Here's the results of some speaker measurements that I made tonight, based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is an
ECM8000 that is a few inches from the woofer cone.

http://www.pcavtech.com/techtalk/doppler/

The first graph shows the broadband response. The large spikes at 50 Hz and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher than
the spike for 50 Hz because the woofer is simply that much more efficient at
4 KHz.

The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair of
large spikes are about 50 Hz on either side of 4 KHz, the second are about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as the
test is contrived to focus on FM.

While I've got this set up, any other data that anyone would find
interesting?

Arny Krueger wrote:

While I've got this set up, any other data that anyone would find
interesting?

Many thanks, Arny. Experimentalist that you are, I had a
feeling you were off doing that. :-)

My question is, wouldn't the kind of distortion claimed as
"Doppler" distortion, which is claimed to be FM, have a
continuous harmonic structure around that 4k peak rather
than the discrete one you are seeing?

Is there any way you can think of to exactly simulate an FM
modulation of 50 Hz on top of 4 kHz to compare?


Bob
--

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

A. Einstein

"Bob Cain" wrote in message

Arny Krueger wrote:

While I've got this set up, any other data that anyone would find
interesting?

Many thanks, Arny. Experimentalist that you are, I had a
feeling you were off doing that. :-)

My question is, wouldn't the kind of distortion claimed as
"Doppler" distortion, which is claimed to be FM, have a
continuous harmonic structure around that 4k peak rather
than the discrete one you are seeing?

No, because the modulating frequency is a pure tone/

Is there any way you can think of to exactly simulate an FM
modulation of 50 Hz on top of 4 kHz to compare?

Sure 2 independent ways. First generate a FM-modulated tone in Audition 1.x
/CE.2.x

These parameters will get you close:

Base frequency: 4000 Hz
Modulate by 1 Hz
Modulation frequency 50 Hz
dB volume -15 dB

FFT analysis with 65536 points, Blackman-Harris windowing

Then, to zoom in on the frequency range around 4 KHz with enough resolution,
right click and drag around 4 KHz on the frequency scale.

The web page at http://www.pcavtech.com/techtalk/doppler/ has been updated
to include the results of this simulation, and the one below:

You can also run the FM modulation model at
http://contact.tm.agilent.com/Agilen...eFM_popup.html

with the following parameters:

Wc = 5.0
Wm = 0.5
m= 1.02

"Arny Krueger" writes:

"Bob Cain" wrote in message

Arny Krueger wrote:

While I've got this set up, any other data that anyone would find
interesting?

Many thanks, Arny. Experimentalist that you are, I had a
feeling you were off doing that. :-)

My question is, wouldn't the kind of distortion claimed as
"Doppler" distortion, which is claimed to be FM, have a
continuous harmonic structure around that 4k peak rather
than the discrete one you are seeing?

No, because the modulating frequency is a pure tone/

That's right. Specifically, you will have sidebands at
integer multiples of the modulating frequency, thus the
spectrum will be discrete. The magnitude of the nth sideband
is given by a Bessel function of the first kind, J_n(B), where
B is the amplitude of the modulating signal.

[From Mischa Schwartz's "Information, Transmission, Modulation,
and Noise," 4th ed.]
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
, 919-472-1124

Would you technical guys agree that the two tone interaction
we are hypothesizing can be approximated to low order by:

l*sin((wh+wld*sin(wl*t))*t) + h*sin((wl+whd*sin(wh*t))*t)

with h and l related to the amplitudes of the HF and LF
components respectively, wh the frequency of the HF tone, wl
the frequency of the LF tone and wld and whd a measure of
the "depth" in Hz of the cross modulations that are related
to the relative strength of the two tones?

If so, I'd appreciate input on what might be a reasonable
set of parameters.


Bob
--

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

A. Einstein

Bob Cain writes:

Would you technical guys agree that the two tone interaction we are
hypothesizing can be approximated to low order by:

l*sin((wh+wld*sin(wl*t))*t) + h*sin((wl+whd*sin(wh*t))*t)

with h and l related to the amplitudes of the HF and LF components
respectively, wh the frequency of the HF tone, wl the frequency of the
LF tone and wld and whd a measure of the "depth" in Hz

wld and whd would be depths in radians.
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

"Arny Krueger" wrote in message
...
These parameters will get you close:

Base frequency: 4000 Hz
Modulate by 1 Hz
Modulation frequency 50 Hz
dB volume -15 dB

FFT analysis with 65536 points, Blackman-Harris windowing

You know, I don't really mind you using my original work, but you could have
at least asked first. My band used to open with the above tone. The college
kids loved it.

"Jim Carr" wrote in message
news:FnOQc.3226$yh.1571@fed1read05
"Arny Krueger" wrote in message
...

These parameters will get you close:

Base frequency: 4000 Hz
Modulate by 1 Hz
Modulation frequency 50 Hz
dB volume -15 dB

FFT analysis with 65536 points, Blackman-Harris windowing

You know, I don't really mind you using my original work, but you
could have at least asked first. My band used to open with the above
tone. The college kids loved it.

LOL!

In alt.music.home-studio and rec.audio.tech, "Arny Krueger"
wrote:

"Jim Carr" wrote in message
news:FnOQc.3226$yh.1571@fed1read05
"Arny Krueger" wrote in message
...

These parameters will get you close:

Base frequency: 4000 Hz
Modulate by 1 Hz
Modulation frequency 50 Hz
dB volume -15 dB

FFT analysis with 65536 points, Blackman-Harris windowing

You know, I don't really mind you using my original work, but you
could have at least asked first. My band used to open with the above
tone. The college kids loved it.

LOL!

Don't worry, Arny, it's not original to him (unless he did it
before the very early '60's), the Beatles did it first in the opening
seconds of "I Feel Fine."
Furthermore, effects like this are more like a "riff" or "lick"
than a melody, and can't be covered under copyright.

-----
http://mindspring.com/~benbradley

On Thu, 5 Aug 2004 22:19:23 -0400, "Arny Krueger"
wrote:

Here's the results of some speaker measurements that I made tonight, based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is an
ECM8000 that is a few inches from the woofer cone.

http://www.pcavtech.com/techtalk/doppler/

The first graph shows the broadband response. The large spikes at 50 Hz and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher than
the spike for 50 Hz because the woofer is simply that much more efficient at
4 KHz.

The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair of
large spikes are about 50 Hz on either side of 4 KHz, the second are about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as the
test is contrived to focus on FM.

While I've got this set up, any other data that anyone would find
interesting?


Well, speakers generally are nonlinear, so what you are seeing here is
intermod. Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-liearity - that is caused by the same
cone reproducing two frequencies simultaneously. The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by the
Doppler effect. Of course, if you do the maths of superposition, this
doesn't happen - the tones coexist perfectly without any doppler.

So this is simple, stright-forward intermodulation between the two
tones.

d

Pearce Consulting
http://www.pearce.uk.com

"Don Pearce" wrote in message


Well, speakers generally are nonlinear, so what you are seeing here is
intermod.

Really?

Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-linearity - that is caused by the same
cone reproducing two frequencies simultaneously.

Agreed.

