On Thu, 5 Jul 2007 20:02:15 -0600, "Bob Myers"
wrote:


"John Fields" wrote in message
.. .

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.

Sorry, John - while the ear's amplitude response IS nonlinear, it
does not act as a mixer.

---
Sorry, Bob, If the ear's amplitude response is nonlinear, it has no
choice _but_ to act as a mixer.
---

"Mixing" (multiplication) occurs when
a given nonlinear element (in electronics, a diode or transistor, for
example) is presented with two signals of different frequencies.
But the human ear doesn't work in that manner - there is no single
nonlinear element which is receiving more than one signal.

---
Not true.

Just look at the tympanic membrane, for example.

Consider it a drumhead stretched across a restraining ring and it
becomes obvious that the excursion of its center with respect to the
pressure exerted on its surface won't be constant for _any_ range of
sound pressure levels it experiences.

Consequently, when it's hit with two different frequencies, its
displacement will vary non-linearly with the pressures they exert
and sidebands will be generated.
---

Frequency discrimination in the ear occurs through the resonant
frequencies of the 20-30,000 fibers which make up the basilar
membrane within the cochlea. Each fiber responds only to those
tones which are at or very near its resonant frequency. While
the response of each fiber to the amplitude of the signal is nonliner,
no mixing occurs because each responds, in essence, only to a
single tone. A model for the hearing process might be 30,000 or
so non-linear meters, each seeing the output of a very narrow-band
bandpass filter covering a specific frequency within the audio
range. There is clearly no mixing, at least as the term is commonly
used in electronics, going on in such a situation, even though there
is non-linearity in some aspect of the system's response.

Audible "beats" are perceived not because there is mixing going on
within the ear, but instead are due to cycles of constructive and
destructive
interference going on in the air between the two original tone

---
Not necessarily.

More on Sunday.



--
JF