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  #1   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

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?


  #2   Report Post  
Bob Cain
 
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Default Doppler Distoriton?



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
  #3   Report Post  
Don Pearce
 
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Default Doppler Distoriton?

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
  #4   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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


  #5   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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.






  #6   Report Post  
Don Pearce
 
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Default Doppler Distoriton?

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
  #7   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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.


  #8   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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?


  #9   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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...


  #10   Report Post  
Don Pearce
 
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Default Doppler Distoriton?

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


  #11   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"Don Pearce" wrote in message

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.


I agree that the actual acoustical measurements may or may not show a
Doppler effect. At best the Doppler distortion is relatively small in the
face of the massive AM effects.

If I turn the volume up, the AM effects seem to get stronger, both overall
and proportionately. And, this is a relatively linear driver being driven
over a wider frequency range than it would be used in a good design.

If I got anything worthwhile out of this, it is the concept of using 3 tones
to separate AM distortion from FM distortion. But you still need an
underlying clear instance of FM distortion to make it worth the trouble. I
suspect that a lot of the purported jitter measurements we've seen are
actually pretty suspect because the common measurements confuse AM and FM
distortion.


  #12   Report Post  
Don Pearce
 
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Default Doppler Distoriton?

On Fri, 6 Aug 2004 10:18:35 -0400, "Arny Krueger"
wrote:

"Don Pearce" wrote in message

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.


I agree that the actual acoustical measurements may or may not show a
Doppler effect. At best the Doppler distortion is relatively small in the
face of the massive AM effects.

If I turn the volume up, the AM effects seem to get stronger, both overall
and proportionately. And, this is a relatively linear driver being driven
over a wider frequency range than it would be used in a good design.

If I got anything worthwhile out of this, it is the concept of using 3 tones
to separate AM distortion from FM distortion. But you still need an
underlying clear instance of FM distortion to make it worth the trouble. I
suspect that a lot of the purported jitter measurements we've seen are
actually pretty suspect because the common measurements confuse AM and FM
distortion.


Certainly in terms of spectrum, narrowband FM is virtually
indistinguishable from AM unless you can get at the relative phase of
the sidebands.

But as for Doppler distortion. Do the sums, assuming a perfectly
linear driver (which should still show the phenomenon if it exists,
since it needs no non-linearity). You will find that the sum of the
tones exactly matches what the trajectory of the cone should be to
prevent such distortion.

d

Pearce Consulting
http://www.pearce.uk.com
  #13   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"Don Pearce" wrote in message

On Fri, 6 Aug 2004 10:18:35 -0400, "Arny Krueger"
wrote:

"Don Pearce" wrote in message

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.


I agree that the actual acoustical measurements may or may not show a
Doppler effect. At best the Doppler distortion is relatively small
in the face of the massive AM effects.

If I turn the volume up, the AM effects seem to get stronger, both
overall and proportionately. And, this is a relatively linear driver
being driven over a wider frequency range than it would be used in a
good design.

If I got anything worthwhile out of this, it is the concept of using
3 tones to separate AM distortion from FM distortion. But you still
need an underlying clear instance of FM distortion to make it worth
the trouble. I suspect that a lot of the purported jitter
measurements we've seen are actually pretty suspect because the
common measurements confuse AM and FM distortion.


Certainly in terms of spectrum, narrowband FM is virtually
indistinguishable from AM unless you can get at the relative phase of
the sidebands.


Measuring the phase of acoustical signals, and signals in general, can be a
vale of tears. I've played this game many times, and while I've had some
success, I feel like I earned it! ;-)

It appears that one can differentiate AM and FM based on the amplitudes of
the sidebands for carriers that have significantly different base
frequencies.

A given AM process will produce sidebands with the same amplitudes over a
wide variety of carrier frequencies. FM processes are very dependent on the
frequency of the carrier.

