On Thu, 05 Jul 2007 18:37:21 -0700, Jim Kelley
wrote:

John Fields wrote:

You missed my point, which was that in a mixer (which the ear is,
since its amplitude response is nonlinear) as the two carriers
approach each other the difference frequency will go to zero and the
sum frequency will go to the second harmonic of either carrier,
making it largely appear to vanish into the fundamental.

Hi John -

Given two sources of pure sinusoidal tones whose individual amplitudes
are constant, is it your claim that you have heard the sum of the two
frequencies?

---
I think so.

A year or so ago I did some casual experiments with pure tones being
fed simultaneously into individual loudspeakers to which I listened,
and I recall that I heard tones which were higher pitched than
either of the lower-frequency signals. Subjective, I know, but
still...

A microphone with an amplitude response following that of the human
ear might do better.

Interestingly, this afternoon I did the zero-beat thing with 1kHz
being fed to one loudspeaker and a variable frequency oscillator
being fed to a separate loudspeaker, with me as the detector.

I also connected each oscillator to one channel of a Tektronix
2215A, inverted channel B, set the vertical amps to "ADD", and
adjusted the frequency of the VFO for near zero beat as shown on the
scope.

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.

Close, though, and as it turned out it wasn't the zero output
amplitude as shown by the scope which made the difference, it was
the amplitude of the signals which got to my ear(s). As fate would
have it, I have two ears, with some distance between them, so
perfect cancellation in one left some uncancelled signal in the
other, obviating what otherwise might have been perfect silence.
Except, perhaps, for the heterodynes.

Anyway, I'm off to the 75th reunion of the Panama Canal Society and
the 50th reunion of the Cristobal High School Class of '57 in
Orlando, so I'll see y'all when I get back on Sunday, GLW.


--
JF