# Doppler in speakers -- a definitive explanation

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Anonymous

Let's stop arguing guys. Let's do a little Gedanken experiment and see -- uh,
hear -- what happens.

I'm going to use a real-world product to make it believable -- the 4" full-range
driver used in so many KLH products. In this case, it's the gray-vinyl covered
speaker that came with the Model Eleven portable.

I've got a little power amp and battery-pack attached to it. And a 3kHz
oscillator.

I'm putting it on top of a train. As the train goes rumbling towards us, then
past, do we hear a Doppler shift upward, then downward? Every hand should be in
the air -- Yes, yes, yes!

Now let's drag out a shake table and attach the speaker tightly to it. Let's
turn the table "upright," then start it oscillating at 100Hz, with an amplitude
of 2" peak-to-peak. Assuming the KLH speaker doesn't fall apart, its average
velocity would be about 400" per second -- 33' per second -- a bit less than 23
mph.

Does this produce a Doppler shift? It better had, because the source is moving
with respect to the listener. Is the shift audible? Almost certainly. But
whether or not it's audible, it's definitely measurable.

Final step. We turn off the shake table and add a 100 Hz signal to the driver
(along with the original 3kHz) strong enough to produce a 2" peak-to-peak
excursion. (The driver can't really move that far, but this is a thought
experiment.)

Now, you tell me... What is the difference between the cone moving because the
speaker cabinet is moved bodily, and the cone moving under electrical influence?

The answer is -- none. There is no difference. The 3kHz signal is being emitted
from a moving surface -- and it doesn't matter "what" causes that surface to
move. The surface is moving with respect to the listener.

QED
Anonymous

William Sommerwerck wrote:

> Let's stop arguing guys. Let's do a little Gedanken experiment and see -- uh,
> hear -- what happens.

William, your Gendanken experiments are not based on enough
physics to be worth considering.

Any of them can be refuted by understanding that Doppler
shift is a consequence of a constant relative motion between
wave because air can transmit any such motion.

Bob
--

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

A. Einstein
Anonymous

in article 10i41jnt308m82a@corp.supernews.com, William Sommerwerck at
williams@nwlink.com wrote on 8/17/04 9:20 AM:
(SNIP)
> Now, you tell me... What is the difference between the cone moving because the
> speaker cabinet is moved bodily, and the cone moving under electrical
> influence?
>
> The answer is -- none. There is no difference. The 3kHz signal is being
> emitted
> from a moving surface -- and it doesn't matter "what" causes that surface to
> move. The surface is moving with respect to the listener.

nice, clear, corrct but... ummm... isn't this where this thread STARTED,
thread seeing as how it went silly real fast (Nice One Bob! You also get a
woody from outrunning prostheticless double AK amputees don't you!).

It must be August...
Anonymous

> nice, clear, corrct but... ummm... isn't this where this thread STARTED,
> thread seeing as how it went silly real fast (Nice One Bob! You also get a
> woody from outrunning prostheticless double AK amputees don't you!).

It was (more or less), but no one seemed to be paying attention, so I thought it
a good idea to beat everyone over the head again.
Related ressources
Anonymous

>> Let's stop arguing guys. Let's do a little Gedanken experiment and see -- uh,
>> hear -- what happens.

> William, your Gendanken experiments are not based on enough
> physics to be worth considering.

> Any of them can be refuted by understanding that Doppler
> shift is a consequence of a constant relative motion between
> wave because air can transmit any such motion.

You're not looking at the broad issues or the basic principles involved.
Anonymous

in article 10i4b5o2qbh9g07@corp.supernews.com, William Sommerwerck at
williams@nwlink.com wrote on 8/17/04 12:03 PM:

>> nice, clear, corrct but... ummm... isn't this where this thread STARTED,
>> thread seeing as how it went silly real fast (Nice One Bob! You also get a
>> woody from outrunning prostheticless double AK amputees don't you!).
>
> It was (more or less), but no one seemed to be paying attention, so I thought
> it
> a good idea to beat everyone over the head again.

heh!

like i said... It's august!

>
Anonymous

In article <BD47AB04.1164%ten.nozirev@dlywsinhoj.com> ten.nozirev@dlywsinhoj.com writes:

> like i said... It's august!

That's almost September, and we don't really have the September effect
any more. Gotta have something to substitute for it.

--
I'm really Mike Rivers (mrivers@d-and-d.com)
However, until the spam goes away or Hell freezes over,
lots of IP addresses are blocked from this system. If
you e-mail me and it bounces, use your secret decoder ring
and reach me here: double-m-eleven-double-zero at yahoo
Anonymous

> like i said... It's august!

I'd like to think I was august, but I'm simply approaching my geezerhood without
developing any dignity.
Anonymous

These are absolutely my final comments on this issue.

Bob, lots of things are understood in physics without math, or even having to
perform experiments. For example, much of Special Relativity -- including time
dilation -- "drops out" simply by assuming the equivalence of inertial frames of
reference.

You need to do more thinking and less arguing.
Anonymous

William Sommerwerck wrote:

> These are absolutely my final comments on this issue.
>
> Bob, lots of things are understood in physics without math, or even having to
> perform experiments. For example, much of Special Relativity -- including time
> dilation -- "drops out" simply by assuming the equivalence of inertial frames of
> reference.

Yes it does and Herr Doktor Einstein showed precisely how
with mathematics in a paper titled "On The Electrodynamics
of Moving Bodies". Give it a read, it's very approachable,
requiring little more than high school mechanics until you
get to the last section, the implications of his new
metrical theory on electrodynamics, and illustrates what is
needed to call something a theory.

He didn't just say "I believe in time dilation" and go away.

His only new axiom was that the speed of light was the same
in all inertial frames of reference. From that he derived
the rest such that testable predictions were possible.

