[LAD] Circular Reasoning
Jens M Andreasen
jens.andreasen at comhem.se
Fri Aug 31 12:59:55 UTC 2007
Late one friday afternoon, a sound-engineer was sitting in his chair
admiring a brand new pair of flat frequency response monitors. He then
observed the following:
For two frequencies represented by sine-waves and an octave apart to
have the same relative loudness, the higher octave will need to have its
amplitude adjusted to half of that of the lower octave.[1]
Both frequencies will then force a membrane to travel the same distance
within a given timeframe - the higher will go half as far but twice as
often than the lower - and they will also both have the same speed or
steepness at the zero-crossing.
Surprisingly, the lower frequency consumes four times as much energy
than the higher[2], although it is apparently not doing any more actual
work.
Therefore, it is a better excersize to take a walk around the block,
rather than running around in small circles.
QED
cheers! // Jens M Andreasen
[1] Assuming that a saw wave has an even distribution
of harmonics and can be written as:
saw(t){ for(k = 1;k < inf;k++) rv += sin(k*t)/k; return rv * 2/M_PI}
[2] Ohms law ...
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