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 ...

```