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:
