**Subject: **Where's the beating?FWD from AUDITORY

**From: **Kevin Austin (*kevin.austin@videotron.ca*)

**Date: **Sun Oct 09 2005 - 12:05:12 EDT

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*>
*

*>Topics of the day:
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*>
*

*> 1. two sine tones simultaneously within one critical band (3)
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*>
*

*>----------------------------------------------------------------------
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*>
*

*>Date: Sat, 8 Oct 2005 11:32:24 -0400
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*>From: Bob Masta <audio@DAQARTA.COM>
*

*>Subject: Re: two sine tones simultaneously within one critical band
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*>
*

*>Dear list:
*

*>
*

*>There is no question that the sum of two
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*>sines can be expressed as the product
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*>of two cosines of sum-and-difference frequencies,
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*>as in:
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*>
*

*>sin(A) + sin(B) = 2*cos(.5(A-B))*sin(.5(A+B))
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*>
*

*>But this most definitely does NOT demonstrate the
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*>production of real acoustic beat frequencies.
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*>It just says that you can think of the two original
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*>sines as the product of two particular cosines.
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*>This is essentially amplitude modulation, with
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*>the sides of the equation reversed. Yes, we
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*>know that if you *multiply* two frequencies, the
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*>product will consist of two other frequencies.
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*>
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*>That's not what we are talking about with beats.
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*>When you add two frequencies linearly, the sum
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*>contains *only* those two frequencies. This is
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*>the definition of linearity. If you get anything else you
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*>have intermodulation distortion from some system
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*>nonlinearity. In fact, the standard test for IM is to drive a
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*>system at two frequencies and look for difference tones.
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*>
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*>The fact that we can hear beats tells us about
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*>the auditory system, not about external reality.
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*>They are not present as real acoustical sound
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*>components, assuming you have taken reasonable
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*>care in the production of the two tones. (Not too
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*>loud from a single speaker or other nonlinear system,
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*>for example.)
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*>
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*>Those with Windows computers are welcome to
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*>download my free DaqGen software <www.daqarta.com>
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*>and visualize this for yourself. You can generate two sine
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*>waves and look at the the waveform and spectrum of the
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*>total before it goes out to your sound card, so it does not
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*>include speaker distortions, etc. You will see only
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*>two spectral peaks. (Assuming you set each primary
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*>"Stream" level at 50% or less, so the sum doesn't clip.)
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*>You will want to use higher frequencies than 99 and 101, to
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*>get better spectral resolution. Try 4000 and 5000. You will
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*>see a 1 msec periodicity in the waveform, but you will not
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*>see any component at 1000 Hz in the spectrum.
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*>
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*>Beats are really, truly "all in your head"!
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*>
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*>Best regards,
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*>
*

*>Bob Masta
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*>
*

*>audioATdaqartaDOTcom
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*>
*

**Next message:**sylvi macCormac: "re: NASA & Puppet Plays wit Rubber Time"**Previous message:**Prof Malone: "Re: indefinite pitch"**Next in thread:**Rick: "Re: Where's the beating?FWD from AUDITORY"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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