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

In article ,
"Ron Baker, Pluralitas!" wrote:

"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.

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

AM electromagnetic waves: 20 KHz modulation frequencyonanastronomically-low carrier frequency
 

In article ,
"Jimmie D" wrote:

"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?


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.

There's no advantage to DSB-SC that SSB-SC doesn't have and several that
SSB-SC alone has. Getting rid of one of the redundant sets of sidebands
halves the required bandwidth, for one. Also, if the two sideband sets
of DSB-SC experience differing phase alteration due to propagation
effects (not too uncommon), the signal can become unintelligible; that
effect is minimized with SSB-SC.

If all broadcasters used SSB-SC and precision frequency control (easy
and inexpensive these days) then SSB-SC receivers are pretty easy. But
that doesn't solve the problem of all those AM receivers...

Things seem to be moving in the direction of digital modulation and even
more complex receivers; whether that's a Good Thing or not, I'm not sure.

Isaac

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

Jim Kelley wrote:
Hein ten Horn wrote:

We hear the average of two frequencies if both frequencies
are indistinguishably close, say with a difference of some few
hertz. For example, the combination of a 220 Hz signal and
a 224 Hz signal with the same amplitude will be perceived as
a 4 Hz beat of a 222 Hz tone.

I have also read this accounting, but from what I've been able to determine
it lacks mathematical and phenomenological support. Here's why. As two
audio frequencies are moved closer and closer together, there is no point
where an average of the two frequencies can be perceived. There is however
a point where no difference in the two frequencies is perceived. Obviously
if we cannot discern the difference between 220Hz and 224Hz (as an example),
we are not going to be able to discern half their difference either. 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.

The math is perfectly describing what is happening in the
course of time at an arbitrary location in the air or in the
medium inside the cochlea. Concerning the varying
amplitude it does a good job.
But does someone (here) actually know how our hearing
system interprets both indistinguishable(!) frequencies (or
even a within a small range rapidly varying frequency) and
how the resulting 'signal' is translated into what we call the
perception? Evidently the math given above doesn't
reckon with any hearing mechanism at all. Hence it cannot
rule out perceiving an average frequency.

For the rest I don't get your point on a varying period.
From a mathematical point of view the function

sin( pi * (f_2 + f_1) * t )

has a constant frequency of (f_2 + f_1)/2
and a constant period of 2/(f_2 + f_1).
This frequency is indeed the arithmetical average and
it is not affected by a multiplication of the function by
a relatively slow varying amplitude.

An interesting related experiment can be performed by setting a sweep
generator to sweep over a narrow range of frequencies. The range can be
adjusted as well as the sweep time. One can then study what sorts of
effects are discernible.

I have found that it is very difficult to fool the ear in some of the ways
that have been suggested. It does not appear, for example, that the claim
for 'perceiving the average' is valid for two arbitrarily close frequencies
any more than it is for any two other frequencies. But I would appreciate
learning of any contradictory research that you might be able to cite.

Apart from the mathematical support, I saw the average
frequency mentioned in several books on physics, unfortunately
without further enclosed proof (as far as I remember).
However, getting some empirical evidence should be a
rather easy piece of work.

gr, Hein

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

"Hein ten Horn" wrote in message
...
| Jim Kelley wrote:
| Hein ten Horn wrote:
|
| We hear the average of two frequencies if both frequencies
| are indistinguishably close, say with a difference of some few
| hertz. For example, the combination of a 220 Hz signal and
| a 224 Hz signal with the same amplitude will be perceived as
| a 4 Hz beat of a 222 Hz tone.
|
| I have also read this accounting, but from what I've been able to
determine
| it lacks mathematical and phenomenological support. Here's why. As two
| audio frequencies are moved closer and closer together, there is no
point
| where an average of the two frequencies can be perceived. There is
however
| a point where no difference in the two frequencies is perceived.
Obviously
| if we cannot discern the difference between 220Hz and 224Hz (as an
example),
| we are not going to be able to discern half their difference either. 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.
|
| The math is perfectly describing what is happening in the
| course of time at an arbitrary location in the air or in the
| medium inside the cochlea. Concerning the varying
| amplitude it does a good job.
| But does someone (here) actually know how our hearing
| system interprets both indistinguishable(!) frequencies (or
| even a within a small range rapidly varying frequency) and
| how the resulting 'signal' is translated into what we call the
| perception? Evidently the math given above doesn't
| reckon with any hearing mechanism at all. Hence it cannot
| rule out perceiving an average frequency.
|
| For the rest I don't get your point on a varying period.
| From a mathematical point of view the function
|
| sin( pi * (f_2 + f_1) * t )
|
| has a constant frequency of (f_2 + f_1)/2
| and a constant period of 2/(f_2 + f_1).
| This frequency is indeed the arithmetical average and
| it is not affected by a multiplication of the function by
| a relatively slow varying amplitude.
|
| An interesting related experiment can be performed by setting a sweep
| generator to sweep over a narrow range of frequencies. The range can be
| adjusted as well as the sweep time. One can then study what sorts of
| effects are discernible.
|
| I have found that it is very difficult to fool the ear in some of the
ways
| that have been suggested. It does not appear, for example, that the
claim
| for 'perceiving the average' is valid for two arbitrarily close
frequencies
| any more than it is for any two other frequencies. But I would
appreciate
| learning of any contradictory research that you might be able to cite.
|
| Apart from the mathematical support, I saw the average
| frequency mentioned in several books on physics, unfortunately
| without further enclosed proof (as far as I remember).
| However, getting some empirical evidence should be a
| rather easy piece of work.
|
| gr, Hein

