"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

"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

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

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

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

Sigh - 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.

"Bob Myers" hath wroth:


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

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

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

Sigh - 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

"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.

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

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

"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.

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

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