>
> You need to do more thinking and less arguing.

Bob
--

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

A. Einstein
Anonymous

>> You need to do more thinking and less arguing.

Unfair. You asked a question, I gave what is probably the correct answer, based
on a rational application of fundamental principles. I've shown you how to work
out the math. Do it yourself.

Bob Cain <arcane@arcanemethods.com> wrote in message news:<cfttqf0jd1@enews3.newsguy.com>...
> William Sommerwerck wrote:
>
> > Let's stop arguing guys. Let's do a little Gedanken experiment and see -- uh,
> > hear -- what happens.
>
> William, your Gendanken experiments are not based on enough
> physics to be worth considering.
>
> Any of them can be refuted by understanding that Doppler
> shift is a consequence of a constant relative motion between
> wave because air can transmit any such motion.
>
>
> Bob

I don't think Doppler shift requires CONSTANT motion, just motion. A
train after all does oscilate back and forth between the stations and
still produces a Doppler shift that is proportional to it's
instananeous velocity. Why should a speaker cone be any different.
The motion of the cone needed to produce 50 Hz creates doppler shift
to the 4 kHz. The motion of the cone needed to produce 50 Hz does NOT
create doppler to the 50 Hz itself. I think that is the key point
that is confusing everybody.

Mark

Mark
Anonymous

Mike Rivers wrote:

> In article <BD47AB04.1164%ten.nozirev@dlywsinhoj.com> ten.nozirev@dlywsinhoj.com writes:

>>like i said... It's august!

> That's almost September, and we don't really have the September effect
> any more.

There are some who would argue that we never really DON'T have the
September effect anymore. At least in the past, we had about 11
good months out of the year.

- Logan
Anonymous

William Sommerwerck wrote:

>>>You need to do more thinking and less arguing.
>
>
>
>
> Unfair. You asked a question, I gave what is probably the correct answer, based
> on a rational application of fundamental principles. I've shown you how to work
> out the math. Do it yourself.
>

Once again, exactly why is it incumbent on me to prove
something that I know is false? You can't get there from
here. Trying to do so is exactly what persuaded me that
there was nothing to prove. Your turn.

Bob
--

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

A. Einstein
Anonymous

Mark wrote:

> I don't think Doppler shift requires CONSTANT motion, just motion. A
> train after all does oscilate back and forth between the stations and
> still produces a Doppler shift that is proportional to it's
> instananeous velocity. Why should a speaker cone be any different.
> The motion of the cone needed to produce 50 Hz creates doppler shift
> to the 4 kHz. The motion of the cone needed to produce 50 Hz does NOT
> create doppler to the 50 Hz itself. I think that is the key point
> that is confusing everybody.

You have definitely hit the key point. Doppler shift is
only defined for constant velocity which produces no
acoustic wave. When the velocity is time varying, it is
incorporated linearly in the acoustic wave.

Only the instantaneous value of a changing piston velocity
determines the value of a point in the velocity/pressure
wave that propegates. How can that value be sensitive to
what came before or after or what was mixed somewhere back
in the chain to get that value?

Bob
--

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

A. Einstein
Anonymous

On Tue, 17 Aug 2004 14:46:50 -0700, Bob Cain
<arcane@arcanemethods.com> wrote:

>
>
>William Sommerwerck wrote:
>
>> Let's stop arguing guys. Let's do a little Gedanken experiment and see -- uh,
>> hear -- what happens.
>
>William, your Gendanken experiments are not based on enough
>physics to be worth considering.
>
>Any of them can be refuted by understanding that Doppler
>shift is a consequence of a constant relative motion between
>wave because air can transmit any such motion.
>

You must be the World's worst scientist, Sorry.
Anonymous

Goofball_star_dot_etal wrote:

>
> You must be the World's worst scientist, Sorry.

Maybe you can produce the expression for sound pressure as a
function of piston velocity that encompasses this effect.

Bob
--

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

A. Einstein
Anonymous

mrivers@d-and-d.com (Mike Rivers) wrote in news:znr1092764815k@trad:

>> like i said... It's august!
>
> That's almost September, and we don't really have the September effect
> any more. Gotta have something to substitute for it.

I had never heard of the "September effect". A quick google search
indicates that a quick google search would negate the effect.
Anonymous

On Wed, 18 Aug 2004 00:13:13 GMT, Carey Carlan <gulfjoe@hotmail.com>
wrote:

>mrivers@d-and-d.com (Mike Rivers) wrote in news:znr1092764815k@trad:
>
>>> like i said... It's august!
>>
>> That's almost September, and we don't really have the September effect
>> any more. Gotta have something to substitute for it.
>
>I had never heard of the "September effect". A quick google search
>indicates that a quick google search would negate the effect.

Google for Endless September. I recall one site giving the "current
date" as something like September 3956, 1993. (that should make some
people both laugh and cry). Apparently, the "September effect" only
lasted a month in the years before 1993.
I was too late to see it, as I didn't show up on Usenet until 1996.
Not coincidentally, that's also the year I got my first email spam.

-----
Anonymous

On 17 Aug 2004 19:36:33 -0700, makolber@yahoo.com (Mark) wrote:

>I don't think Doppler shift requires CONSTANT motion, just motion. A
>train after all does oscilate back and forth between the stations and
>still produces a Doppler shift that is proportional to it's
>instananeous velocity. Why should a speaker cone be any different.

I've asked Bob that several times, and he hasn't given an
explanation I've considered satisfactory.

>The motion of the cone needed to produce 50 Hz creates doppler shift
>to the 4 kHz. The motion of the cone needed to produce 50 Hz does NOT
>create doppler to the 50 Hz itself.

