AM electromagnetic waves: 20 KHz modulation frequency on an astronomically-low carrier frequency

[craigm]

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.

 

[Ron Baker, Pluralitas!]

How did you jump to that conclusion.

Is "DSBSC" DSB?

 

[Dana]

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??

 

[Ron Baker, Pluralitas!]

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.

 

[Ron Baker, Pluralitas!]

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.

 

[Ron Baker, Pluralitas!]

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.

 

[Ron Baker, Pluralitas!]

...
...
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?

 

[Ron Baker, Pluralitas!]

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.


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".

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.

 

[Jimmie D]

Is "DSBSC" DSB?

There have been attempts to remove the carrier but receivers could not be
manufatured at a reasonable price that would demodulate the signal with the
fidelity of an AM BCB signal. Probably could be done today but what would
you l do with all those AM rx that suddenly dont work when the transition is
made.

 

[Don Bowey]

I see Jimmie talked all around your question.

I'll answer it AGAIN, though I'm still sure your only a troll.....

DSB says nothing about the carrier; DSBSC is still DSB.

You can have DSBSC (Suppressed Carrier), DSBRC (Reduced Carrier), and DSB
with Full Carrier. You can look up the abbreviation for the latter if you
need it.

Broadcast medium wave radio, slang term "AM Radio," is DSB with full
Carrier.

 

[Bob Myers]

Is "DSBSC" DSB?

Obviously, since it has both sidebands. What it's
missing, vs. "normal" AM, is the carrier.

Bob M.

 

[Ian Jackson]

I see Jimmie talked all around your question.

I'll answer it AGAIN, though I'm still sure your only a troll.....

DSB says nothing about the carrier; DSBSC is still DSB.

You can have DSBSC (Suppressed Carrier), DSBRC (Reduced Carrier), and DSB
with Full Carrier. You can look up the abbreviation for the latter if you
need it.

Broadcast medium wave radio, slang term "AM Radio," is DSB with full
Carrier.

Just out of interest....
http://www.vkham.com/vk8da/documents/ModesOfOperation.pdf
Ian.
--

 

[Jim Kelley]

Jim Kelley wrote:




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.

And hence, the misconception.

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.

Evidently you have not actually studied the waveform as a function of
time.

jk

 

[Jim Kelley]

...



Ok.

The period of the 'enveloped' waveform (or the arcane, beat



??

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

The error here is in assuming that the sin and cos terms in the
equivalent expression are representative of individual waves. They
are not. The resultant wave can only be accurately described as the
sum of the constituent waves sin(a) and sin(b), or as the function
2sin(.5(a+b))cos(.5(a-b)). That function, plotted against time
appears exactly as I have described. I have simply reported what is
readily observable.

jk

 

[craigm]

The error here is in assuming that the sin and cos terms in the
equivalent expression are representative of individual waves. They
are not. The resultant wave can only be accurately described as the
sum of the constituent waves sin(a) and sin(b), or as the function
2sin(.5(a+b))cos(.5(a-b)). That function, plotted against time
appears exactly as I have described. I have simply reported what is
readily observable.

jk

I would submit you plotted it wrong and/or misinterpreted the results.

 

[Jim Kelley]

Jim Kelley wrote:





I would submit you plotted it wrong and/or misinterpreted the results.

Always a possibility, admitedly. However the superposition of two
waves each having a different frequency does not yield a resultant
waveform having a constant period. But you are certainly welcome to
try to demonstrate otherwise.

jk

 

[Dana]

I see Jimmie talked all around your question.

Actually Jimmie gave a plausable reason to your statement/question that AM
broadcasters are wasting money by generating a carrier.

I'll answer it AGAIN, though I'm still sure your only a troll.....

DSB says nothing about the carrier; DSBSC is still DSB.

You still have to have a carrier to modulate.

You can have DSBSC (Suppressed Carrier), DSBRC (Reduced Carrier), and DSB
with Full Carrier. You can look up the abbreviation for the latter if you
need it.

And you still need to modulate a carrier. So your statement/question that AM
broadcasters are wasting money by generating a carrier was illogical in the
context of this thread.

Broadcast medium wave radio, slang term "AM Radio," is DSB with full
Carrier.

So then you agree that the Broadcasters are not wasting money by generating
a carrier.

 

[Don Bowey]

Actually Jimmie gave a plausable reason to your statement/question that AM
broadcasters are wasting money by generating a carrier.

Actually, he talked about the topic without answering the question asked by
the OP.

You still have to have a carrier to modulate.

Obviously a reference carrier is required..... So what's your point? "DSB"
tells us NOTHING about the carrier; is it suppressed, reduced, or full in
the transmitted signal?

Maybe you should read an entire post before replying.

And you still need to modulate a carrier. So your statement/question that AM
broadcasters are wasting money by generating a carrier was illogical in the
context of this thread.

I did not ever say AM broadcasters are wasting money by generating a
carrier. Get your story straight.

You need a reference carrier for generating sidebands, but you do not "need"
to transmit the carrier unless it's required by a specific service.

So then you agree that the Broadcasters are not wasting money by generating
a carrier.

Read the sentence just above your above sentence. A transmitted, full
carrier is required for the broadcast service. Other services don't require
it.

 

[isw]

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.

And you still didn't address the original point. Why not?

Isaac

 

[isw]

Red herring.

It's important to know when a statement like: "There's no mixing
happening in the air. compression of air is very linear" is nearly
correct (because it's never precisely correct), and when it's really
pretty incorrect. You can call that a "red herring" if you like; others
might call it "knowing what you're talking about".

Isaac