Actually the human ear can detect a beat note down to a few cycles.

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

"NotMe" hath wroth:

(Please learn to trim quotations)

Actually the human ear can detect a beat note down to a few cycles.

No, you cannot. Figure on 20Hz to 20KHz for human hearing:
http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml

What happens when you zero beat something is that your brain is
filling in the missing frequencies. As you tune across the frequency,
and the beat note goes down in frequency, most people overshoot to the
other side, and then compensate by splitting the different. As you
approach zero beat, your perception of the sound drops. If the lack
of hearing below 20Hz doesn't make it disappear, the frequency rolloff
in the audio amplifier stages will probably also drop off at about
20-300Hz depending on whether it's a hi-fi or communications radio. I
have a home made DC coupled hi-fi and can see the speaker moving in
and out slowly at very low frequencies. I don't hear a thing.

However, you don't have to hear it to detect infrasonic sounds.
http://en.wikipedia.org/wiki/Infrasound
Your inner ear, which is responsible for your sense of balance, can do
that for you. You don't actually hear the tone, but your body
certainly responds to it. Depending on frequency and level, tones
below about 20Hz will bring on confusion, nausia, disorientation, and
all manner of sensory anomalies. It's been used for effects in music,
sound tracks, and military weapon systems. I've experienced the
effects personally and can assure you that it was not pleasant.

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

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

On Wed, 11 Jul 2007 22:52:17 -0700, Jeff Liebermann wrote:

"NotMe" hath wroth:

(Please learn to trim quotations)

Actually the human ear can detect a beat note down to a few cycles.

No, you cannot. Figure on 20Hz to 20KHz for human hearing:
http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml

What happens when you zero beat something is that your brain is filling in
the missing frequencies. As you tune across the frequency, and the beat
note goes down in frequency, most people overshoot to the other side, and
then compensate by splitting the different.

No, you've got it all wrong. The beat note happens because, when the
signals are close to 180 degrees out of phase, they cancel out such that
there is, in fact, no sound. This is what your ear detects. Now, if
you're zero-beating, say, 400 Hz against 401 Hz, I don't know if the
801 Hz component is audible or if it's even really there, but
mathematically, it kinda has to, doesn't it?

Thanks,
Rich

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

Rich Grise hath wroth:

On Wed, 11 Jul 2007 22:52:17 -0700, Jeff Liebermann wrote:

"NotMe" hath wroth:

(Please learn to trim quotations)

Actually the human ear can detect a beat note down to a few cycles.

No, you cannot. Figure on 20Hz to 20KHz for human hearing:
http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml

What happens when you zero beat something is that your brain is filling in
the missing frequencies. As you tune across the frequency, and the beat
note goes down in frequency, most people overshoot to the other side, and
then compensate by splitting the different.

No, you've got it all wrong.

Sorry, I'm perfect and never make misteaks.

The beat note happens because, when the
signals are close to 180 degrees out of phase, they cancel out such that
there is, in fact, no sound. This is what your ear detects. Now, if
you're zero-beating, say, 400 Hz against 401 Hz, I don't know if the
801 Hz component is audible or if it's even really there, but
mathematically, it kinda has to, doesn't it?

