Re: Sine wave construction using calculous or some approximation thereof - question.

In article <1140111842.413925.15850@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
jhuie <jehuie@xxxxxxxxxxxxx> wrote:
Interesting. I've been looking at some of the examples and it's
fascinating. The main reason I've been curious is because I thought
you could make up and function from a series of smaller (lower
amplitude) waves. But I'm not sure that's true by looking at the
examples.

In terms of an example, say you had 1,000 tiny speakers. Could you
some how arrange those and control them with a computer so that they
"add up" to create the sound of one large speaker? Could you somehow
approximate a very low note from a combination of speakers that
individually can only produce high notes? See where I'm going with
this?

I'm confused about what you're asking. Is the issue amplitude or
frequency? If it's amplitude, then yes, the sum of a bunch of
functions a_n sin(w t) is (sum of the a_n) sin(w t). You can make
a large-amplitude wave from a lot of small-amplitude waves of the
same frequency. If it's frequency, then no, you can't add a bunch
of high notes to get a low note. However, you can run the sum
through a nonlinear process to get a low note. That's exactly
what your AM radio does, taking a radio-frequency input and
extracting an audio-frequency output.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


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