Fw: audible resultant from two supersonic frequencies?

Sarah Fox sarah@gendernet.org
Wed, 4 Dec 2002 11:02:52 -0500


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----- Original Message -----=20
From: Sarah Fox=20
To: Donald Mannino=20
Sent: Wednesday, December 04, 2002 10:35 AM
Subject: Re: audible resultant from two supersonic frequencies?


Hi Don,

<<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.>>

That should do it.

<<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.>>

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.

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.

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.)

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.

Peace,
Sarah
Peace,
Sarah


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