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 higher2?, 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:
