On Sun, 08 Jul 2007 19:46:18 -0700, Jeff Liebermann

Interesting. So, using my original example, if I take two ultrasonic
tones, above human hearing, you suggest that I do *HEAR* a beat, but
that there's no actual component at the beat frequency. The does
present a problem because if this is true, then the mixing has to
occurring somewhere in order for my brain to detect the beat
frequency. Is it mixing in my ear, in the cochlea, in the nerves
going to the brain, or in the brain somewhere? I don't think it's any
of these because when I do this experiment, I don't hear any such beat
note.

---
Agreed. I've done the same experiment, and it seems that if the
non-linear detector is presented with tones it can't recognize then
no cross-products are generated.

Same like a mixer with lowpass filters on its inputs, but I can't
seem to pin down your position.

What point are you arguing?


--
JF

"Jim Kelley" wrote in message
...
....
sin(a) + sin(b) = 2sin(.5(a+b))cos(.5(a-b))

A plot of the function reveals that cos(.5(a-b)) describes the envelope.

Ok.

The period of the 'enveloped' waveform (or the arcane, beat
modulated waveform) then can be seen to vary continuously and
repetitiously over time - from 1/a at one limit to 1/b at the other.

?

At a particular instant in time the period does in fact equal the average
of the two. But this is true only for an instant every 1/(a-b) seconds.

??

How do you come up with anything but a period of of the average of the two
for the enveloped waveform?

Jim Kelley wrote:

I suspect the
notion may have originated from a trigonometric identity which has
what could be interpreted as an average term in it.

sin(a) + sin(b) = 2sin(.5(a+b))cos(.5(a-b))

A plot of the function reveals that cos(.5(a-b)) describes the
envelope. The period of the 'enveloped' waveform (or the arcane, beat
modulated waveform) then can be seen to vary continuously and
repetitiously over time - from 1/a at one limit to 1/b at the other.
At a particular instant in time the period does in fact equal the
average of the two. But this is true only for an instant every
1/(a-b) seconds.



If you have two values, a and b, the average is (a+b)/2, which is precisely
the frequency in your above equation. So the sin(.5(a+b)) term is at the
average frequency.

The sin's term amplitude is modified by the cos term, 2cos(.5(a-b)). This
does not change the timing of the zero crossings of the sin term in any
way. Therefore the period of the resulting waveform is fixed.

The cos term does add a few additional zero crossings when it evaluates to
0, but there is no continuous variation in the period as you have
described.

"Dana" wrote in message
...

"Ron Baker, Pluralitas!" wrote in message
...
Do you understand that a DSB signal *is* AM?

So all the AM broadcasters are wasting money by
generating a carrier?

How did you jump to that conclusion.

Is "DSBSC" DSB?

"Ron Baker, Pluralitas!" wrote in message
...

"Dana" wrote in message
...

"Ron Baker, Pluralitas!" wrote in message
...
Do you understand that a DSB signal *is* AM?

So all the AM broadcasters are wasting money by
generating a carrier?

How did you jump to that conclusion.

Is "DSBSC" DSB?

Why can't you answer the question?
How or why do you think AM broadcasters are wasting money by generating a
carrier??

"Jeff Liebermann" wrote in message
...
"Bob Myers" hath wroth:

"Ron Baker, Pluralitas!" wrote in message
. ..

No nonlinearity is necessary in order to hear
a beat?
Where does the beat come from?

An audible beat tone is produced by the constructive and destructive
interference between two sound waves in air. Look at a pictorial
representation (in the time domain) of the sum of sine waves,of similar
amplitudes, one at, say, 1000 Hz and the other at 1005, and you'll
see it.

Bob M.

I beg to differ. There's no mixing happening in the air. compression
of air is very linear (Boyles Law or PV=constant). If there were
mixing, you would be able to hear the beat note when one generates two
ultrasonic tones. I belch 25KHz and 26KHz from two transducers, by
our logic, air mixing would create a 1KHz beat note. It doesn't and
you hear nothing.

What seems to be the problem here is the model of the human ear is not
what one would assume. It is NOT a broadband detector. The cochlea
cilia (hairs) resonate at individual frequencies. Each one resonantes
at only one frequency (and possibly some sub-harmonics). Therefore,
the human ear model is a collection of narrow band filters and
detectors. Unless the two frequencies involved both cause a single
cilia to simultaneously vibrate at both frequencies, there isn't going
to be any mixing. Each detector can be individually quite non-linear,
but as long as it vibrates at only one frequency, there isn't going to
be any mixing.

Well done.
Finally, someone who gets it.


Meanwhile, I would greatly appreciate it if everyone would kindly trim
quotations. This thread is becoming difficult to read. Thanks.

--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

"isw" wrote in message
...
In article ,
Jeff Liebermann wrote:

"Bob Myers" hath wroth:

"Ron Baker, Pluralitas!" wrote in message
.. .

No nonlinearity is necessary in order to hear
a beat?
Where does the beat come from?

An audible beat tone is produced by the constructive and destructive
interference between two sound waves in air. Look at a pictorial
representation (in the time domain) of the sum of sine waves,of similar
amplitudes, one at, say, 1000 Hz and the other at 1005, and you'll
see it.

Bob M.

I beg to differ. There's no mixing happening in the air. compression
of air is very linear (Boyles Law or PV=constant).