The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by the
Doppler effect. Of course, if you do the maths of superposition, this
doesn't happen - the tones coexist perfectly without any doppler.

Tell that to the AES! ;-)

So this is simple, straight-forward intermodulation between the two
tones.

Two reasons I think this really is predominantly FM:

(1) The sideband structure looks a lot more like FM than AM, per the
simulations I added to http://www.pcavtech.com/techtalk/doppler/ .

(2) I redid the experiment using high frequency tones at 1 KHz and 4 KHz.

All other things being equal, AM is frequency-independent. FM is
frequency-dependent. Since the stimulus for the IM is the 50 Hz tone, the
stimulus for 50 Hz sidebands for both the 1 KHz tone and the 4 KHz tone is
the same.

I did a simulation in Audition of pure FM, and the sidebands on the 1 KHz
tone were about 12 dB lower than the ones on the 4 KHz tone, which exactly
follows this theory.

However, speakers don't have just one kind of distortion.

I have added the results of triple tone test results to
http://www.pcavtech.com/techtalk/doppler/ .

Comparing the amplitudes of the first two sidebands around 1 KHz and 4 KHz,
I find that there is an approximate difference of 6 dB. The sidebands around
the 4 KHz average about 6 dB higher than those around the 1 KHz tone. If
this was pure FM distortion, I would expect a 12 dB difference. I conclude
that there is a mixture of AM and FM.

On Fri, 6 Aug 2004 07:30:49 -0400, "Arny Krueger"
wrote:

"Don Pearce" wrote in message


Well, speakers generally are nonlinear, so what you are seeing here is
intermod.

Really?

Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-linearity - that is caused by the same
cone reproducing two frequencies simultaneously.

Agreed.

The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by the
Doppler effect. Of course, if you do the maths of superposition, this
doesn't happen - the tones coexist perfectly without any doppler.

Tell that to the AES! ;-)

A great deal of BS has emanated from that organ!

So this is simple, straight-forward intermodulation between the two
tones.

Two reasons I think this really is predominantly FM:

(1) The sideband structure looks a lot more like FM than AM, per the
simulations I added to http://www.pcavtech.com/techtalk/doppler/ .

(2) I redid the experiment using high frequency tones at 1 KHz and 4 KHz.

All other things being equal, AM is frequency-independent. FM is
frequency-dependent. Since the stimulus for the IM is the 50 Hz tone, the
stimulus for 50 Hz sidebands for both the 1 KHz tone and the 4 KHz tone is
the same.

I did a simulation in Audition of pure FM, and the sidebands on the 1 KHz
tone were about 12 dB lower than the ones on the 4 KHz tone, which exactly
follows this theory.

However, speakers don't have just one kind of distortion.

I have added the results of triple tone test results to
http://www.pcavtech.com/techtalk/doppler/ .

Comparing the amplitudes of the first two sidebands around 1 KHz and 4 KHz,
I find that there is an approximate difference of 6 dB. The sidebands around
the 4 KHz average about 6 dB higher than those around the 1 KHz tone. If
this was pure FM distortion, I would expect a 12 dB difference. I conclude
that there is a mixture of AM and FM.




The only way to verify this is to look at the phase as well as the
amplitude of the sidebands.

d

Pearce Consulting
http://www.pearce.uk.com

"Don Pearce" wrote in message

On Fri, 6 Aug 2004 07:30:49 -0400, "Arny Krueger"
wrote:

"Don Pearce" wrote in message


Well, speakers generally are nonlinear, so what you are seeing here
is intermod.

Really?

Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-linearity - that is caused by the
same cone reproducing two frequencies simultaneously.

Agreed.

The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by
the Doppler effect. Of course, if you do the maths of
superposition, this doesn't happen - the tones coexist perfectly
without any doppler.

Tell that to the AES! ;-)

A great deal of BS has emanated from that organ!

So this is simple, straight-forward intermodulation between the two
tones.

Two reasons I think this really is predominantly FM:

(1) The sideband structure looks a lot more like FM than AM, per the
simulations I added to http://www.pcavtech.com/techtalk/doppler/ .

(2) I redid the experiment using high frequency tones at 1 KHz and 4
KHz.

All other things being equal, AM is frequency-independent. FM is
frequency-dependent. Since the stimulus for the IM is the 50 Hz
tone, the stimulus for 50 Hz sidebands for both the 1 KHz tone and
the 4 KHz tone is the same.

I did a simulation in Audition of pure FM, and the sidebands on the
1 KHz tone were about 12 dB lower than the ones on the 4 KHz tone,
which exactly follows this theory.

However, speakers don't have just one kind of distortion.

I have added the results of triple tone test results to
http://www.pcavtech.com/techtalk/doppler/ .

Comparing the amplitudes of the first two sidebands around 1 KHz and
4 KHz, I find that there is an approximate difference of 6 dB. The
sidebands around the 4 KHz average about 6 dB higher than those
around the 1 KHz tone. If this was pure FM distortion, I would
expect a 12 dB difference. I conclude that there is a mixture of AM
and FM.

The only way to verify this is to look at the phase as well as the
amplitude of the sidebands.

That's one way, but it's a very hard row for me to hoe.

So, you decline to believe that the relative amplitudes of the sidebands are
different and relevant, as the frequency has increased?

"Arny Krueger" wrote in message


The only way to verify this is to look at the phase as well as the
amplitude of the sidebands.

That's one way, but it's a very hard row for me to hoe.

So, you decline to believe that the relative amplitudes of the
sidebands are different and relevant, as the frequency has increased?

BTW, I added some simulations of the triple tone test, showing the differing
results for AM and FM distortion.

The simulations have a darker blue-green border around them, while the lab
measurements have a lighter blue border.

http://www.pcavtech.com/techtalk/doppler/

Between the differences in the sideband structure and the amplitudes of the
first two sidebands, it seems like this triple-tone test might have some
general application. I'm thinking about jitter testing...

On Fri, 6 Aug 2004 07:47:24 -0400, "Arny Krueger"
wrote:

The only way to verify this is to look at the phase as well as the
amplitude of the sidebands.

That's one way, but it's a very hard row for me to hoe.

So, you decline to believe that the relative amplitudes of the sidebands are
different and relevant, as the frequency has increased?


No, not at all. But I am not convinced that with the complex
interactions of a speaker you can reach your conclusion as simply as
you have. Non-linearities of various orders can cause a multiplication
function which results in phase modulation. But to put this down to
Doppler effect is a leap too far for me.

d

Pearce Consulting
http://www.pearce.uk.com

"Arny Krueger" wrote in message


Correction:

Comparing the amplitudes of the first two sidebands around 1 KHz and
4 KHz, I find that there is an approximate difference of 2 dB in levels
relative to the carriers. The
sidebands around the 4 KHz average about 2 dB higher than those
around the 1 KHz tone. If this was pure FM distortion, I would expect
a 12 dB difference. I conclude that there is a mixture of AM and FM,
predominantly AM.