I dare say it does (in the form of a distorted sine wave), but that
is a VERY small effect, surely immesurable and overwhelmed by the
other distortions in any driver. When the cone is at the positive
peak, it's at a smaller distance to the mic than when it's at the
negative peak, so the posive peak is received (very slightly) sooner
than if doppler distortion didn't exist, and likewise the negative
peak is received (very slightly) later.
But if you make a device that moves sinusoidally in air at a
substantial fraction of the speed of sound (the engine piston with the
cylinder head opened up, as I mentioned earlier, driven at high speed
would be a good candidate), the signal picked up by a microphone would
show distortion in the waveshape. If I'm visualising it correctly, the
waveform will be a 'morph' between a sine and a sawtooth.

> I think that is the key point
>that is confusing everybody.
>
>Mark
>
>Mark

-----
Anonymous

> On 17 Aug 2004 19:36:33 -0700, makolber@yahoo.com (Mark) wrote:
>
>
>
>>I don't think Doppler shift requires CONSTANT motion, just motion. A
>>train after all does oscilate back and forth between the stations and
>>still produces a Doppler shift that is proportional to it's
>>instananeous velocity. Why should a speaker cone be any different.
>
>
> I've asked Bob that several times, and he hasn't given an
> explanation I've considered satisfactory.

Haven't you noticed that _all_ formal descriptions of
Doppler shift are descriptions involving a constant
velocity? Odd, that.

If there is one anywhere that's dynamic (and it's correct)
then I'm wrong and will begin preparation of my hat. I will
post pictures.

Bob
--

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

A. Einstein
Anonymous

news:upl5i01je0vseq6a7bg3l3ke630umjqgoe@4ax.com

> I dare say it does (in the form of a distorted sine wave), but that
> is a VERY small effect, surely immeasurable

It's been measured a number of ways by a number of people, including myself.

> and overwhelmed by the other distortions in any driver.

Now, that I'll agree to. It's a nit!
Anonymous

Bob Cain wrote:
> You have definitely hit the key point. Doppler shift is only defined
> for constant velocity which produces no acoustic wave. When the
> velocity is time varying, it is incorporated linearly in the acoustic wave.

I don't follow your reasoning. To my mind, Dopper shift (in the sense
where you can quantify the shift in frequency by measuring the speed
of transducer relative to the speed of propagation through the
medium) is an oversimplification. Or at least not a sufficiently
general principle to fully describe things.

The thing that matters to me is this: if you move the transducer by
a certain displacement, then some number of extra cycles of a periodic
signal will arrive out at infinity distance (the listener in the case of
audio). The number of extra cycles will be equal to the displacement
(of the transducer) divided by the wavelength of the signal.

Actually, I should put that a little differently. If a transducer
starts at rest and then moves a distance S towards the listener and
ends up at rest again, and if the speed of propagation in the medium
is P, and if the transducer is oscillating at a frequency F, then
during that time, then the listener will hear (P/F)/S extra peaks
in the frequency F sound. Note that the extra peaks should be
path-independent; in other words, it shouldn't matter just how
the driver travels the distance S, with the possible exception that
it shouldn't go faster than the speed of propagation anywhere along
the way. (It's pretty clear we're not talking about that, and I
don't want to think about supersonic doppler shift. It hurts
my brain.)

Anyway, the point is, the driver doesn't need to travel at a constant
distance. All that needs to happen is that it needs to change its
position while continue to oscillate at the same rate. The wave
propagates at a particular speed and thus takes a specific amount
of time to get to its destination (the listener, whatever). If
you decrease the distance, you decrease the time it takes for the
sound to reach its destination. There is a net difference in
propagation time when you displace the transducer. The net difference
doesn't depend on what speed the transducer is moving.

> Only the instantaneous value of a changing piston velocity determines
> the value of a point in the velocity/pressure wave that propegates.

It seems like you are talking about amplitude here, not frequency.
Am I failing to understand what you're saying? By the way, I'm not
exactly sure what quantity you're describing when you save "value
of a point in the ... wave". Are you talking about the pressure
at a point in time?

- Logan
Anonymous

Logan Shaw wrote:

>>Only the instantaneous value of a changing piston velocity determines
>>the value of a point in the velocity/pressure wave that propegates.
>
>
> It seems like you are talking about amplitude here, not frequency.

Yes. The frequency comes out of how that instantaneous
value is changing with time.

> Am I failing to understand what you're saying? By the way, I'm not
> exactly sure what quantity you're describing when you save "value
> of a point in the ... wave". Are you talking about the pressure
> at a point in time?

Or the velocity, they are in phase and proportional to each
other in an acoustic plane wave.

I'm saying that the instantaneous velocity of the piston is
transfered to the wave in the right position, since it is
moving in step with it, to propegate that velocity out as an
acoustic wave. It is _in_ the acoustic wave it is creating
and it is at the right place at all times to deliver the
correct velocity _because_ it is in it.

It doesn't matter what signals might have been mixed
upstream to get the signal that controls the velocity of
that piston. It will be moving in lock step with the wave
defined by that signal and will always be in the right place
to deliver the right velocity to the outgoing wave.

If the above is truly crazy, then I'll agree that I'm over
the edge. But I don't think so. What, exactly, is wrong
with it?

Bob
--

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

A. Einstein

<< You have definitely hit the key point. Doppler shift is
only defined for constant velocity which produces no
acoustic wave. When the velocity is time varying, it is
incorporated linearly in the acoustic wave.

Only the instantaneous value of a changing piston velocity
determines the value of a point in the velocity/pressure
wave that propegates. How can that value be sensitive to
what came before or after or what was mixed somewhere back
in the chain to get that value?

Bob >>

Actually, doppler shift may be determined by replacing the constant velocity
with a suitable function representing the relative motion, regardless of
whether the motion is linear, cyclic or what-have-you.

