This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment ----- 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 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/37/0a/b8/59/attachment.htm ---------------------- multipart/alternative attachment--
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