On Fri, 06 Aug 2004 06:49:53 +0100, Don Pearce
wrote:

On Thu, 5 Aug 2004 22:19:23 -0400, "Arny Krueger"
wrote:

Here's the results of some speaker measurements that I made tonight, based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is an
ECM8000 that is a few inches from the woofer cone.

http://www.pcavtech.com/techtalk/doppler/

The first graph shows the broadband response. The large spikes at 50 Hz and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher than
the spike for 50 Hz because the woofer is simply that much more efficient at
4 KHz.

The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair of
large spikes are about 50 Hz on either side of 4 KHz, the second are about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as the
test is contrived to focus on FM.

While I've got this set up, any other data that anyone would find
interesting?


Well, speakers generally are nonlinear, so what you are seeing here is
intermod. Doppler distortion in speakers is supposedly a "built-in"
effect - nothing to do with non-liearity - that is caused by the same
cone reproducing two frequencies simultaneously. The argument goes
that if a speaker is reproducing a 1kHz tone, but is simultaneously
moving back and forth at 50Hz, the 1kHz tone must be modulated by the
Doppler effect. Of course, if you do the maths of superposition, this
doesn't happen - the tones coexist perfectly without any doppler.


I don't think anyone intended that "superposition" be used
willie-nilly. How about an explanation of why a moving "tweeter"
does not produce doppler.


So this is simple, stright-forward intermodulation between the two
tones.

d

Pearce Consulting
http://www.pearce.uk.com

On Thu, 5 Aug 2004 22:19:23 -0400, "Arny Krueger"
wrote:

Here's the results of some speaker measurements that I made tonight, based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is an
ECM8000 that is a few inches from the woofer cone.

http://www.pcavtech.com/techtalk/doppler/

The first graph shows the broadband response. The large spikes at 50 Hz and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher than
the spike for 50 Hz because the woofer is simply that much more efficient at
4 KHz.

The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair of
large spikes are about 50 Hz on either side of 4 KHz, the second are about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as the
test is contrived to focus on FM.

While I've got this set up, any other data that anyone would find
interesting?

Knowing that the amplitude of the sidebands should be proportional
(or at least some type of direct relation) to the amplitude of the 50
Hz signal. lower it by 10 or 20dB, and let's see how the sidebands
drop, hoping they don't fall into the noise. Regardless, you already
have me convinced you're measuring doppler distortion.
-----
http://mindspring.com/~benbradley

"Ben Bradley" wrote in message


Knowing that the amplitude of the sidebands should be proportional
(or at least some type of direct relation) to the amplitude of the 50
Hz signal. lower it by 10 or 20dB, and let's see how the sidebands
drop, hoping they don't fall into the noise.

OK, the data from 10 dB lower input is the second set of triple-tone
experimental data (light yellow background) at
http://www.pcavtech.com/techtalk/doppler/

Regardless, you already
have me convinced you're measuring Doppler distortion.

Well, a mixture. I'm convinced that AM distortion usually dominates, but
that Doppler is also always there, if its large enough to find.

Arny Krueger wrote:

Well, a mixture. I'm convinced that AM distortion usually dominates, but
that Doppler is also always there, if its large enough to find.

Arny, are you aware of any mathematical model of the typical
loudspeaker non-linearity? Just the transducer part, not
Doppler.


Bob
--

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

A. Einstein

"Bob Cain" wrote in message

Arny Krueger wrote:

Well, a mixture. I'm convinced that AM distortion usually dominates,
but that Doppler is also always there, if its large enough to find.

Arny, are you aware of any mathematical model of the typical
loudspeaker non-linearity? Just the transducer part, not
Doppler.

http://www.gedlee.com/Audio_trans.htm

Arny Krueger wrote:


Arny, are you aware of any mathematical model of the typical
loudspeaker non-linearity? Just the transducer part, not
Doppler.


http://www.gedlee.com/Audio_trans.htm

Thanks, Arny. Looks like a pretty comprehensive book but
outside my immediate means. I did note that in the chapter
on distortion there was nothing in the contents that
indicated a treatment of Doppler. If you have it, is that true?


Bob
--

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

A. Einstein

In article ,
"Arny Krueger" wrote:

Here's the results of some speaker measurements that I made tonight, based
on passing 50 Hz & 4 KHz mixed 1:1 at about 1.2 volts rms, through a
Peerless 6.5 inch woofer with about 6 mm Xmax (relatively large for a woofer
its size). The speaker is mounted in a roughly 0.4 cubic foot box with no
vent. The power amp is a QSC USA 850. This is not very loud. The mic is an
ECM8000 that is a few inches from the woofer cone.

http://www.pcavtech.com/techtalk/doppler/

The first graph shows the broadband response. The large spikes at 50 Hz and
4 KHz are clearly visible. The second and third harmonics of the 50 Hz tone
are about 30 dB down. The spike for the 4 KHz tone is about 5 dB higher than
the spike for 50 Hz because the woofer is simply that much more efficient at
4 KHz.

The second graph is taken from the same test, with the frequency scale
enlarged to show about 400 Hz on either side of 4 KHz. The first pair of
large spikes are about 50 Hz on either side of 4 KHz, the second are about
100 Hz on either side of 4 KHz, and so on. The distortion products are
probably a mixture of AM and FM distortion, with FM predominating, as the
test is contrived to focus on FM.

While I've got this set up, any other data that anyone would find
interesting?

Paul Klipsch used to do a doppler distortion comparison between some
arbitrary 12" direct radiator and one of his big horns. Even when the
difference in amplitudes was 10dB (the K-Horn being louder), the
difference in sideband amplitude was significant (the horn being a much
lower percentage). He was careful to keep the higher tone low enough in
frequency so that both tones were emitted by the woofer.

There was an obvious audible difference between the two, with the direct
radiator sounding "rougher", even when 10dB lower in amplitude.

As I remember, he wanted to find some way to determine the relative AM
to FM contributions, but couldn't figure out how to do it with the
technology of the times (late '60s to early '70's, AFAIR).

I think he published at least one paper on it.

Isaac

"Isaac Wingfield" wrote in message



Paul Klipsch used to do a doppler distortion comparison between some
arbitrary 12" direct radiator and one of his big horns.

Modulation Distortion in Loudspeakers
Author(s): Klipsch, Paul W.
Publication: Preprint 562; Convention 34; April 1968

Abstract: When comparing 2 loudspeakers, one with direct radiator bass
system and the other with horn loaded bass, a subjective judgment was that
the one with the horn loaded bass is ·cleaner.· Both speakers were by the
same manufacturer. Various tests were applied and by process of elimination
it appears the difference in listening quality is due to frequency
modulation distortion. Beers and Belar analyzed this form of distortion in
1943, but since that time the effect has been almost ignored. Now, with
amplifiers and source material reaching new lows in distortion, differences
between good loudspeakers begin to appear significant. The mathematical
analysis has been reviewed, and measurements have been made using a spectrum
analyzer. These have been correlated with listening tests by preparing tapes
of oscillator tones and music with and without a low frequency source to
produce frequency modulation distortion. The spectrum analyses corroborate
the mathematical analysis and the listening tests offer a subjective
evaluation. The conclusion is that frequency modulation in loudspeakers
accounts in large measure for the masking of ·inner voices.· As Beers and
Belar put it, ·The sound is just not clean.· Reduction of diaphragm
excursions at lower frequencies reduces FM distortion. Horn loading,
properly applied, offers the greatest reduction, while simultaneously
improving bass power output capability. Tentatively it is wondered if FM
distortion in loudspeakers may be the last frontier in loudspeaker
improvement.