Consider the alternative mechanical system, if a microphone is placed on a
piston moving some displacement at a cyclic rate of 50hz and the 4khz tone is
emitted from a stationary source, is there a measureable shift in frequency
corresponding to the relative motion?

I'd venture a, "you betcha."

Also one must remember that relativity does figure into the acoustical doppler
formula, but is usually ignored since it isn't significant at the velocities
that are considered in most acoustical systems.

The other very interesting thing is to consider that the practical loudspeaker
is a decidedly non-linear device. What happens when two distinct fundamental
frequencies sum into a non-linear system?

--
Dr. Nuketopia
Sorry, no e-Mail.
Spam forgeries have resulted in thousands of faked bounces to my address.
Anonymous

nuke wrote:

> Actually, doppler shift may be determined by replacing the constant velocity
> with a suitable function representing the relative motion, regardless of
> whether the motion is linear, cyclic or what-have-you.

Incorrect. The constant velocity, and only the constant
velocity, cannot be "transduced" by the piston. At f=0 it
abruptly looses the ability to make a wave. This results in
the piston always being in the wrong position to deliver the
velocity implied by the sum of the signal and the constant
velocity. The error is Doppler shift. Otherwise it moves
_in_ the wave and is always in the correct position to
impart the commanded velocity.

Bob
--

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

A. Einstein
Anonymous

Bob Cain wrote:

>
>
> nuke wrote:
>
>
>> Actually, doppler shift may be determined by replacing the constant
>> velocity
>> with a suitable function representing the relative motion, regardless of
>> whether the motion is linear, cyclic or what-have-you.
>
>
> Incorrect. The constant velocity, and only the constant velocity,
> cannot be "transduced" by the piston. At f=0 it abruptly looses the
> ability to make a wave.

Correction, looses it's ability to do so in the free field.
In the enclosed tube I've been using as a toy system I'm
not quite sure whether or not a constant motion translates
to a wave. At first blush I think it might but the nature
of it escapes me.

Bob
--

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

A. Einstein
Anonymous

On Wed, 18 Aug 2004 05:52:15 -0400, "Arny Krueger" <arnyk@hotpop.com>
wrote:

>news:upl5i01je0vseq6a7bg3l3ke630umjqgoe@4ax.com
>
>> I dare say it does (in the form of a distorted sine wave), but that
>> is a VERY small effect, surely immeasurable
>
>It's been measured a number of ways by a number of people, including myself.

A SINGLE sine wave produced by a driver, and doppler-distorted?
Please give details of one or more of these measurements.

>> and overwhelmed by the other distortions in any driver.
>
>Now, that I'll agree to. It's a nit!
>
>

-----
Anonymous

In this place, William Sommerwerck was recorded saying ...
> > nice, clear, corrct but... ummm... isn't this where this thread STARTED,
> > thread seeing as how it went silly real fast (Nice One Bob! You also get a
> > woody from outrunning prostheticless double AK amputees don't you!).
>
> It was (more or less), but no one seemed to be paying attention, so I thought it
> a good idea to beat everyone over the head again.

It's also what I (and a couple of others) stated several times over in
alt.music.home-studio - where this all started.

Long ago - in a place far away .... ;^)

--

George
Newcastle, England

Problems worthy of attack
Prove their worth, by hitting back [Piet Hein]
Anonymous

In this place, Bob Cain was recorded saying ...
>
>
> William Sommerwerck wrote:
>
> >>>You need to do more thinking and less arguing.
> >
> >
> >
> >
> > Unfair. You asked a question, I gave what is probably the correct answer, based
> > on a rational application of fundamental principles. I've shown you how to work
> > out the math. Do it yourself.
> >
> > Don't ask other people to do your work for you.
>
> Once again, exactly why is it incumbent on me to prove
> something that I know is false? You can't get there from
> here. Trying to do so is exactly what persuaded me that
> there was nothing to prove. Your turn.

Bob - can we look at this another way then. We can experimentally show
that a speaker reproducing both a LF tone at high amplitude (read large
cone excursion) modulates another tone at higher frequency.

Please explain the mechanism causing this effect.

--

George
Newcastle, England

Problems worthy of attack
Prove their worth, by hitting back [Piet Hein]
Anonymous

I'm posting this to multiple threads. If you don't understand my explanation...
Well...

>> So, it's easy to find the formula that shows how Doppler works (train
>> example) without taking into consideration the movement of the plane
>> of the source that is creating the sound. I've seen numerous sites talk
>> about Doppler Distortion, but I've yet to uncover one that shows the actual
>> mathematical representation.

I understand what you're saying, and YOU'RE WRONG. The velocity of the sound
source "adds to" the velocity of the sound it produces. It doesn't matter
whether the sound source is attached to the moving object, or the moving object
IS the sound source. It doesn't matter whether the speaker is moved bodily, or
the cone only is moved. To quote Galileo -- "Nevertheless, it does move."

The other way of looking at it is that, as the sound propagates from the moving
source, the source either "catches up with" or "lags behind" the propagating
sound, thus (from the point of hearing of the observer) reducing or increasing
its wavelength. That is, you're "squeezing" more cycles into a given space, or
spreading them over a longer distance.

Exactly the same thing happens with a driver producing LF and HF sounds at the
same time. I'm going to spell this out in excruciating detail so you can SEE
what happens...

Suppose we feed a 5kHz signal into our classic KLH driver. As the driver
vibrates, it alternately compresses and rarefies the air. These compressions and
rarefactions propagate from the driver at the speed of sound -- about 1100 feet
per second. This is much faster than the driver itself moves.

Now let's add a strong 100Hz signal to the 5kHz signal, enough to visibly "pump"
the driver. We'll also imagine that our senses have been speeded up by a
thousand times or more ("The New Accelerator," anyone?) so we can "see" what's
happening in front of the driver.

