On Fri, 06 Jul 2007 19:04:00 -0000, Jim Kelley
wrote:

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

So if you have for example, a 300 Hz signal and a 400 Hz signal, your
claim is that you also hear a 700 Hz signal? You'd better check
again. All you should hear is a 300 Hz signal and a 400 Hz signal.
The beat frequency is too high to be audible.

---
Well, I'm just back from the Panama Canal Society's 75th reunion and
I haven't read through the rest of the thread, but it case someone
else hasn't already pointed it out to you, it seems you've missed
the point that a non-linear detector, (the human ear, for example)
when presented with two sinusoidal carriers, will pass the two
carrier frequencies through, as outputs, as well as two frequencies
(sidebands) which are the sum and difference of the carriers.

In your example, with 300Hz and 400Hz as the carriers, the sidebands
would be located at:

f3 = f1 + f2 = 300Hz + 400Hz = 700Hz

and

f4 = f2 - f1 = 400Hz - 300Hz = 100Hz


both of which are clearly within the range of frequencies to which
the human ear responds.
---

(Note that if the beat
frequency was a separate, difference signal as you suggest, at this
frequency it would certainly be audible.)

---
Your use of the term "beat frequency" is confusing since it's
usually used to describe the products of heterodyning, not the
audible warble caused by the vector addition of signals close to
unison.
---

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...

Excessive cone excursion can produce significant 2nd harmonic
distortion. But at normal volume levels your ear does not create
sidebands, mixing products, or anything of the sort. It hears the
same thing that is shown on both the oscilloscope and on the spectrum
analyzer.

---
No, it doesn't.

Since the response of the ear is non-linear in amplitude it has no
choice _but_ to be a mixer and create sidebands.

What you see on an oscilloscope are the time-varying amplitude
variations caused by the linear vector summation of two signals
walking through each other in time, and what you see on a spectrum
analyzer is the two spectral lines caused by two signals adding, not
mixing. If you want to see what happens when the two signals hit
the ear, run them through a non-linear amp before they get to the
spectrum analyzer and you'll see at least the two original signals
plus their two sidebands.
---

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.

My comments were based on my results in that experiment, common
knowledge, and professional musical and audio experience.

---
Your "common knowledge" seems to not include the fact that a
non-linear detector _is_ a mixer.
---

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.

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.

---
The "beat" heard wasn't an actual beat frequency, it was the warble
caused by the change in amplitude of the summed signals and isn't a
real, spectrally definable signal.

The reason you didn't hear the real difference frequency is because
it was below the range of audible frequencies and the reason you
didn't hear the sum frequency is because it was close enough to the
second harmonic of the output of either oscillator (with the
oscillators close to unison) that you couldn't discern it from the
fundamental(s).

There also seems to be a reticence, on your part, to believe that
the ear is, in fact, a mixer and, consequently, you hear what you
want to.

But...

In order to bring this fol-de-rol to an end,I propose an experiment
to determine whether the ear does or does not create sidebands:

+-------+ +--------+
| OSC 1 |----| SPKR 1 |---/AIR/--- TO EAR
+-------+ +--------+

+-------+ +--------+
| OSC 2 |----| SPKR 2 |---/AIR/--- TO EAR
+-------+ +--------+

+-------+ +--------+
| OSC 3 |----| SPKR 3 |---/AIR/--- TO EAR
+-------+ +--------+

1. Set OSC 1 and OSC 2 to two harmonically unrelated frequencies
such that their frequencies and the sum and difference of their
frequencies lie within the ear's audible range of frequencies.

2. Slowly tune OSC 3 so that its output crosses the sum and
difference frequencies of OSC 1 and OSC 2.

If a warble is heard in the vicinity of either frequency, the ear is
creating sidebands.

I'll do the experiment sometime today, if I get a chance, and post
my results here. Since you're all set up you may want to do the
same thing.



--
JF