Even when the
difference in amplitudes was 10dB (the K-Horn being louder), the
difference in sideband amplitude was significant (the horn being a
much lower percentage). He was careful to keep the higher tone low
enough in frequency so that both tones were emitted by the woofer.

As things evolve, this makes it harder to prove that the modulation
distortion at hand is FM, mot AM

There was an obvious audible difference between the two, with the
direct radiator sounding "rougher", even when 10dB lower in amplitude.

Direct radiator drivers have improved considerably since then. For example,
the spec Xmax was introduced some decades later.

As I remember, he wanted to find some way to determine the relative AM
to FM contributions, but couldn't figure out how to do it with the
technology of the times (late '60s to early '70's, AFAIR).

The paper I cited was published in 1968. Ironically, the FFT-based
measurement technology we enjoy today was just becoming well-known at that
time.

I think that the triple tone test and modern spectrum analyzer technology
provides valuable insights into this area. I think that I've established
that when there are two upper-frequency probe tones, FM distortion will
produce sidebands with a higher amplitude with the highest frequency tone,
all other things being equal. This finding can be, and probably should be
applied to investigations relating to both Doppler distortion and jitter.

Arny Krueger wrote:


As things evolve, this makes it harder to prove that the modulation
distortion at hand is FM, mot AM

Right. The horn loaded system has a smaller excursion so
that AM would be reduced to a similar, and perhaps greater
degree.



Bob
--

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

A. Einstein

Bob Cain writes:

Right. The horn loaded system has a smaller excursion so that AM
would be reduced to a similar, and perhaps greater degree.

Agreed - the Klipschorn will perform better either way.

--A Klipschorn pair owner

--
% Randy Yates % "Remember the good old 1980's, when
%% Fuquay-Varina, NC % things were so uncomplicated?"
%%% 919-577-9882 % 'Ticket To The Moon'
%%%% % *Time*, Electric Light Orchestra
http://home.earthlink.net/~yatescr

On Sat, 7 Aug 2004 07:02:36 -0400, "Arny Krueger"
wrote:

.....stuff deleted........

I think that the triple tone test and modern spectrum analyzer technology
provides valuable insights into this area. I think that I've established
that when there are two upper-frequency probe tones, FM distortion will
produce sidebands with a higher amplitude with the highest frequency tone,
all other things being equal. This finding can be, and probably should be
applied to investigations relating to both Doppler distortion and jitter.


To get an idea of the magnitude of any Doppler (FM) artifacts, you
need to know the cone velocity. It is my understanding, that in the
area where a speaker has a flat response, the velocities are fairly
consistent as frequency changes. So within this area, you should be
able to analyze and predict the Doppler effects.
I don't have much data that represents typical cone velocities at
different power levels (or SPL level, at say, 1 meter). From some of
the data shown on the Linkwitz site, he has a woofer with about 1.5
Meters/sec at 86db @1meter (that's reasonably loud). Does anyone have
typical data for other loudspeakers, especially at higher frequencies
(tweeters, midrange)?

Using 1.5 M/s peak cone velocity, the speed of sound is about 340
M/sec, that should vary all the frequencies whose velocities were
supposed to be something else. Usually for the purpose of analysis, we
assume that all the other ones are pretty small. Anyhow, with those
numbers, you get about 0.44% change in frequency, higher or lower
depending which way the cone is moving. If the signal causing the 1.5
meter/sec was 50 Hz , and you had another signal of 4 KHz, then your
4khz note appears to be changing from 4khz to 4017 khz, then back then
to a low of 3983 khz, 50 times a second. In the frequency domain (your
ears, spectrum analyzer) things get weird. The result frequencies
(there are more than what you put in) depend on the ratio of the
change in frequency divided by the modulating frequency - this is the
modulation index - M. The total energy is unchanged, so that the
addition of extra stuff comes at the expense the main peak (unlike IM
distortion, where the modulating frequency has to add energy). If the
modulation index is less than 0.3, then there are 2 extra frequencies
(distortion), each one has an amplitude of 1/2 times M (modulation
index), or the total grunge is M . For low values of M, you get 2
extra freq., the sum and difference (just like IM distortion, but out
of phase with each other, and may sound QUITE different) . At higher M
the calculation is very complex, you can have almost all distortion
with almost no fundamental.
Using the above numbers, change in frequency is about 17 Hz,
modulation freq. is 50 Hz, so M=0.34 , or about 17% for each extra
frequency. These will be at 4050 and 3950. This is NOT IM distortion.
The thing to note is that theamount of distortion changes with
modulating frequency! At 10Hz modulating freq,. M is about 1.7 - that
will mess up the waveform badly. The worst case is when the
frequencies are very different. With high values of M, the note
spreads out in frequency - instead of a fundamental and two satellite
tones, there is an almost contiuous block of frequencies. With a 5 or
10 Hz modulation, instead of 4 KHz and 2 extra peaks, you get an
almost continuous band of frequencies around 4 KHz.
The sound? High M values are VERY noticeable, usually a warbling
sound, or noticeable extra frequencies. As M decreases to about 0.3,
the original pure tone sounds indistinct in pitch, or you might just
notice extra "stuff", and as M decreases to less than 0.1, it's very
hard to tell (for me). These were done at 4 KHz, with varying
amplitudes and frequency of the modulation frequency. This was not a
really good listening test, the real Golden Ears might be better at
finding the threshold. I used 2 signal generators, one modulating the
others frequency. I used a spectrum analyzer to determine M, and
adjusted the signal generators to vary M as I listened to the "tones".
My good signal generators are at work, so if you're interested, I can
compare IM and FM (Doppler) distortion with the same frequencies. I'm
sure Arny has the equipment more readily available - and may even have
..wav files for your listening pleasure, so you can hear for yourself
what the effects are. What would be really nice, is to frequency shift
a chunk of music with different delta-freq, and different modulation
frequencies, i.e., varying M with different conditions. Multi-tone and
real music should the preferred way to check this out.
The cure? Keep wide ranges of frequencies OUT of a loudspeaker,
i.e., use 2 or 3 way systems. Because the modulation index (M) is
calculated with the modulating frequency as DENOMINATOR, avoiding low
modulating frequencies reduces the distortion. That bears out in my
listening tests. As the modulating frequency increases, the less
noticeable things are. A 3 way system can have a 10 to 1 range of
frequencies for each driver, compared to almost a 1000 to 1 range for
a singe wide range speaker. That will make a big difference when you
calculate M, the modulation index.

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

"Paul Guy" wrote in message

On Sat, 7 Aug 2004 07:02:36 -0400, "Arny Krueger"
wrote:

....stuff deleted........

I think that the triple tone test and modern spectrum analyzer
technology provides valuable insights into this area. I think that
I've established that when there are two upper-frequency probe
tones, FM distortion will produce sidebands with a higher amplitude
with the highest frequency tone, all other things being equal. This
finding can be, and probably should be applied to investigations
relating to both Doppler distortion and jitter.