Let's pick a point on the 100Hz signal where the driver is all the way back and
is moving forward. Superimposed on that forward motion is the 5kHz signal. In
the time the driver moves from back to front, 25 cycles of the 5kHz signal are
generated and move away from the driver. Because THE DRIVER IS MOVING, each 5kHz
cycle is generated "closer" to the previous cycle than it would be if the driver
weren't moving, thus "squeezing" the wavelength. This is exactly the mechanism
that creates Doppler shift.

The opposite effect occurs when the driver moves "backwards."

What you're forgetting, Bob, is that the acoustic waves generated are not
"attached" to the cone. Once created, they move independently. If the sound
source is moving -- for WHATEVER reason -- successive waves will be "closer to"
or "farther from" the preceding waves.

Suppose we could get the front surface of THE LOCOMOTIVE ITSELF to produce a
1kHz sound. Are you telling me that you WOULDN'T hear a Doppler shift as the
train passed? If you think you wouldn't, then you don't understand Doppler
shift.
Anonymous

George Perfect wrote:

>
> Bob - can we look at this another way then. We can experimentally show
> that a speaker reproducing both a LF tone at high amplitude (read large
> cone excursion) modulates another tone at higher frequency.
>
> Please explain the mechanism causing this effect.

Problem is, George, that what you say remains highly
equivocal. No experiment has yet been done that isolates
"Doppler distortion" as a phenomenon. There are so many
other sources of distortion in the experiments that have
been put forth that no conclusions can be drawn from them.

Bob
--

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

A. Einstein
Anonymous

news:c0s6i0d3l8jc01ev54momkunnuubu1bqs4@4ax.com
> On Wed, 18 Aug 2004 05:52:15 -0400, "Arny Krueger" <arnyk@hotpop.com>
> wrote:
>
>> news:upl5i01je0vseq6a7bg3l3ke630umjqgoe@4ax.com
>>
>>> I dare say it does (in the form of a distorted sine wave), but
>>> that is a VERY small effect, surely immeasurable
>>
>> It's been measured a number of ways by a number of people, including
>> myself.
>
> A SINGLE sine wave produced by a driver, and doppler-distorted?

Did I say that?

I didn't mean to!
Anonymous

> But if you make a device that moves sinusoidally in air at a
> substantial fraction of the speed of sound (the engine piston with the
> cylinder head opened up, as I mentioned earlier, driven at high speed
> would be a good candidate), the signal picked up by a microphone would
> show distortion in the waveshape. If I'm visualising it correctly, the
> waveform will be a 'morph' between a sine and a sawtooth.

** This site ( which I posted 4 days ago) gives the maths and waveshape for
single frequency ( and twin ) Doppler.

http://www.geocities.com/kreskovs/Doppler1.html

.......... Phil
Anonymous

> Final step. We turn off the shake table and add a 100 Hz signal to the driver
> (along with the original 3kHz) strong enough to produce a 2" peak-to-peak
> excursion. (The driver can't really move that far, but this is a thought
> experiment.)

if so, if the table was oscillating at 100hz, and the tone generator
was generating a 100hz tone in opposite polarity to the shake table,
the cone would effectively not move, thus no air would move, right?

therefore, the cone would emit a 100hz tone when it was being shook by
the table, right?

armchair theoretician,
cd /..
Anonymous

"nuke"

>
> Consider the alternative mechanical system, if a microphone is placed on a
> piston moving some displacement at a cyclic rate of 50hz and the 4khz tone
is
> emitted from a stationary source, is there a measureable shift in
frequency
> corresponding to the relative motion?
>
> I'd venture a, "you betcha."
>

** Absolutely correct.

Relative motion is the key.

All the rest here is the result of crippled imaginations.

.............. Phil

Then lets clarify what each of us are trying to say.

We have a speaker cone vibrating at both 50 Hz and 4 kHz.

QUESTION 1
Does the 50 Hz cone vibration produce Doppler shift to the 4 kHz?
I believe yes it does and that is what is shown on the spectrum
analyzer previously.

QUESTION 2
Does the 50 Hz cone vibration produce Doppler shift to the 50 Hz?
I believe no it does not, the 50 Hz cone vibration is producing the 50
Hz wave and as far as the 50 Hz wave is concerned there is no
additional movement. In any case, this is a very small effect and not
the question I believe most of us are discussing. I believe most of

I think it would be helpful in the discussion to clarify which of
these two questions you are discussing.

Mark
Anonymous

"Mark" <makolber@yahoo.com> wrote in message
> Then lets clarify what each of us are trying to say.
>
>
> We have a speaker cone vibrating at both 50 Hz and 4 kHz.
>
> QUESTION 1
> Does the 50 Hz cone vibration produce Doppler shift to the 4 kHz?

Yes, indoubatbly.

> I believe yes it does and that is what is shown on the spectrum
> analyzer previously.

Thank you!

> QUESTION 2

> Does the 50 Hz cone vibration produce Doppler shift to the 50 Hz?

The actual Doppler shift isn't the same as the frequency of the sidebands.

The carrier frequency's shifting around can be calculated from the vector
sum of the sidebands and the carrier. Somebody has correctly pointed out
that the reason why there is no change in the height of an FM-modulated
envelope is the fact that the sidebands are out of phase by 180 degrees.
They always cancel out in the amplitude directon, but in the process they
cause the vector sum to change in phase. The sidebands of an AM-modulated
wave are in phase, and they add up to make the envelope of the carrier go up
and down or change in amplitude.

The sidebands are at 50 Hz and multiples because 50 Hz is the modulating
frequency.