For a given rate of change in timing, the higher frequency carrier will show
a larger shift in frequency. This increases the Modulation Index, which is
the quotient of the maximum deviation/divided by the modulating frequency.
The higher modulation index increases the size and number of sidebands.
Therefore, higher frequency carriers will produce more sidebands and
sidebands that have a larger amplitude.

My Audition/CoolEdit simulations show this quite clearly.

But as for Doppler distortion. Do the sums, assuming a perfectly
linear driver (which should still show the phenomenon if it exists,
since it needs no non-linearity).


That would be a more complex theoretical exercise.

You will find that the sum of the
tones exactly matches what the trajectory of the cone should be to
prevent such distortion.


I don't see it. And as I've now pointed out several times, the JAES doesn't
seem to see it, either. IOW, there are a goodly number of refereed papers
that give abundant positive evidence that it does exist. I see that train
coming towards me, and I see that cone coming towards me!




  #14   Report Post  
Randy Yates
 
Posts: n/a
Default Doppler Distoriton?

"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
  #15   Report Post  
Jim Carr
 
Posts: n/a
Default Doppler Distoriton?

"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.




  #16   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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!


  #17   Report Post  
Ben Bradley
 
Posts: n/a
Default Doppler Distoriton?

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
  #18   Report Post  
Ben Bradley
 
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Default Doppler Distoriton?

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
  #19   Report Post  
Isaac Wingfield
 
Posts: n/a
Default Doppler Distoriton?

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
  #20   Report Post  
Jim Carr
 
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Default Doppler Distoriton?

"Ben Bradley" wrote in message
...

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.


Did you not get get that I was making a joke?




  #21   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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.


  #22   Report Post  
Steve Maki
 
Posts: n/a
Default Doppler Distoriton?

On Fri, 6 Aug 2004 10:54:46 -0400, "Arny Krueger" wrote:

But as for Doppler distortion. Do the sums, assuming a perfectly
linear driver (which should still show the phenomenon if it exists,
since it needs no non-linearity).


That would be a more complex theoretical exercise.


You will find that the sum of the
tones exactly matches what the trajectory of the cone should be to
prevent such distortion.


I don't see it. And as I've now pointed out several times, the JAES doesn't
seem to see it, either. IOW, there are a goodly number of refereed papers
that give abundant positive evidence that it does exist. I see that train
coming towards me, and I see that cone coming towards me!


FWIW, a friend of mine (a pretty sharp physics dude) claims he
became interested in this topic around the time Klipsch was
talking about it, and worked it out, and came to the same conclusion
that Don Pearce does.

He tried to explain it to my dumb brain by saying that the sound
source is not the cone, but an area out in front of the cone, which
is not moving. Doesn't make sense to me of course

--
Steve Maki
  #23   Report Post  
Arny Krueger
 
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Default Doppler Distoriton?

"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.


  #24   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?



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
  #25   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?



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


  #26   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?



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
  #27   Report Post  
Randy Yates
 
Posts: n/a
Default Doppler Distoriton?

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
  #28   Report Post  
Randy Yates
 
Posts: n/a
Default Doppler Distoriton?

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
  #29   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?



Randy Yates wrote:

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.


Right, my bad.


Bob
--

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

A. Einstein
  #30   Report Post  
Arny Krueger
 
Posts: n/a
Default Doppler Distoriton?

"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




  #31   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?



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
  #32   Report Post  
Randy Yates
 
Posts: n/a
Default Doppler Distoriton?

Bob Cain writes:

Randy Yates wrote:

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.


Right, my bad.


And also my bad(der)! That should have been radians/second!
--
% 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
  #33   Report Post  
Arny Krueger
 
Posts: n/a
Default Doppler Distoriton?

"Bob Cain" wrote in message

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.


The author graciously gave me a copy, probably partially because of our
discussions about nonlinear distortion, based on an earlier manuscript.