To get an idea of the magnitude of any Doppler (FM) artifacts, you
need to know the cone velocity. It is my understanding, that in the
area where a speaker has a flat response, the velocities are fairly
consistent as frequency changes. So within this area, you should be
able to analyze and predict the Doppler effects.

I don't have much data that represents typical cone velocities at
different power levels (or SPL level, at say, 1 meter). From some of
the data shown on the Linkwitz site, he has a woofer with about 1.5
Meters/sec at 86db @1meter (that's reasonably loud). Does anyone have
typical data for other loudspeakers, especially at higher frequencies
(tweeters, midrange)?

If you can't see the motion, it must be 1/16 or less. Multiply the maximum
motion by 2 pi F to get peak velocity. Remember that peak possible cone
motion happens just below system resonance, and is less at higher
frequencies.

Using 1.5 M/s peak cone velocity, the speed of sound is about 340
M/sec, that should vary all the frequencies whose velocities were
supposed to be something else. Usually for the purpose of analysis, we
assume that all the other ones are pretty small. Anyhow, with those
numbers, you get about 0.44% change in frequency, higher or lower
depending which way the cone is moving.

Seems about right.

If the signal causing the 1.5
meter/sec was 50 Hz , and you had another signal of 4 KHz, then your
4khz note appears to be changing from 4khz to 4017 khz, then back then
to a low of 3983 khz, 50 times a second. In the frequency domain (your
ears, spectrum analyzer) things get weird.

Well, they get Besselized. ;-)

The result frequencies
(there are more than what you put in) depend on the ratio of the
change in frequency divided by the modulating frequency - this is the
modulation index - M. The total energy is unchanged, so that the
addition of extra stuff comes at the expense the main peak (unlike IM
distortion, where the modulating frequency has to add energy). If the
modulation index is less than 0.3, then there are 2 extra frequencies
(distortion), each one has an amplitude of 1/2 times M (modulation
index), or the total grunge is M . For low values of M, you get 2
extra freq., the sum and difference (just like IM distortion, but out
of phase with each other, and may sound QUITE different) . At higher M
the calculation is very complex, you can have almost all distortion
with almost no fundamental.

Agreed.

Using the above numbers, change in frequency is about 17 Hz,
modulation freq. is 50 Hz, so M=0.34 , or about 17% for each extra
frequency. These will be at 4050 and 3950. This is NOT IM distortion.

Well, its not AM distortion. Whether FM distortion is IM is controversial. I
think that FM is IM because that's what the words seem to mean to me.

The thing to note is that theamount of distortion changes with
modulating frequency! At 10Hz modulating freq,. M is about 1.7 - that
will mess up the waveform badly. The worst case is when the
frequencies are very different. With high values of M, the note
spreads out in frequency - instead of a fundamental and two satellite
tones, there is an almost contiuous block of frequencies. With a 5 or
10 Hz modulation, instead of 4 KHz and 2 extra peaks, you get an
almost continuous band of frequencies around 4 KHz.

That agrees with experimental results. However, you can get a similar family
of tones if your modulating signal is not a pure sine wave.

The sound? High M values are VERY noticeable, usually a warbling
sound, or noticeable extra frequencies. As M decreases to about 0.3,
the original pure tone sounds indistinct in pitch, or you might just
notice extra "stuff", and as M decreases to less than 0.1, it's very
hard to tell (for me). These were done at 4 KHz, with varying
amplitudes and frequency of the modulation frequency. This was not a
really good listening test, the real Golden Ears might be better at
finding the threshold. I used 2 signal generators, one modulating the
others frequency.

One can also use the tone generator in Audition/CE or a bunch of other
software. Then, everything is rigidly phase locked.

I used a spectrum analyzer to determine M, and
adjusted the signal generators to vary M as I listened to the "tones".
My good signal generators are at work, so if you're interested, I can
compare IM and FM (Doppler) distortion with the same frequencies.


I'm
sure Arny has the equipment more readily available - and may even have
.wav files for your listening pleasure, so you can hear for yourself
what the effects are.

Slightly different context, but its all FM:

http://www.pcabx.com/technical/jitter_power/index.htm

What would be really nice, is to frequency shift
a chunk of music with different delta-freq, and different modulation
frequencies, i.e., varying M with different conditions. Multi-tone and
real music should the preferred way to check this out.

It's just a matte of twidding in the parameters with software like
Audition/CE.

The cure? Keep wide ranges of frequencies OUT of a loudspeaker,
i.e., use 2 or 3 way systems. Because the modulation index (M) is
calculated with the modulating frequency as DENOMINATOR, avoiding low
modulating frequencies reduces the distortion. That bears out in my
listening tests. As the modulating frequency increases, the less
noticeable things are. A 3 way system can have a 10 to 1 range of
frequencies for each driver, compared to almost a 1000 to 1 range for
a singe wide range speaker. That will make a big difference when you
calculate M, the modulation index.

Agreed, and since 2-way speakers are almost endemic.., and get to be 3-way
when subwoofers are added...

On Thu, 19 Aug 2004 11:03:32 -0400, "Arny Krueger"
wrote:

......some stuff deleted.....

I'm
sure Arny has the equipment more readily available - and may even have
.wav files for your listening pleasure, so you can hear for yourself
what the effects are.

Slightly different context, but its all FM:

http://www.pcabx.com/technical/jitter_power/index.htm

What would be really nice, is to frequency shift
a chunk of music with different delta-freq, and different modulation
frequencies, i.e., varying M with different conditions. Multi-tone and
real music should the preferred way to check this out.


I tried listening to your jitter samples in a less than optimum
environment. You have some castanet samples castanets-060.wav
(unjittered) and castanets_060_jit-20FF2.wav (-20 db 60 Hz jitter). I
can barely tell them apart. To my ears, the jitter version is slightly
duller, but the difference is so tiny, I could easily be fooled. All
the other samples are far too similiar to the reference.
Your piano selections (piano1_1644.wav [unjittered] and
piano1_1644_-20FF2.wav [-20db 60 Hz jitter])are indistinguishable to
me. I noticed that they are both distorted somewhat, nowhere as nice
as your reference piano_nlref.wav file.
Either my ears are totally wrecked (not likely), but the jitter
(FM) page you have really makes the case that it is not a very big
deal. From your spectral analysis, most of the crud is very close to
the fundamentals, and as such will be largely masked. Have you
synthesized higher or lower frequency jitter components to see their
audibility?
What is the prevaling opinion about the jitter (or FM "distortion")
samples you put on your site?
From my own testing, the sidebands need to be more like -10db (or
-10 db jitter as you specify it) before they begin to be audible.
That's pretty disgusting! 30% crud! Masking theory does confirm what
my ears tell me, namely that junk very close to the fundamental is
very well masked i.e., inaudible. It interesting that conventional
spectrum analyzers have the same difficulty. The ear does have much of
the behaviour of a poor dynamic range (30db) spectrum analyzer, with
strange post processing and AGC.
Readers of this newsgroup would be well advised to read up about the
ear (especially the cochlea) to understand masking and other
mechanisms the ears uses as "garbage cleanup".