>nuke wrote:
>
>
>> Actually, doppler shift may be determined by replacing the constant velocity
>> with a suitable function representing the relative motion, regardless
>of
>> whether the motion is linear, cyclic or what-have-you.
>
>Incorrect. The constant velocity, and only the constant
>velocity, cannot be "transduced" by the piston. At f=0 it
>abruptly looses the ability to make a wave. This results in
>the piston always being in the wrong position to deliver the
>velocity implied by the sum of the signal and the constant
>velocity. The error is Doppler shift. Otherwise it moves
>_in_ the wave and is always in the correct position to
>impart the commanded velocity.
>
>
>Bob
>--

No, you missed the point: In the mathematics, the factor representing velocity
of each party may be a constant or it may be a function. Constants are easy
math, functions of course will require at least a little cowboy calculus to
resolve. If the relative motion is a function dT, then the Fout will also be a
function of dT.

The limitation you're getting at is specific to the case of pistons with
limited stroke. If the piston has unlimited excursion, then f=0 is in the
domain of the function. ;-)

Weirdly enough, the 4khz in the example case does modulate the 50hz as well as
the 50hz does the 4khz!

--
Dr. Nuketopia
Sorry, no e-Mail.
Spam forgeries have resulted in thousands of faked bounces to my address.
Anonymous

nuke wrote:

> The limitation you're getting at is specific to the case of pistons with
> limited stroke. If the piston has unlimited excursion, then f=0 is in the
> domain of the function. ;-)

Correct, but it's not in the domain of the air it's driving
and that is the crucial difference.

Bob
--

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

A. Einstein
Anonymous

I agree, Ben.
You don't need two separate tones to observe Doppler distortion.
A single freq will have its zero-crossings displaced.
Here is a MATLAB script which simulates a single piston moving
sinusoidally in a cylinder at 100Hz, with peak-to-peak excursions
up to 0.78 meter (big, huh?).
The script plots the pressure wave recorded by a stationary probe elsewhere
in the cylinder. Most of the assumptions and constraints are stated in
the comments at the beginning of the file. Six plots are made for different
amplitudes, showing the increasing displacement of the zero crossings of the
sinusoid. Keep in mind that for the biggest amplitude, the piston achieves
a velocity of over 245 meters/sec, or about 70% of mach 1. I chose this
as the biggest amplitude because at this point the pressure trough is about
equal to 1 bar, and the air will achieve total vacuum (clip) in the rarified
segment of the wave.
Here is what's interesting: Integrating the observed waveforms shows a DC
component which grows with the amplitude of oscillation. To me, this seems
strange since that would mean that the density of air in the cylinder has
changed (?!) For amplitudes of 0.0000001, 0.1, 0.2, 0.3, 0.39 meters,
the DC component of pressure comes out as:
0.00,-9.24,-18.48,-27.72,-36.04 as percentage of peak amplitude.
So, there is either 1) a bug in the code, 2) a bogus approximation I made,
or 3) a shortcoming of the linear acoustics model. Or, is this actually true?
To me, it's very suspicious. Anyway, here's the script if you want to check
it out--

Dave

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%sinevel.m
%simulation of piston whose velocity is sinusoidal, at 100Hz.
%assumed facts: the air in front of the piston has a real
%impedance, so that the pressure generated is
%proportional to the (instantaneous) velocity of the piston.
%The piston is assumed to have a planar front, and is facing
%into a cylindrical, infinitely long tube. Viscous losses
%are ignored, and linear acoustics only are considered.
%Flow is laminar. Boundary effects are not included. The air
%stays at constant temperature (no shock waves).
%
%The pressure resulting from the piston's motion is picked
%up from 10 meters away by a stationary probe.

Z=410; %impedance of air, newton seconds/meter cubed.
%1 bar is 100,000 N/square meter
%p at sea level is 1013mBar, or 101,300 N/square meter.
%so 247m/S is max speed allowed before air "clips"(?)

fs=96000; % sampling rate
freq=100; % 100 Hz sine wave
listloc=10; % listen from 10 meters away.
c=340; % speed of sound, m/s
timespan=0.020; %create 20mS, or two cycles
timefun=linspace(0,timespan,timespan*fs); %create 20mS, or two cycles

Amplitude=[0.0000001 0.1 0.2 0.3 0.39]; %Amplitude of oscillation
% in meters. The biggest one
% has peak-to-peak excursion
% of 0.78 meters.
cmap=['k','r' , 'y', 'g', 'b','m']; % color map for plots
pmax=zeros(size(Amplitude)); % record of peak pressure amplitudes
DCcomp=zeros(size(Amplitude)); % record of DC components
figure(1)
for Index=1:length(Amplitude)
pos=Amplitude(Index)*sin(timefun*freq*2*pi); %piston moves sinusoidally
p=1.0*cos(timefun*freq*2*pi); %normalized pressure wave
%(derivative of the position).
pmax(Index)=2*pi*freq*Amplitude(Index); %actual peak pressure
dist=listloc-pos; %distance from source to listener
%distance divided by speed of sound.
plot(timereceived,p,cmap(Index)) %plot pressure as function of time
hold on
%numerically integrated
end
grid on
hold off
xlabel('Time, S')
ylabel('pressure at listening position')
title('Single-Frequency Doppler Distortion')
DCcomp %display DC component vector
pmax %display max pressure vector
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