In general, that's true, but take a look at what happens in the throats
of high-powered horn loudspeakers. You can find info in e.g. "Acoustics"
by Beranek.

Isaac

Red herring.

"Bob Myers" wrote in message
...

"Jeff Liebermann" wrote in message
news
Nor did I say there was. The phenomenon of interference
between two compression waves in a given medium is not
an example of "mixing."

You didn't say that. You that a beat note would be produced. From
your posting at:
http://groups.google.com/group/sci.electronics.basics/msg/f18c6dfefbd55a82
"An audible beat tone is produced by the constructive and
destructive interference between two sound waves in air."

That's wrong. There's no audible beat note produced in the air.

Sigh -

Argument from histrionics.

which, again, is as I explained it further on. I said that
there is no actual component at the "beat" frequency. You do
HEAR a "beat,"

So one hears it but it is not there.

however, and that is the result of the amplitude

And amplitude is an absolute linear phenomenon
and independent of perception.

variation caused by the interference, as noted. You cannot hear
the beat effect (I won't use the word "tone" here, which I admit
was a possible source of confusion in the original wording) if the
two original tones are too far apart, simply because you can only

simply because...

perceive such amplitude variations if they occur below a certain
rate.

a "certain rate" is natural truth and certainly
not a limitation of human physiology.


I have never ever said that "mixing" (multiplication) occurs in air.
If you're going to pick apart what someone is saying, then please
read everything they've said before starting.

And whether or not you READ all the postings in a thread is one
thing - whether or not you choose to respond to a given posting
out of its context is something else entirely.

Bob M.

"David L. Wilson" wrote in message
news:Wcyki.7231$MV6.3335@trnddc01...

"Hein ten Horn" wrote in message
...
...
So take another example: 25000 Hz and 25006 Hz.
Again, constructive and destructive interference produce 6 Hz
amplitude variations in the air.
But, as we can't hear ultrasonic frequencies, we will not produce
a 25003 Hz perception in our brain. So ther's nothing to hear,
no tone and consequently, no beat.
...
If one looks at an oscilloscope of the audio converted to voltage, one
still can see the 6Hz variations on the 25003 Hz and still refers to those
as tone and beat. These exist in mathematically formulation of the
resulting waveforms not just as something in the brain.

What is the mathematical formulation?

"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:

"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:


--snippety-snip--

You said you are a physicist/engineer.
What does "linear" mean?

Let's not get too far off the subject here. We were discussing
whether
the "tuning beat" that you use to tune a musical instrument involved
a
nonlinear process (ie. "modulation").

Then linearity is at the core of the matter.
What does "linear" (or "nonlinear") mean to you?

OK, if you insist -- *in this case* it means "linear enough to not
produce IM products of significant amplitude".

Good enough.
Then spectrum analyzers and the human auditory
system are not linear.
Stay with me here.


I said that it does not, and that
it could be detected by instrumentation which was proveably linear
(i.e.
not "perfectly" linear, because that's not required, but certainly
linear enough to discount the requirement for "modulation").

No nonlinearity is necessary in order to hear
a beat?
Where does the beat come from?

As the phase of the two nearly equal waves move past each other, there
is simple vector summation which varies the amplitude.

Consider two sine waves of precisely the same frequency, where one of
them is adjustable in phase -- use a goniometer, for instance. Use a
set
of resistors to sum the two signals, and observe the summing point with
a 'scope or a loudspeaker. By altering the phase of one source, you can
get any amplitude you want from zero up to twice the amplitude of
either
one.

Now just twiddle that phase knob around and around as fast as you can.

You've just slightly altered the instantaneous frequency of one of the
generators (but only while you twiddle), and accomplished pretty much
the same effect as listening to the beat between two guitar strings at
nearly zero frequency offset. With no nonlinear processes in sight.

Isaac

You put some effort into that. I give you
credit for that.

The socratic thing isn't working, so here
you go.

I would appreciate it if you would take the time to list *in detail* any
errors in what I wrote. If it "isn't working", I need to know why,
because I don't like to be confused about things.

Is an envelope detector linear? The answer is no.

That's correct, and I'm well aware of it, but so what?

No you're not.

"Yup. And the spectrum analyzer is (hopefully) a very linear system,
producing no intermodulation of its own."

Hopefully?

Is a spectrum analyzer linear?
"I'm sure there's more than one way to do it, but I feel certain..."
Dodging the question.

Which of them is linear?

"a bolometer just turns the signal power into heat; nothing
nonlinear there..."

(Bolometers are no more linear than envelope detectors.)

What does "linear" mean?

"Let's not get too far off the subject here."

Dodging the subject because you don't
understand the subject.



--dissertation on how an envelope detector works snipped--

Vain "editing".


Do you see how this applies to spectrum analyzers
and the human auditory system?

Sure. But

1) It is possible -- if not practical -- to build a "detectorless" (in
the nonlinear process sense) spectrum analyzer, and

Red herring.


2) None of it is even remotely significant to the subject at hand.

A repeat of your earlier dodging.


Here it is again: the "beat" one hears when tuning a guitar or other
instrument does *not* require any nonlinear process for its production.
Period.

You didn't know a spectrum analyzer is nonlinear.
You didn't/don't know that a bolometer is nonlinear.
You wouldn't and don't know nonlinearity even when you
hear it.


Isaac

You are a poseur.