Re: two sine tones simultaneously within one critical band (Piotr Majdak )

Subject: Re: two sine tones simultaneously within one critical band
From:    Piotr Majdak  <piotr.majdak(at)OEAW.AC.AT>
Date:    Fri, 7 Oct 2005 16:32:12 +0200

Bob Masta wrote:

 > I am completely at a loss to understand how you arrived
 > at your last formula.  It appears that you have not simply
 > added the pressure waves, but multiplied them.


cos(2pi*t) * cos(100 * 2pi*t) = cos(99*2pi*t) + cos(101*2pi*t)

This can be derived using:

cos(x1)*cos(x2) = 1/2*cos(x1-x2) + 1/2*cos(x1+x2)

Another explanation can be: two frequencies (99Hz and 101Hz) can be seen 
as one absent carrier (100Hz) modulated with a modulator (1Hz).

br, Piotr Majdak


-- 
Piotr Majdak
Acoustic Research Institute
Austrian Academy of Sciences
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