> On 17 Aug 2004 19:36:33 -0700, makolber@yahoo.com (Mark) wrote:
>
>
> >I don't think Doppler shift requires CONSTANT motion, just motion. A
> >train after all does oscilate back and forth between the stations and
> >still produces a Doppler shift that is proportional to it's
> >instananeous velocity. Why should a speaker cone be any different.
>
> I've asked Bob that several times, and he hasn't given an
> explanation I've considered satisfactory.
>
> >The motion of the cone needed to produce 50 Hz creates doppler shift
> >to the 4 kHz. The motion of the cone needed to produce 50 Hz does NOT
> >create doppler to the 50 Hz itself.
>
> I dare say it does (in the form of a distorted sine wave), but that
> is a VERY small effect, surely immesurable and overwhelmed by the
> other distortions in any driver. When the cone is at the positive
> peak, it's at a smaller distance to the mic than when it's at the
> negative peak, so the posive peak is received (very slightly) sooner
> than if doppler distortion didn't exist, and likewise the negative
> peak is received (very slightly) later.
> But if you make a device that moves sinusoidally in air at a
> substantial fraction of the speed of sound (the engine piston with the
> cylinder head opened up, as I mentioned earlier, driven at high speed
> would be a good candidate), the signal picked up by a microphone would
> show distortion in the waveshape. If I'm visualising it correctly, the
> waveform will be a 'morph' between a sine and a sawtooth.
>
> > I think that is the key point
> >that is confusing everybody.
> >
> >Mark
> >
> >Mark
>
> -----
Anonymous

In this place, Bob Cain was recorded saying ...
>
>
> George Perfect wrote:
>
> >
> > Bob - can we look at this another way then. We can experimentally show
> > that a speaker reproducing both a LF tone at high amplitude (read large
> > cone excursion) modulates another tone at higher frequency.
> >
> > Please explain the mechanism causing this effect.
>
> Problem is, George, that what you say remains highly
> equivocal. No experiment has yet been done that isolates
> "Doppler distortion" as a phenomenon. There are so many
> other sources of distortion in the experiments that have
> been put forth that no conclusions can be drawn from them.

Both the Linkwitz article I referred you to and more recently Arny's
experiments have demonstrated FM sideband components and phasing
consistent with Doppler shift caused by a reciprocating body imposing
its movement on a tone.

They are the same components produced when a speaker is placed on a
shaker table which is driven in similar fashion.

arise.

--

George
Newcastle, England

Problems worthy of attack
Prove their worth, by hitting back [Piet Hein]
Anonymous

George Perfect wrote:

> Please explain how these components (the ones from Linkwitz and Krueger)
> arise.

Can't. The system is too complex. Before the piston/air
interface it is comprised of a continuous, distributed
mixture of linear and non-linear effects. That is not
amenable to analysis that anyone knows how to do.

It remains to be seen what is exhibited by a system in which
these effects have been eliminated by correlating the
movement of the piston, whatever it might end up being after
all of that, with the sound wave it generates. That would
be the telling experiment.

Bob
--

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

A. Einstein
Anonymous

Bob Cain wrote:

>
>
> nuke wrote:
>
>
>> The limitation you're getting at is specific to the case of pistons with
>> limited stroke. If the piston has unlimited excursion, then f=0 is in the
>> domain of the function. ;-)
>
>
> Correct, but it's not in the domain of the air it's driving and that is
> the crucial difference.
>
>
> Bob

Coupling is the key whether there's a shift (no shift with efficient
coupling - a train's motion is NOT well-coupled to the air but the
whistle is) and waves from a woofer don't Doppler-warp themselves.

Do those two assertions make DD's non-existence any more intuitive?
Anonymous

In this place, Bob Cain was recorded saying ...
>
>
> George Perfect wrote:
>
> > Please explain how these components (the ones from Linkwitz and Krueger)
> > arise.
>
> Can't. The system is too complex. Before the piston/air
> interface it is comprised of a continuous, distributed
> mixture of linear and non-linear effects. That is not
> amenable to analysis that anyone knows how to do.

With respect, Bob, it seems to me that you are trying to have your cake
and eat it. It's a bit rich for you to throw out the challenge to others
to provide a mathematical proof of something you claim not to exist
while simultaneously declining yourself to provide mathematical
exlanation for a physical effect that can be observed and measured.

And, what do you mean by "Before the piston/air interface it is
comprised of a continuous, distributed mixture of linear and non-linear
effects."? Are you claiming that something in the amplifier or elsewhere
in the signal chain is causing FM sidebands *before* the electrical
signal reaches the speaker?

If so, some evidence please. Personally, I have both eyebrows raised at
that sort of claim.

> It remains to be seen what is exhibited by a system in which
> these effects have been eliminated by correlating the
> movement of the piston, whatever it might end up being after
> all of that, with the sound wave it generates. That would
> be the telling experiment.

That wouls also require a level of physical perfection that is, alas,
unattainable - as you must surely know.

It remains for you to explain how those FM sidebands that remain after
other possible distortions are removed are caused.

--

George
Newcastle, England

Problems worthy of attack
Prove their worth, by hitting back [Piet Hein]
Anonymous

George Perfect wrote:

> With respect, Bob, it seems to me that you are trying to have your cake
> and eat it. It's a bit rich for you to throw out the challenge to others
> to provide a mathematical proof of something you claim not to exist
> while simultaneously declining yourself to provide mathematical
> exlanation for a physical effect that can be observed and measured.

I'm simply saying that system prior to the piston face is
too complex to yield to analysis. Do you think what happens
to the air as a function of the motion of the piston face to
be anywhere near as complex and inscrutable? Perhaps it is
in the end, but is far from obvious why.

>
> And, what do you mean by "Before the piston/air interface it is
> comprised of a continuous, distributed mixture of linear and non-linear
> effects."? Are you claiming that something in the amplifier or elsewhere
> in the signal chain is causing FM sidebands *before* the electrical
> signal reaches the speaker?

I'm talking about everything that happens on the way to
making a signal into motion of the face of a piston. I'm
looking for an analysis of what propegates from the piston
that only considers its motion and not any of the complex
factors that made it move that way.