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

Well, I've asked for help on the general equation for pressure at
a point removed from an ideal piston in an infinite tube as a
function of the force applied to the piston that includes the
effects of Doppler distortion in alt.sci.physicw and on the
moderated group sci.physics.research where the real guns hang
out and there has been no answer.

What I've found is that any attempt to write the expression
from conditions at the interface results in a recursion or
infinite regress unless the term included to account for
the motion of the piston is set to zero. It's really tricky.

So let's look at an argument by reciprocity. Assume an
acoustic pulse of any arbitrary shape running down the tube
with an ideal pistion (no mass, stiff, infinite compliance)
in place.

1. The piston will move exactly in step with the motion of
the air molecules as the pulse passes by it.

Now let's measure and record the velocity of that piston as
the pulse passes by. Next let's mount a voltage to velocity
transducer, again ideal with a zero mechanical impedence, on
the side of the piston from which the pulse came when we
measured it.

2. When we drive that piston so as to reproduce the velocity
that was recorded we will get the identical pulse propegating
off of it as originally measured.

3. Because air is air, the resulting pressure pulse will be
in phase with that velocity and given by p(t) = v(t) * Ra,
where Ra is the characteristic impedence or air, and that
pressure pulse will be identical to the one that the
measured pulse had.

Because this should be true with a pulse of any shape it will
be true of a supposition of any such pulses which implies that
it is true of any signal and is thus a linear transducer with
no distortion of any kind.


Bob
--

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

A. Einstein

"Bob Cain" wrote in message
...

1. The piston will move exactly in step with the motion of
the air molecules as the pulse passes by it.

Disclaimer: I am *not* stating anything here as an expert in this field.
Other than being a musician and doing some recording at home, my only other
"experience" in mathematical acoustics was building my own bass cabinet
years ago. I used some formulas from a book to cut in the proper port for
this particular woofer and cabinet volume. I'm just trying to use logic and
imagination.

With that said, I respectfully disagree with #1. :-)

First, the piston will stop moving at some point and return to its starting
position. The air molecules will keep moving until they run out of energy.

Second, think about there being two pulses. If the second pulse arrives
after the piston returns to its starting position, then the duration between
the pulses will be exactly known. Therefore, the frequency of the pulses is
exactly known. If the second pulse arrives while the piston is still moving
forward with the first pulse, then the second pulse strikes the piston while
it's in a different position than when the first pulse struck it. That pulse
has traveled farther than in our first scenario. If you were to measure the
duration between the pulses in this scenario, it would be greater.
Therefore, a form of distortion is introduced.

Another way to imagine this is if the piston did *not* return to its
starting point. Assume at some known point in relation to the energy of the
wave that the wave can no longer push the piston. The piston then becomes
stationary at that new position. The next pulse that came along would strike
it at some distance X from where the first pulse struck it. This pulse in
turn would carry it some distance. Then the next pulse and so forth. No one
would argue that such a piston would accurately reflect the frequency of the
pulses. That would be Doppler in its truest form, right?

Let's resolve this premise before we move on.

Jim Carr wrote:


With that said, I respectfully disagree with #1. :-)

Respectfully accepted as such. :-)


First, the piston will stop moving at some point and return to its starting
position. The air molecules will keep moving until they run out of energy.

No, I specified that the piston have infinite compliance and
zero mass and I should have added, no friction. If that is
true, it will follow the motion of the air just because
there is no reason for it not to.

Piston motion is in response to the difference in pressure
on each side. Since mass, compliance and friction are not
restraining it, it moves so that the pressure differential
is always zero. To do that, it must move with the air
particles because not doing so is the only way to generate a
pressure differential. This is a key point.

This part is only gendanken to come up with a signal to be
reproduced. If the driven, reproducing piston contains
mass, non-zero compliance or friction, which are all linear,
then the driving signal can be pre-compensated by the
inverse of the resulting mechanical impedence so as to
eliminate their effects and result in the motion required by
the signal. These things are all logically between the
signal and the piston/air interface so have no effect on
what happens there in the sense of a distortion mechanism.


Second, think about there being two pulses. If the second pulse arrives
after the piston returns to its starting position, then the duration between
the pulses will be exactly known. Therefore, the frequency of the pulses is
exactly known. If the second pulse arrives while the piston is still moving
forward with the first pulse, then the second pulse strikes the piston while
it's in a different position than when the first pulse struck it. That pulse
has traveled farther than in our first scenario. If you were to measure the
duration between the pulses in this scenario, it would be greater.
Therefore, a form of distortion is introduced.

If the principle is true for any arbitrary pulse, and that
was a starting propositon, then it is true for the
superpostion of any number of pulses because any
superposition is just another arbitrary pulse.


Bob
--

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

A. Einstein

"Bob Cain" wrote in message
...
First, the piston will stop moving at some point and return to its
starting
position. The air molecules will keep moving until they run out of
energy.

No, I specified that the piston have infinite compliance and
zero mass and I should have added, no friction. If that is
true, it will follow the motion of the air just because
there is no reason for it not to.

Let's start here. Air is made up of a bunch of loosely packed molecules
constantly and randomly banging into one another. Am I correct?

If so, suppose I manage to start a single pulse by some method that is
hopefully immaterial. Air molecules start banging into each other in
essentially one direction. Now, I grant they spread out, but there is a
pattern when compared to the normal random collisions. Each collision uses
up some energy. Eventually there's not enough energy for any more
collisions. Would you agree or disagree that this happens?

If you agree, then we can say that a sound wave is not really a set of air
molecules going from point A to point B but rather *energy* traveling from
point A to point B through a series of air molecules colliding in an
identifiable pattern we call a wave. Can we agree on that? Again, I want to
repeat that I am simply building up a theory from a relatively small base of
knowledge and what I hope is some sound logic. If I sound condescending,
then I am doing so to myself, not you. I am trying to lay this out so *I*
understand what I'm talking about. :-)

So let's shove your piston in there. By definition the piston is not really
following the motion of the air because the air really isn't moving like a
breeze. It has to react to the energy hitting it just like the air molecules
do. Therefore, to say the piston "follows the motion of the air" is
imprecise.

What I think you are trying to say is that the piston is acted upon by the
energy of the sound wave in the *exact* same way as the air molecules. So,
how far does it move? The exact same distance as one molecule of air moves?
If so, I doubt we could induce a voltage in a coil.

Since we are in fact talking about inducing voltage in a coil and and in the
case of a speaker the subsequent movement of a piston in reaction to that
voltage, we have to include that parameter as part of the discussion.
Doppler distortion wouldn't exist if the piston *only* moved like a single
molecule.

The piston must move the coil to induce a voltage. It has to move a finite
and extremely limited distance compared to distance the energy from a sound
wave travels. The piston also must move backwards at some point otherwise it
would only react to the first pulse.

In my opinion there is no possible way to find a formula to describe Doppler
Distortion without these limiting factors of the piston. Without using any
formula I would say that Doppler Distortion comes about *because* the piston
moves a greater distance and at a slower speed than energy through the air
and because the piston also has a device which pulls it back to center
whereas the air molecules do not.