Ok, I'll bite. I think you'll find that if you actually do that with
a non-distorting audio mixer[1], and look at an oscilloscope, you'll
see the 1Hz envelope, but the 400 and 401 Hz tones will still be
there. Same on a spectrum analyzer, where the two carriers (400/401)
are still there. If they're there, you'll hear them. The tones may
be going up and down once per second (1Hz), but you'll still hear
tones in between. No way are they going to disappear with a 1Hz
separation. However, if they're exactly on the same frequency, and
exactly 180 degrees otto phase, they will cancel.

The zero beat example I offered is more a psychology problem than
acoustics or hearing. Our ears and brain expect the sweep through
zero beat to be continuous, that we fill in the missing frequencies.
It's really apparent in ham radio, where tuning across carriers is a
common event. I've watched how people do it, and noticed that they
always overshoot and come back to the perceived center. If you ask
them to nail the frequency to within 10Hz without overshooting, they
usually have a difficult time.

[1] no compression, limiting, fuzz box, reverb, equalizer, etc.

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

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

Rich Grise wrote:

On Wed, 11 Jul 2007 22:52:17 -0700, Jeff Liebermann wrote:

"NotMe" hath wroth:

(Please learn to trim quotations)

Actually the human ear can detect a beat note down to a few cycles.

No, you cannot. Figure on 20Hz to 20KHz for human hearing:
http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml

What happens when you zero beat something is that your brain is filling
in
the missing frequencies. As you tune across the frequency, and the beat
note goes down in frequency, most people overshoot to the other side, and
then compensate by splitting the different.

No, you've got it all wrong. The beat note happens because, when the
signals are close to 180 degrees out of phase, they cancel out such that
there is, in fact, no sound. This is what your ear detects. Now, if
you're zero-beating, say, 400 Hz against 401 Hz, I don't know if the
801 Hz component is audible or if it's even really there, but
mathematically, it kinda has to, doesn't it?

Thanks,
Rich

No, It doesn't have to be there (the 801 Hz frequency). If your method
of 'beating' two signals together is by adding them, then there is no 801
Hz tone, only the 400 and 401 Hz tones.

With two function generators and a spectrum analyzer you can see this.

With a scope, you can see that the zero crossings in the summation occur at
a 400.5 Hz rate.

This is exactly what the trig identity earlier in the thread indicates.

If your method of beating is via multiplication, then there will be 0, 400,
401 and 801 Hz signals present (assuming the mixer is not balanced).

When you are discussing 'beating' two signals together you need to indicate
whether you are adding or multiplying the signals. The results are
different.

If you are multiplying two signals to find a zero beat with your ear, that
is difficult as you will be trying to hear tones less than 20 Hz.

If you are adding two signals to find a zero beat, that is easy because you
are listening to a tone that is at the average frequency. In the above
example, at 400.5 Hz.

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

Hein ten Horn wrote:

The math is perfectly describing what is happening in the
course of time at an arbitrary location in the air or in the
medium inside the cochlea. Concerning the varying
amplitude it does a good job.
But does someone (here) actually know how our hearing
system interprets both indistinguishable(!) frequencies (or
even a within a small range rapidly varying frequency) and
how the resulting 'signal' is translated into what we call the
perception?

Evidently the math given above doesn't
reckon with any hearing mechanism at all. Hence it cannot
rule out perceiving an average frequency.

The mathematics doesn't provide the possibility except, as I have
noted, for brief instants of time. There exists no "wave of average
frequency" in the frequency spectrum of the sum of two waves. A
Fourier analysis of the function doesn't reveal one. The ear doesn't
"produce" one. And I can tell you from personal and professional
experience that it does not hear one. (A triad chord would be truly
awful to experience if it did.)

For the rest I don't get your point on a varying period.
From a mathematical point of view the function

sin( pi * (f_2 + f_1) * t )

has a constant frequency of (f_2 + f_1)/2
and a constant period of 2/(f_2 + f_1).
This frequency is indeed the arithmetical average and
it is not affected by a multiplication of the function by
a relatively slow varying amplitude.

Yes. But when multiplied by a sinusoidal function of a different
frequency (as is the actual equation), the amplitude is affected in a
way which varies in both magnitude and sign with time, and which
affects both the peak spacing and the zero crossings differently from
one cycle to the next as a function of relative phase. If one defines
the period of a waveform as the length of one cycle of a waveform,
then this length of time varies in the way I have previously
described. Please consider using Mathematica or your favorite
plotting program to examine this for yourself.

