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<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
title=sarah@gendernet.org href="mailto:sarah@gendernet.org">Sarah =
Fox</A> </DIV>
<DIV><B>To:</B> <A title=donmannino@attbi.com
href="mailto:donmannino@attbi.com">Donald Mannino</A> </DIV>
<DIV><B>Sent:</B> Wednesday, December 04, 2002 10:35 AM</DIV>
<DIV><B>Subject:</B> Re: audible resultant from two supersonic
frequencies?</DIV></DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Hi Don,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><<I agree- it would be in the playback. I used a high =
sampling
rate to try to eliminate the possibility of interference with the usual =
44.1 kHz
CD sampling rate. Zooming in on the waverform view in Cool Edit (the =
program I
used to create the file) shows 24 samples for each 5 cycles, so this =
verified
the 96kHz sample rate.>></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>That should do =
it.</FONT><BR><BR><<I don't
really know how the computer DACs deal with this, though. Maybe =
there are
distortions taking place there, if they cannot deal directly with the =
96kHz
sample rate. But the 500hz tone is easily identified, sounds like =
a sine
wave, and the pitch is spot on, as verified by tunelab (thanks, Bob!) on =
my
Pocket PC.>></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The DAC can deal with the 96 kHz sample =
rate just
fine, and with amazing linearity. I never cease to be amazed at =
just how
good even the crummiest el-cheapo sound card can be.</FONT><BR><BR><FONT =
face=Arial size=2>After some reflection, I'm almost certain which =
nonlinearities
underlie the effect you've created. It's nothing to do with =
the
sampling of the two tones. It is irrelevant whether you computed =
the
tones or created them with a signal generator. It is also =
irrelevant
whether the individual tones have any distortion products, since those =
would be
ultrasonic as well. All that matters is interactions between the =
tones --
one tone interfering with how the other tone is reproduced or =
propagated, which
is of course due to some nonlinearity somewhere. It's probably not =
any
nonlinearity in the DAC, since those things are so amazingly good. =
It's
probably not any nonlinearity in the speakers/headphones, since the cone =
excursion would be almost zero at those frequencies. Rather (and =
I'd bet
money on it), it's a nonlinearity in the amplifier circuitry -- probably =
inside
the PC speakers into which you plugged your headphones. If you =
have your
headphones plugged directly into the sound card, it's the same story, =
since
sound cards stop being linear under load, owing to the power demands on =
their
analog circuitry.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>While digital cirtuitry is amazingly =
good, and
while some amplifier circuitry is also amazingly good, the little amps =
inside PC
speakers are pretty crummy and create a lot of distortion. This =
distortion
probably takes the form of "soft clipping," in which the peak voltages =
in the
waveform aren't quite as high or low as they should be. Why is =
this?
The amplifier simply can't keep up with the current demands of the =
speaker at
the higher voltages in the waveform, so the voltage sags a bit. =
Now if
this happens more on one side than the other (e.g. on the negative side =
of the
waveform), then you have a nonlinearity that could very easily generate =
the 500
Hz difference tone. (For those of you who are curious, yes, =
voltage does
usually sag more on one side of the waveform.)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>How does this all work? =
Think of it this
way: The speakers probably can't reproduce (and you probably can't =
hear)
the 20 kHz signals. What they can reproduce and what you can hear =
is the
average voltage in the waveform. Assuming linearity in the =
waveform, the
average voltage wouldn't vary over time. Howwever, if there is =
soft
clipping on one side of the waveform, the average does move. When =
the two
signals are interfering destructively (resulting in lower amplitude), =
the output
is probably linear, and the average voltage is zero. When the two =
signals
interfere constructively (resulting in higher amplitude), and when one =
side of
the waveform (e.g. the negative side) can't reach its full amplitude =
because of
soft clipping, then the average voltage of the waveform is no longer =
zero.
If the soft clipping is on the negative side of the waveform, the =
average
voltage will stray towards the positive. And thus there is a 500 =
Hz
fluctuation in voltage between zero and some small (but quite audible) =
positive
voltage. Again, I'd bet money that this is the source of your
effect.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Peace,</FONT></DIV>
<DIV><FONT face=Arial size=2>Sarah</FONT></DIV>
<DIV><FONT face=Arial size=2>Peace,</FONT></DIV>
<DIV><FONT face=Arial size=2>Sarah</FONT></DIV>
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