>>It remains to be seen what is exhibited by a system in which
>>these effects have been eliminated by correlating the
>>movement of the piston, whatever it might end up being after
>>all of that, with the sound wave it generates. That would
>>be the telling experiment.
>
>
> That wouls also require a level of physical perfection that is, alas,
> unattainable - as you must surely know.

Not really. It just means an accurate measuremnt of the
actual motion, in time, of the piston face. That isn't
particularly difficult at all. The signal going into the
system to move it is not such a measurement.

>
> It remains for you to explain how those FM sidebands that remain after
> other possible distortions are removed are caused.

Hasn't been done yet. Maybe then with whatever remains.

Bob
--

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

A. Einstein
Anonymous

S O'Neill wrote:

> Coupling is the key whether there's a shift (no shift with efficient
> coupling - a train's motion is NOT well-coupled to the air but the
> whistle is) and waves from a woofer don't Doppler-warp themselves.
>
> Do those two assertions make DD's non-existence any more intuitive?

The first paragraph is totally correct. The question is a
reason that has been stated and repeated just about
everywhere. That is utterly false.

If it were valid, it would exist in a particular situation
which physics says very clearly that it won't.

Bob
--

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

A. Einstein
Anonymous

In this place, Bob Cain was recorded saying ...
>
> I'm simply saying that system prior to the piston face is
> too complex to yield to analysis. Do you think what happens
> to the air as a function of the motion of the piston face to
> be anywhere near as complex and inscrutable? Perhaps it is
> in the end, but is far from obvious why.

Excuse me? I thought we were discussing the theoretical perfect piston
in a simple model that assumed perfect translation of electrical signal
to sound waveform.

What on earth are these "complex" mechanisms that exist "prior to the
piston face"?

> > And, what do you mean by "Before the piston/air interface it is
> > comprised of a continuous, distributed mixture of linear and non-linear
> > effects."? Are you claiming that something in the amplifier or elsewhere
> > in the signal chain is causing FM sidebands *before* the electrical
> > signal reaches the speaker?
>
> I'm talking about everything that happens on the way to
> making a signal into motion of the face of a piston. I'm
> looking for an analysis of what propegates from the piston
> that only considers its motion and not any of the complex
> factors that made it move that way.

That surely is encapsulated in the "perfect piston" we have been
discussing.

More significantly, in what way does this prevent you answering my
question?

> > It remains for you to explain how those FM sidebands that remain after
> > other possible distortions are removed are caused.
>
> Hasn't been done yet. Maybe then with whatever remains.

Sorry to press the point but it has been done. Linkwitz (and others)
have presented experimental test data showing an effect. Arny and a
couple of others in this thread have shown how to isolate the FM
sidebands due to Doppler from the various AM/IM clutter.

I ask you again - how do you explain the presence of the FM sidebands
revealed by the various experiments that have been conducted into this
matter.

I'm not trying to trip you up - just lead you to a perspective that
determinedly heading up a cul-de-sac so far! ;^)

--

George
Newcastle, England

Problems worthy of attack
Prove their worth, by hitting back [Piet Hein]
Anonymous

George Perfect wrote:

> In this place, Bob Cain was recorded saying ...
>
>>I'm simply saying that system prior to the piston face is
>>too complex to yield to analysis. Do you think what happens
>>to the air as a function of the motion of the piston face to
>>be anywhere near as complex and inscrutable? Perhaps it is
>>in the end, but is far from obvious why.
>
>
> Excuse me? I thought we were discussing the theoretical perfect piston
> in a simple model that assumed perfect translation of electrical signal
> to sound waveform.

I was talking about a real system that could be measured.
Thought you were too.

>
> What on earth are these "complex" mechanisms that exist "prior to the
> piston face"?

What exists in a real speaker.

>
>
>>>And, what do you mean by "Before the piston/air interface it is
>>>comprised of a continuous, distributed mixture of linear and non-linear
>>>effects."? Are you claiming that something in the amplifier or elsewhere
>>>in the signal chain is causing FM sidebands *before* the electrical
>>>signal reaches the speaker?

No, I am talking about what the speaker does between the
electrical signal and the face of the piston. We were
talking about real experiments involving measurement,
weren't we? It makes little sense to talk of ideal pistons
in that case.

> That surely is encapsulated in the "perfect piston" we have been
> discussing.

If that's what we were discussing, but I, at least, wasn't.

>>Hasn't been done yet. Maybe then with whatever remains.
>
>
> Sorry to press the point but it has been done. Linkwitz (and others)
> have presented experimental test data showing an effect. Arny and a
> couple of others in this thread have shown how to isolate the FM
> sidebands due to Doppler from the various AM/IM clutter.

Now we are back to real rather than ideal systems again.
That system is subject to my criticism.

>
> I ask you again - how do you explain the presence of the FM sidebands
> revealed by the various experiments that have been conducted into this
> matter.

Again, there is nothing yet to explain because we haven't
done the experiment that will eliminate the effects a real
speaker has between the signal and the face of the piston.

> I'm not trying to trip you up - just lead you to a perspective that
> might answer your original question as you appear to have been
> determinedly heading up a cul-de-sac so far! ;^)

I understand. No offense taken whatsoever. Have I
clarified my perspective?

Bob
--

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

A. Einstein
Anonymous

Bob Cain wrote:

> Again, there is nothing yet to explain because we haven't done the
> experiment that will eliminate the effects a real speaker has between
> the signal and the face of the piston.

This is too good not to pass on. I was at the doctor's
office with a friend today and there was this huge book on
the history of medicine, mostly in the arts. I stumbled
across this in the text:

"For when many things together produce a result there is
difficulty. Sequences of single phenomena are more
managable, and are more easily learnt by the senses."

Hippocrates, 5th century B.C.

Bob
--

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

A. Einstein