It sounds like you're trying to say that your imaginary piston (which can
never exist, BTW) would behave exactly as the air molecules do, therefore,
there is no distortion. Of course not. Your constraints on the piston
essentially describe a single molecule of air. There's no way to pick a
molecule of air and say that's distortion. The movement of the molecule as
the energy passes through it is what we're trying to measure in the first
place.

The reality is that the piston does *not* act like an air molecule, so you
need to look for a way to explain the vibration of the piston and contrast
that against the vibration of air molecules. It's that difference that
causes Doppler Distortion as I understand it.

Jim Carr wrote:

No, I specified that the piston have infinite compliance and
zero mass and I should have added, no friction. If that is
true, it will follow the motion of the air just because
there is no reason for it not to.


Let's start here. Air is made up of a bunch of loosely packed molecules
constantly and randomly banging into one another. Am I correct?

At the lowest level, but for the purposes of acoustics, and
other than in consideration of noise, they can be
statistically treated as a continuous compressible gas from
which the acoustic laws are derived. In brief you need not
consider the molecular compostion in working with its dynamics.

If you agree, then we can say that a sound wave is not really a set of air
molecules going from point A to point B but rather *energy* traveling from
point A to point B through a series of air molecules colliding in an
identifiable pattern we call a wave. Can we agree on that? Again, I want to
repeat that I am simply building up a theory from a relatively small base of
knowledge and what I hope is some sound logic. If I sound condescending,
then I am doing so to myself, not you. I am trying to lay this out so *I*
understand what I'm talking about. :-)

With that, I think you stated what I did above in a
different way. Yes I agree.


So let's shove your piston in there. By definition the piston is not really
following the motion of the air because the air really isn't moving like a
breeze. It has to react to the energy hitting it just like the air molecules
do. Therefore, to say the piston "follows the motion of the air" is
imprecise.

Not so. It is constrained by the condition that no pressure
differential, dP, is allowed across it because of its ideal
definition. If it did, it would accelerate at infinite
rate. A=dP*D/M. A is infinite because M is zero. D is the
diameter. The only way it can maintain that is to move with
the bulk velocity of the air so as to keep dP equal to zero.
Think of it as a compressible fluid. If you think of an
infinitessimal volume of that fluid, the piston will move in
concert with those volumes that are in contact with it. To
do otherwise would create a pressure difference from one
side to the other and it would move to zero it without
delay. That's what it is doing, moving without delay to
keep the pressure differential at zero. Since it is never
at any other value than zero, it is moving precisely with
the bulk velocity of the air.

Since we are in fact talking about inducing voltage in a coil and and in the
case of a speaker the subsequent movement of a piston in reaction to that
voltage, we have to include that parameter as part of the discussion.

What parameter is that?


The piston must move the coil to induce a voltage. It has to move a finite
and extremely limited distance compared to distance the energy from a sound
wave travels. The piston also must move backwards at some point otherwise it
would only react to the first pulse.

We need not consider coils or voltages at the point of
determining the velocity of that ideal piston.


In my opinion there is no possible way to find a formula to describe Doppler
Distortion without these limiting factors of the piston. Without using any
formula I would say that Doppler Distortion comes about *because* the piston
moves a greater distance and at a slower speed than energy through the air
and because the piston also has a device which pulls it back to center
whereas the air molecules do not.

But you can't say that without writing some formula. I say
it can't be written because it would violate the conditions
I described which are due to physical laws.


It sounds like you're trying to say that your imaginary piston (which can
never exist, BTW)

Doesn't matter because if the ideal case can't generate
Doppler distortion then nothing can that contains linear
components of friction, mass and compliance. I showed how
their effects could be eliminated in the reproducer in the
post you are responding to. The ideal measuring device just
tells you what the velocity is without disturbing the
acoustic field it measures.

would behave exactly as the air molecules do, therefore,
there is no distortion. Of course not. Your constraints on the piston
essentially describe a single molecule of air. There's no way to pick a
molecule of air and say that's distortion. The movement of the molecule as
the energy passes through it is what we're trying to measure in the first
place.

To refute my argument you have to show that an ideal passive
piston wouldn't track the bulk velocity of the medium.
You don't need to interact with it in a signifigant way to
measure it's velocity, you could use a laser interferometer,
for example (which has in fact been proposed for a
microphone sensor.) All I've really described is a large,
ideal microphone.


The reality is that the piston does *not* act like an air molecule, so you
need to look for a way to explain the vibration of the piston and contrast
that against the vibration of air molecules. It's that difference that
causes Doppler Distortion as I understand it.

If you followed it, you should be able to see by now why it
would. Remember, we are considering the net effect of a
whole lot of these molecules.

If you won't accept any of these arguments would you accept
that there is some way in principle to measure the bulk
velocity without distrubing what you are measuring, at least
for all practical purposes? How about tracking the motion
of a smoke particle?

If you can then we can move on to the reproduction half of
the problem. It wasn't really necessasary to employ the
piston for measurement but it illustrates the principle of
reciprocity of measurement and transduction which is well known.


Bob
--

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

A. Einstein

"Jim Carr" wrote in message news:JvERc.3628$yh.1495@fed1read05...
Let's start here. Air is made up of a bunch of loosely packed molecules
constantly and randomly banging into one another. Am I correct?

Yes, and, in fact, it can be considered NEARLY and ideal gas for
the purpose of most human-tolerable sound pressure levels, that is,
it can be considered a medium consisting of infinitesimally small
point objects engaged in (nearly) perfect elestic collisions,

If so, suppose I manage to start a single pulse by some method that is
hopefully immaterial. Air molecules start banging into each other in
essentially one direction. Now, I grant they spread out, but there is a
pattern when compared to the normal random collisions. Each collision uses
up some energy. Eventually there's not enough energy for any more
collisions. Would you agree or disagree that this happens?

Physics would disagree quite vehemently. The collisions themselves
are damned near perfectly lossless. Thus, the collisions themselves
dissipate essentially NO energy whatseoever.

Now, what DO you think happens to the energy?

If you agree, then we can say that a sound wave is not really a set of air
molecules going from point A to point B but rather *energy* traveling from
point A to point B through a series of air molecules colliding in an
identifiable pattern we call a wave.

WOW! What a neat f*cking idea! Analyzing sound based on the concepts
of the kinetic theory of gasses!

Keep going, gents, and you may well figure out why a substantial
portion of the sacrosanct "principles" of audio, notably a bunch
of religiously held believes by the high-end, is really a big
stinking crock of sh*t.

Okay, let's get back to it.

If you're assertion is that we're adding some energy to a group
of molecules, what do you think that means? What KIND of energy?
Well, according to you, these things are moving around and bumping
into each other. If you add energy to them by bumping into them,
what kind of energy are you adding to them. you have two choices:
kinietic or potential. (hint: it's kinetic because bumping into
makes them move a little faster).

Now, if you guessed "kinetic" then you're probably right. Now,
remeber back to your high-school physics class. By moving the piston
you've added some energy, and the average energy of our gas molecules
has gone up (we talk about the "average" because it makes no sense to
talk about one: one molecule does not propogate sound).

