"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.