becomes frequency modulated by the back and forth motion of the
source. The measurement further shows that the received,
FM-demodulated signal follows the instantaneous velocity of the
source. This result is exactly what is expected on the basis of
Doppler frequency shift extrapolated from constant velocity to dynamic
velocity conditions. While some might argue that the observed
FM-like sidebands and the trapezoidal demodulated waveform are the
result of IM distortion, and not Doppler FM, the ball is in their
court. It is now up to them to provide an explanation/analysis
involving an IM producing mechanism in the present experimental setup
that accounts for the present experimental result. Finally, it must
be noted that the purpose of the present measurement was to
demonstrate fundamental phenomenological behavior. The 10KHz carrier
and the 50-msec peridiocity for the displacement of the linear motor
were chosen solely to accommodate the hardware on hand. There is
presently no reason to believe that the outcome of the present
measurement would be different if other carrier frequencies or other
source displacement periodicities or waveshapes were used.


I agree with everything you've said, except that it doesn't apply to
loudspeakers, you've just come up with a fancier variation of the
train/whistle model, which doesn't apply to speakers because the speaker is
reproducing a complex soundwave in toto from a single complex driving
source, what you're doing is the same as picking up the speaker and moving
it back and forth and that will certainly produce Doppler shift. It isn't
that the motion is dynamic, it's that the motion is coming from a single
source which producing a complex sound, that is the reason a speaker doesn't
produce doppler shift when reproducing music.




  #36   Report Post  
Mark
 
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He was correct and you are not. It is entirely a matter of
the frequency dependant coupling.


Bob,

If you set up your coupling tube so that the speaker cone pushes the
air completly and the air moves in the tube without loss and at the
far end the air pushes the mic diaphram completly SO THAT THE SPEKAER
CONE AND MIC DIPHRAM ARE MOVING TOGETHER IN LOCK STEP WITH THE SAME
DISPLACEMENT, then you are correct, there is no Doppler effect. Note
that in this case the distance between the Rx and Tx is constant and
there is no Doppler effect.


In any other case where the mic diaphram is not moving in lock step
with the cone, there will be a Doppler effect.

Mark
  #37   Report Post  
Michael Squires
 
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Sorry to come in so late on this thread, but wasn't this topic the subject
of Dr. Klipsch's research and the basis of the K-horn design?

Mike Squires
--

Mike Squires (mikes at cs.indiana.edu) 317 233 9456 (w) 812 333 6564 (h)
mikes at siralan.org 546 N Park Ridge Rd., Bloomington, IN 47408
  #38   Report Post  
The Ghost
 
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Bob Cain wrote in message ...
The Ghost wrote:

......... The absence of a quantitative description of a
phenomenon is not a justifiable excuse for denying its existence. In
the history of science, there are many phenomena that were
demonstrated first and quantified later.



Evidence for existence of a phenomenon requires elimination
of spurious causes one way or another, either by
experimental setup or by having a _good_ characterization of
the spurious phenomena so that their effect can be removed
from the test data. How does your "experiment" do either so
that what remains can be legitimately regarded as evidence
of Doppler distortion?


I contend that my experiment has no so-called spurious phenomena.
Since you are the one claiming that it does, it is your responsibility
to identify them and demonstrate, with your own measurements, that my
measurement results are invalidated when the so-called spurious
phenomena are removed. Given that my measurement result agree with
expectation that the instantaneous FM-demodulated propagating signal
follows in time the instantaneous trapezoidal velocity of the source,
I seen no need to go looking for so-called spurious phenomena which
exist only in your mind.


And even if it satisfied that requirement, the phenomenon in
question now is not simply Doppler distortion but the
mechanism that produces it so a predictive model is
absolutely required. Why, if the mechanism is as simple as
is described, has no such model been forthcoming?


The mechanism for instantaneous Doppler shift is instantaneous
relative motion between the source and the observer. Beyond that, any
predictive model would necessarily have to be situation specific, and
in that regard, the simplest situations to model are the most
difficult to experimentally verify and vice versa.

This is basic stuff and should not have to be spoon fed to
anyone who claims to be an experimental scientist.


It is you, not I, who is having problems understianding this basic
stuff.
  #39   Report Post  
Bob Cain
 
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Mark wrote:


If you set up your coupling tube so that the speaker cone pushes the
air completly and the air moves in the tube without loss and at the
far end the air pushes the mic diaphram completly SO THAT THE SPEKAER
CONE AND MIC DIPHRAM ARE MOVING TOGETHER IN LOCK STEP WITH THE SAME
DISPLACEMENT, then you are correct, there is no Doppler effect.


Yes, exactly. And if they aren't I'd like to be shown why,
exactly and without any unparamaterized or underived
formulas. All axioms should be stated for purposes of
criticism and a derivation proceed from there to a proof
that reciprocity fails in this case. Because if it doesn't,
then if you make the active piston passive and measure
motion due to passage of a wave (coming from the side of it
opposite the receiver) and then make the piston active to
generate the same motion, the reciever at the end will see
two different things. I don't believe it.

I really don't expect any of my opponents in this debate to
address this because it seems they never do if they can't
explain it and then it remains invalid by their silence as
if it had never been uttered.


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein
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