Klarinet Archive - Posting 000521.txt from 2001/02

From: Grant Green <gdgreen@-----.com>
Subj: Re: [kl] The combination paradox
Date: Wed, 14 Feb 2001 14:13:33 -0500

>Now, if a simple sine wave, of frequency P, excites a medium such as air
>that responds linearly to the excitation, then the excitation is
>transmitted as a sound wave, and consists entirely of the frequency P on
>arrival. And *because of what linearity of response means*, if I have
>another frequency Q that excites the air simultaneously, then the
>resultant excitation consists of the sum of the excitations P and Q, and
>nothing else.

Realization dawns :-) This is what is missed before. The beat
phenomena occurs due to the simple addition of two waves, which due
to their frequency difference move in and out of phase. The
difference frequency occurs only in the ear (or other non-linear
system), because the heterodyne effect requires nonlinearity in order
to happen. Thus, beats are "real", but the difference frequency
should not register on a linear detector.

Tony, thanks for your explanation and patience :-)

Grant

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