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

"Bob Myers" hath wroth:

"Jeff Liebermann" wrote in message
.. .
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.

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.

You can demonstrate it to yourself with a suitable audio spectrum
analyzer and tone generators. I recommend "Visual Analyzer 8"
http://digilander.libero.it/hsoft/
Generate two sine waves at any frequencies. Use a cheap microphone to
pickup the audio and display it with the audio SA. You won't see any
sums, differences, or intermodulation products unless you over drive
the microphone or try to produce the tones from a single loudspeaker.

Kindly supply a suitable correction or explanation. I'll gladly
entertain the possibility that I'm wrong.

That was exactly my point. Please read ALL responses I've
made re this topic.

My appologies for not reading all of the 269 posting to this thread.
The thread is a classic case of topic drift. I though I would check
the topic de jure and found your posting.

--
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
 

"Jeff Liebermann" wrote in message
...
isw hath wroth:

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

What am I suppose to look for? I appreciate your recommended research
project, but frankly, I don't care what happens inside a high powered
horn loudspeaker. I prefer to stay fairly on topic about the original
allegation that mixing somehow occurs in open air, which is not true.

Incidentally, if mixing did occur in open air or inside the ear, you
would not be able to comfortably listen to hi-fi music, as all you
would hear would be intermodulation products.

Yes everything would become ultra sonici

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

"Jeff Liebermann" wrote in message
...
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 - 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," however, and that is the result of the amplitude
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
perceive such amplitude variations if they occur below a certain
rate.

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.

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

"Bob Myers" hath wroth:


"Jeff Liebermann" wrote in message
.. .
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 - which, again, is as I explained it further on. I said that
there is no actual component at the "beat" frequency.

So, there's no "component" of the "beat" frequency. Well, in my
limited knowledge of what the term "beat" means in RF circuitry, it's
normally used in the context of a multiplicative mixing function, such
as BFO (beat frequency oscillator). Is there some other way to create
a "beat" frequency other than multiplicative (mixing)? I don't know
of any.

Also, what's a "component" of the beat frequency? Is that just one of
the numerous N*F1 +/- M*F1 multiplicative mixer products?

You do
HEAR a "beat," however, and that is the result of the amplitude
variation caused by the interference, as noted.

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.

I'm also having a problem with your use of the term interference. In
the present context, I would presume this to be something involving
interferometer or quantum wave mechanics. I guess I've been out of
the broadcast business for too long.

I did manage to find a nifty Java applet that shows the effects of
acoustic interference:
http://falstad.com/interference/
It appears to refer to variations in amplitude across the area where
both tones are present. What's missing is any reference to any beat
note. Certainly additive mixing is present as this is what causes the
variations in amplitude. However, I don't see any reference to "beat"
notes in any of the articles explaining audio interference phenomenon.
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
perceive such amplitude variations if they occur below a certain
rate.

I'll make it easy. The difference of the two tones are in the audible
range. For example, 25KHz and 26KHz to produce a 1KHz beat note. The
amplitude component is certainly there as you demonstrated with your
explanation of audio "interference". So, do I hear the 1KHz, or don't
I hear the 1KHz? If I hear it, where does the mixing occur?

I have never ever said that "mixing" (multiplication) occurs in air.
"An audible beat tone is produced by the constructive and
destructive interference between two sound waves in air."
How else are you going to produce an *audible* beat note except by
multiplicative mixing?

Actually, I have an issue with only one word in the above quotation.
It's not audible. Drop that word and it's mostly correct.

If you're going to pick apart what someone is saying, then please
read everything they've said before starting.

Actually I did. I read most of the 270 odd articles in this thread,
but I ignored any that were obviously a waste of time, such as those
consisting of massive quotation with one line of worthless drivel
added.

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.

Are my comments really out of context? I had issues with much of what
was said in this thread. Never mind the topic drift and inane
responses. I resisted temptation and did not respond to any of these
until someone, in this case you, went off what I consider to be the
deep end. I did not question your qualifications, did not send you
off on some reading adventure, and addressed your specific statements
directly, as I'm doing in this reply.

However, I can do it your way. Your previous reply reeks of
blustering and I would advise you cease and desist.



--
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
 

"Jeff Liebermann" wrote in message
...
So, there's no "component" of the "beat" frequency.

"At" the beat frequency is what I said; by that, I mean there is no
signal at that frequency. "Component" is commonly used when
speaking in the frequency domain.