What's another name for the "average kinetic energy" of a gas?
(hint: it's spelled t-e-m-p-e-r-a-t-u-r-e).

So, if you now guessed temperature, you'd probably get a point for
that question. Fine, so pushing the piston in THAT direction raises the
temperature of the air, because it raises the temperature of the air,
because the two are saying EXACTLY the same thing. (and, if you wanted
to, you could say that it raises the average molecular velocity as
well, since, very simply, e = 1/2 mv^2. Given that each m is VERY
small, what do you think v is equal to at room temperature?)

Now, if I raise the temperture of a gas HERE, what do you think happens
to the gas THERE? (hint: think about how something wants to maintain
equilibrium with its surrounding). How do you think it will do this,
and how fast do you think it will do so?

So let's shove your piston in there. By definition the piston is not really
following the motion of the air because the air really isn't moving like a
breeze. It has to react to the energy hitting it just like the air molecules
do. Therefore, to say the piston "follows the motion of the air" is
imprecise.

The piston, if allowed to move, will do so ONLY if there is a net
force on it. Assume the gas currounding the piston is of uniform
composition and density, it can only do so if the average net force
of collisions on one side is gerater than that on the other, and,
given the assumptions of identical composition and density, can only
do so if the average collision velocity is different.

And since the everage kinetic energy of the gas geos as the square
of the average velocity, and since the temperature is a direct measure
of the avergae kinetic energy, guess what: a net force on the diaphragm
means a NET INSTANTANEOUS PRESSURE DIFFERENCE between the two sides.

What I think you are trying to say is that the piston is acted upon by the
energy of the sound wave in the *exact* same way as the air molecules. So,
how far does it move? The exact same distance as one molecule of air moves?

Depends upon how far the higher temperature side must move the diaphragm
such that it imparts enough energy on the other side such that it reaches
mechanical (and, indeed, euivalently) THERMAL equilibrium with it,

OR

it reaches mechanical equilibrium with whatever other force pooses its
motion.

The reality is that the piston does *not* act like an air molecule,

And, in a more precise fashion, there is no analysis of a single
molecule can lead to any clue about the propogation of sound.

need to look for a way to explain the vibration of the piston and contrast
that against the vibration of air molecules. It's that difference that
causes Doppler Distortion as I understand it.

Consider the following analytical tool: instead of a physical diaphragm,
look at the flow of energy past an arbitrary plane at right angles to
the flow of energy: can we consider the bulk proprties of the gas or
must we analyze each individual molecule as it interacts with this
plane? (hint, if you choose the latter, we'll all die before you
come back with an answer).

There's a LOT more lurking under here than you might imagine, but the
power of it is rather immense.

Jim Carr wrote:

Disclaimer: I am *not* stating anything here as an expert in this field.

You will be when I'm done with you. :-)


Bob
--

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

A. Einstein

"Bob Cain" wrote in message
...


Jim Carr wrote:

Disclaimer: I am *not* stating anything here as an expert in this field.

You will be when I'm done with you. :-)

LOL! You guys make me think, that's for sure. I contrast this against the
football newsgroup I'm in that spent the off-season arguing the question: If
you were filming Hillary Clinton swimming and you saw she was drowing, what
would you do?

Jim Carr wrote:

"Bob Cain" wrote in message
...


Jim Carr wrote:


Disclaimer: I am *not* stating anything here as an expert in this field.

You will be when I'm done with you. :-)


LOL! You guys make me think, that's for sure. I contrast this against the
football newsgroup I'm in that spent the off-season arguing the question: If
you were filming Hillary Clinton swimming and you saw she was drowing, what
would you do?

I give.


Bob
--

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

A. Einstein

Aargh! I sent that by accident. It is a work in progress and
The final conclusion remains to be written or justified. That
conclusion is, however, that a pressure signal, such as is
present in recordings, is just as linearly reproduced by a force
driven piston and that Doppler distortion doesn't exist.
I really love that hat.

In the mean time I'd appreciate it if any tech-heads
can find flaw so far. The three points on which the last
paragraph is based should be enough to support it and seem,
to me anyway, to be unassailable. Have at it.


Bob

Bob Cain wrote:


Well, I've asked for help on the general equation for pressure at
a point removed from an ideal piston in an infinite tube as a
function of the force applied to the piston that includes the
effects of Doppler distortion in alt.sci.physicw and on the
moderated group sci.physics.research where the real guns hang
out and there has been no answer.

What I've found is that any attempt to write the expression
from conditions at the interface results in a recursion or
infinite regress unless the term included to account for
the motion of the piston is set to zero. It's really tricky.

So let's look at an argument by reciprocity. Assume an
acoustic pulse of any arbitrary shape running down the tube
with an ideal pistion (no mass, stiff, infinite compliance)
in place.

1. The piston will move exactly in step with the motion of
the air molecules as the pulse passes by it.

Now let's measure and record the velocity of that piston as
the pulse passes by. Next let's mount a voltage to velocity
transducer, again ideal with a zero mechanical impedence, on
the side of the piston from which the pulse came when we
measured it.

2. When we drive that piston so as to reproduce the velocity
that was recorded we will get the identical pulse propegating
off of it as was originally measured.

3. Because air is air, the resulting pressure pulse will be
in phase with that velocity and given by p(t) = v(t) * Ra,
where Ra is the characteristic impedence or air, and that
pressure pulse will be identical to the one that the
measured pulse had.

Because this should be true with a pulse of any shape it will
be true of a supposition of any such pulses which implies that
it is true of any signal and is thus a linear transducer with
no distortion of any kind.


Bob

--

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

A. Einstein

On Sun, 08 Aug 2004 18:45:54 -0700, Bob Cain
wrote:


Well, I've asked for help on the general equation for pressure at
a point removed from an ideal piston in an infinite tube as a
function of the force applied to the piston that includes the
effects of Doppler distortion in alt.sci.physicw and on the
moderated group sci.physics.research where the real guns hang
out and there has been no answer.

What I've found is that any attempt to write the expression
from conditions at the interface results in a recursion or
infinite regress unless the term included to account for
the motion of the piston is set to zero. It's really tricky.

So let's look at an argument by reciprocity.

Ah, you are basing your argument on the system being linear with
reciprocity and superposition being applicable.

Assume an
acoustic pulse of any arbitrary shape running down the tube
with an ideal pistion (no mass, stiff, infinite compliance)
in place.

1. The piston will move exactly in step with the motion of
the air molecules as the pulse passes by it.

Now let's measure and record the velocity of that piston as
the pulse passes by. Next let's mount a voltage to velocity
transducer, again ideal with a zero mechanical impedence, on
the side of the piston from which the pulse came when we
measured it.

2. When we drive that piston so as to reproduce the velocity
that was recorded we will get the identical pulse propegating
off of it as originally measured.

3. Because air is air, the resulting pressure pulse will be
in phase with that velocity and given by p(t) = v(t) * Ra,
where Ra is the characteristic impedence or air, and that
pressure pulse will be identical to the one that the
measured pulse had.

Because this should be true with a pulse of any shape it will
be true of a supposition of any such pulses which implies that
it is true of any signal and is thus a linear transducer with
no distortion of any kind.



Circular. . .