Apart from the mathematical support, I saw the average
frequency mentioned in several books on physics, unfortunately
without further enclosed proof (as far as I remember).

Apart from the mathematical support, that is also what I have found.
However, I believe this usage has been disappearing in recent years as
re-evaluation replaces reiteration as a means for producing text
books. All I can say is that it appears the claim may have been made
by someone without sufficient experience in the particular field. I
can find no support, anecdotal, phenomenological, psychoacoustical, or
mathematical for the contention (repeated by rote from what I can
tell) that the ear hears the average when the two frequencies are
arbitrarily 'close'.

I've never heard it, and I've been playing musical instruments for 47
years, doing audio electronics for almost 30, and physics for the last
20. The notion appears to me to be speculation based upon little more
than a perfunctory analysis of the underlying mathematics.

It might be more reasonable to claim that what is heard is a slight,
slow warble in frequency, back and forth, from one pitch to the other
accompanyied by a corresponding change in volume. But when the beat
frequency is low, the two pitches are so close together that the
difference between them is not discernable.

However, getting some empirical evidence should be a
rather easy piece of work.

Easier to say than do, certainly, but an interesting and enjoyable
endeavor nevertheless. :-)

jk

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

Jim Kelley wrote:

Hein ten Horn wrote:

The math is perfectly describing what is happening in the
course of time at an arbitrary location in the air or in the
medium inside the cochlea. Concerning the varying
amplitude it does a good job.
But does someone (here) actually know how our hearing
system interprets both indistinguishable(!) frequencies (or
even a within a small range rapidly varying frequency) and
how the resulting 'signal' is translated into what we call the
perception?

Evidently the math given above doesn't
reckon with any hearing mechanism at all. Hence it cannot
rule out perceiving an average frequency.

The mathematics doesn't provide the possibility except, as I have
noted, for brief instants of time. There exists no "wave of average
frequency" in the frequency spectrum of the sum of two waves. A
Fourier analysis of the function doesn't reveal one. The ear doesn't
"produce" one. And I can tell you from personal and professional
experience that it does not hear one. (A triad chord would be truly
awful to experience if it did.)

For the rest I don't get your point on a varying period.
From a mathematical point of view the function

sin( pi * (f_2 + f_1) * t )

has a constant frequency of (f_2 + f_1)/2
and a constant period of 2/(f_2 + f_1).
This frequency is indeed the arithmetical average and
it is not affected by a multiplication of the function by
a relatively slow varying amplitude.

Yes. But when multiplied by a sinusoidal function of a different
frequency (as is the actual equation), the amplitude is affected in a
way which varies in both magnitude and sign with time, and which
affects both the peak spacing and the zero crossings differently from
one cycle to the next as a function of relative phase.


How can the zero crossings be affected? Zero multiplied by any other value
is still 0. All zero crossings in sin( pi * (f_2 + f_1) * t ) occur at the
expected time. Multiplication by a cos term does not change a single one.
(It will add a few additional ones where the cos term evaluates to 0.)
There are no phase effects here.

If one defines
the period of a waveform as the length of one cycle of a waveform,
then this length of time varies in the way I have previously
described. Please consider using Mathematica or your favorite
plotting program to examine this for yourself.

Defining the period as time between zero crossings leads to the frequency
not changing as you describe.


Apart from the mathematical support, I saw the average
frequency mentioned in several books on physics, unfortunately
without further enclosed proof (as far as I remember).

Apart from the mathematical support, that is also what I have found.
However, I believe this usage has been disappearing in recent years as
re-evaluation replaces reiteration as a means for producing text
books. All I can say is that it appears the claim may have been made
by someone without sufficient experience in the particular field. I
can find no support, anecdotal, phenomenological, psychoacoustical, or
mathematical for the contention (repeated by rote from what I can
tell) that the ear hears the average when the two frequencies are
arbitrarily 'close'.

I've never heard it, and I've been playing musical instruments for 47
years, doing audio electronics for almost 30, and physics for the last
20. The notion appears to me to be speculation based upon little more
than a perfunctory analysis of the underlying mathematics.

It might be more reasonable to claim that what is heard is a slight,
slow warble in frequency, back and forth, from one pitch to the other
accompanyied by a corresponding change in volume. But when the beat
frequency is low, the two pitches are so close together that the
difference between them is not discernable.

However, getting some empirical evidence should be a
rather easy piece of work.

Easier to say than do, certainly, but an interesting and enjoyable
endeavor nevertheless. :-)

jk