Well, in my
limited knowledge of what the term "beat" means in RF circuitry,

And you're correct within that context, but remember we're talking
about sound waves in air in the examples being discussed here. Within
THAT context, "beat" is commonly used to refer to the audible wavering
of the perceived sound when two tones are sounded which are very
close in frequency. For instance, when tuning a stringed instrument - a
guitar, let's say - you will often sound the desired pitch by fingering a
string which is already known to be in tune, and then adjusting the string
being tuned by listening for the "beat" between its note and the reference.
As the "beat" slows and eventually vanishes altogether, you know you
have properly tuned that string.


it's
normally used in the context of a multiplicative mixing function, such
as BFO (beat frequency oscillator). Is there some other way to create
a "beat" frequency other than multiplicative (mixing)? I don't know
of any.

See above. Different context, different use of the same word.


Also, what's a "component" of the beat frequency? Is that just one of
the numerous N*F1 +/- M*F1 multiplicative mixer products?

Again, the phrase was "component AT the beat frequency." Meaning
that, of the total signal being considered (which must always be either
a pure sinusoid itself, or something which can be represented as the sum
of sinusoids), no part of that complete signal is a sinusoid at the "beat"
frequency.


Interesting. So, using my original example, if I take two ultrasonic
tones, above human hearing, you suggest that I do *HEAR* a beat,

Not at all - remember, the "beat" in question here is actually just the
low-frequency amplitude variation of the combined signal (which is
the sum of two sinusoids). But if you can't hear a signal at the
frequencies
in question anyway, you certainly can't hear the amplitude variation.
Again, take a look at what this summed signal looks like in the time
domain, and you'll see what I mean.


I'm also having a problem with your use of the term interference. In
the present context, I would presume this to be something involving
interferometer or quantum wave mechanics. I guess I've been out of
the broadcast business for too long.

"Interference" is commonly used to refer to the effect that two signals
have upon each other, esp. when said signals are at similar or
identical frequencies. For example, if two signals are added which are
at the same frequency and amplitude, but 180 degrees out of phase, you
have complete cancellation - which may then be referred to as an example
of "destructive interference." Addition of the same signals but IN phase
would be "constructive interference."


I did manage to find a nifty Java applet that shows the effects of
acoustic interference:
http://falstad.com/interference/
It appears to refer to variations in amplitude across the area where
both tones are present. What's missing is any reference to any beat
note. Certainly additive mixing is present as this is what causes the
variations in amplitude.

Exactly - and this is the "beat" as that word is used in acoustic or
musical contexts. Again, please keep in mind that we've been discussing
the behavior of sound waves in air, not electrical signals within a
circuit. This would typically not be referred to as "mixing," though,
in any context in which that might be confused with the effects of
multiplication.



I'll make it easy. The difference of the two tones are in the audible
range. For example, 25KHz and 26KHz to produce a 1KHz beat note. The
amplitude component is certainly there as you demonstrated with your
explanation of audio "interference". So, do I hear the 1KHz, or don't
I hear the 1KHz? If I hear it, where does the mixing occur?


You do not hear it, per the above. Thee is no actual 1 kHz tone
generated, but there IS an amplitude variation in the "envelope" of
the combined signal. (You wouldn't hear it even if the signals in
question were within the audible range, as a 1 kHz variation is too
rapid for human perception to detect.)


I have never ever said that "mixing" (multiplication) occurs in air.
"An audible beat tone is produced by the constructive and
destructive interference between two sound waves in air."
How else are you going to produce an *audible* beat note except by
multiplicative mixing?

I've already said that my use of the word "tone" was a possible source
of confusion. There IS, however, an audible effect at the beat rate, if
the signals in question are close enough together in frequency. Have
you ever tuned an instrument?

However, I can do it your way. Your previous reply reeks of
blustering and I would advise you cease and desist.

Hopefully, you now, at this point, have a different opinion. If not,
well, I don't suppose there's much more to be said.

Bob M.

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

In article ,
Jeff Liebermann wrote:

isw hath wroth:

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

What am I suppose to look for?

Information about the nonlinearity of air; what else? You said
"compression of air is very linear", but there are situations in
acoustics where it is not.

Isaac

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

Jeff Liebermann wrote:


As I stated earlier in this thread
(though more towards its tail)...

quote
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.
unquote

Let me use this example to take away
some possible misinterpretations.

"An audible beat tone is produced by the constructive and
destructive interference between two sound waves in air."

The statement above is true if you leave out the word "tone".
From the example: there's no 222 Hz tone in the air.
In our perception however the 222 Hz tone 'exists'
and that's why we don't have to leave out the word "audible".
Yet, I'd preferred this one:
A beat is produced by the constructive and destructive
interference between two sound waves in air.
To be complete, using the word "tone" referring to 4 Hz
would make the statement misleading because we do not
hear frequences as low as 4 Hz.