The book is highly mathematical, and attacks AM nonlinear distortion for all
it's worth. It's not a big book, but it's very detailed and pithy.

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?


Yes, and I confirmed that with the author a few days ago.

I would say that the author has the orthodox view, which is that Doppler
distortion definately exists, but it is submerged in the relatively immense
amounts of AM distortion present in speakers under the operational
conditions where Doppler might be a concern. He has no regrets about
ignoring it.


  #34   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Doppler Distoriton?

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


  #35   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Doppler Distoriton?

On Sun, 8 Aug 2004 06:51:19 -0400, "Arny Krueger"
wrote:

"Bob Cain" wrote in message

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.


The author graciously gave me a copy, probably partially because of our
discussions about nonlinear distortion, based on an earlier manuscript.

The book is highly mathematical, and attacks AM nonlinear distortion for all
it's worth. It's not a big book, but it's very detailed and pithy.

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?


Yes, and I confirmed that with the author a few days ago.

I would say that the author has the orthodox view, which is that Doppler
distortion definately exists, but it is submerged in the relatively immense
amounts of AM distortion present in speakers under the operational
conditions where Doppler might be a concern. He has no regrets about
ignoring it.



John's dad say: "Speaker at 50 Hz much like LP doing 3000 rpm.

I've got the radio if you get the urge to broasdcast the raw data,


  #36   Report Post  
Goofball_star_dot_etal
 
Posts: n/a
Default Doppler Distoriton?

On Sun, 8 Aug 2004 19:14:50 +0200, "Wessel Dirksen"
wrote:


"Goofball_star_dot_etal" wrote in message
...
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.


IM effects, of which doppler summation are a part IMO, are also dependant on
total piston excursion. Thus large diameter woofers suffer less from such
effect at low frequencies. Since cone excursion is reduced inversely with
increasing frequency, IM effects become progressively more negligable.
Arny's 2 different frequency suites seem to show this. Also a two tone test
suite is never free of FM affects because a complete higher frequency cycle
will always originate at different excursion locations within the excursion
pattern governed by the low frequency leading to the lower frequency
modulated phase shifting. Ideally one would want to use a non-harmonic or
randomized stimulus at a low frequency/high excursion and then measure the
effect on the higher signal.


Well, this is all very interesting but it does not address whether The
Pinciple of Linear Superposition is applicable to this case.

Don Pearce claims, in effect, to have THE LAWS OF PHYSICS and MATHS on
his side. However, he argues that (he wishes) there is no FM
therefore superposition proves that he is correct in his original wish
that the system is linear, so that superposition applies, and
therefore no FM occurs.


Wessel


I note that you did not take the hint (in the thread "Speaker
transient analysis") that I thought your statement:

"So yes,the acoustical output is directly proportional to the velocity
(not the force applied)" was incorrect.

Svante wrote:

p=U*rho0*w/(4*pi*r)

where U is the volume flow in m3/s (=surface*velocity), rho0=1.2kg/m3,
w is the angular frequency, and r is the distance.
After some thinking about this equation, one can realise that sound
pressure is roportional to the piston *acceleration* (comes from w*U,
ie derivative of the flow).

Nobody else seemed to notice that these two statements were different.
.. .




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

d

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





  #37   Report Post  
Arny Krueger
 
Posts: n/a
Default Doppler Distoriton?

"Goofball_star_dot_etal" wrote in message


I've got the radio if you get the urge to broadcast the raw data...


Sounds like an idea. I'm going to try to not pull an John Atkinson
hide-the-data trick on you. I didn't save the data from the two three-tone.
I'm going to do several tests in quick succession so that the acoustical
setup remains the same. I'll also try to do it when its acoustically quiet.


  #38   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?


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
  #39   Report Post  
Bob Cain
 
Posts: n/a
Default Doppler Distoriton?

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
  #40   Report Post  
Jim Carr
 
Posts: n/a
Default Doppler Distoriton?

"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.


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