I did manage to find a nifty Java applet that shows the effects of
acoustic interference:
http://falstad.com/interference/
It appears to refer to variations in amplitude across the area where
both tones are present. What's missing is any reference to any beat
note.

Well, try this one.
http://www.ngsir.netfirms.com/englishhtm/Beats.htm


I'll make it easy. The difference of the two tones are in the audible
range. For example, 25 kHz and 26 kHz to produce a 1 kHz beat note.

We can hear beat frequencies up to say 15 Hz.
Our auditory organ is not able to follow faster amplitude
variations.
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.

And with two very different frequencies within the audible
range, for instance 220 Hz and 880 Hz, we here only these
two frequencies. No average frequency and no beat.

HTH

gr, Hein

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

"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.

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

On Sun, 08 Jul 2007 11:12:56 -0700, Jeff Liebermann
wrote:

isw hath wroth:

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

What am I suppose to look for? I appreciate your recommended research
project, but frankly, I don't care what happens inside a high powered
horn loudspeaker. I prefer to stay fairly on topic about the original
allegation that mixing somehow occurs in open air, which is not true.

---
That's not true. The original allegation was mine, and was that
since the ear is a device with an "output" which doesn't change
linearly with linearly changing input amplitudes, it's a non-linear
device, is incapable of _not_ producing harmonics and heterodynes
and, as such, is where the mixing occurs.

My contention was that zero-beat was the difference frequency
between two input tones close to unison, and I still maintain that's
true and that that difference frequency is in there. However, your
contention that zero-beat is the result of the vector summation of
two tones close to unison is also valid, since a non-linear detector
is capable of doing that summation well enough to allow that be the
dominant phenomenon as evidenced by the fact that the ear is
incapable of directly detecting (say) a 1Hz tone but is fully
capable of hearing the 1Hz amplitude warble which would result from
the vector addition of the two tones.
---

Incidentally, if mixing did occur in open air or inside the ear, you
would not be able to comfortably listen to hi-fi music, as all you
would hear would be intermodulation products.

---
_All_ you would hear?

That's grossly untrue. What do you think would happen to the
_played_ notes?

They'd all disappear in a cacophony of chaos just because some
lower-level cross-products were being produced?

Nonsense.

In fact, contrary to what you may believe, the ear _is_ a non-linear
detector and, consequently, _cannot_ help but heterodyne its inputs.

That's why, after thousands of years of experimenting with what
notes sound good when they're played together and which notes don't,
music is written the way it is.

Something else you may not be aware of is that musical instruments
are inherently non-linear and, as such, will generate harmonics of
any fundamental notes played on them and heterodynes if two or more
notes are played simultaneously.


--
JF

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

Hein ten Horn wrote:

Jim Kelley wrote:

On Jul 5, 9:38 pm, John Fields wrote:

Sure enough, I heard the beat even though it came from different
sources, but I couldn't quite get it down to DC even with the
scope's trace at 0V.

Of course you heard beats. What you didn't hear is the sum of the
frequencies. I've had the same setup on my bench for several months.
It's also one of the experiments the students do in the first year
physics labs. Someone had made the claim a while back that what we
hear is the 'average' of the two frequencies. Didn't make any sense
so I did the experiment. The results are as I have explained.


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.

gr, Hein

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.

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.

Regards,
jk

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

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

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

"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?

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

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.

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

"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?

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

"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??

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

"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

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

"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.

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

"Bob Myers" wrote in message
...

"Jeff Liebermann" wrote in message
...
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.

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

"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?

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

"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.

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

"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.

AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
 

On 7/10/07 3:26 AM, 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?

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.



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.

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

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

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

How did you jump to that conclusion.

Is "DSBSC" DSB?

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

Bob M.

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

In message , Don Bowey
writes
On 7/10/07 3:26 AM, 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?

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.



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.



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

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

David L. Wilson wrote:

"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?

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

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

Jim Kelley wrote:

David L. Wilson wrote:

"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?

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.

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

craigm wrote:
Jim Kelley wrote:


David L. Wilson wrote:


"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?

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.

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

AM electromagnetic waves: 20 KHz modulationfrequencyonanastronomically-low carrier frequency
 

"Don Bowey" wrote in message
...
On 7/10/07 3:26 AM, 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?

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.



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.

AM electromagnetic waves: 20 KHzmodulationfrequencyonanastronomically-low carrier frequency
 

On 7/10/07 6:54 PM, in article ,
"Dana" wrote:


"Don Bowey" wrote in message
...
On 7/10/07 3:26 AM, 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?

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.

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


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.

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.


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.

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.


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.

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



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.

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 ,
"Ron Baker, Pluralitas!" wrote:

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

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.

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

Isaac

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