[LAD] Circular Reasoning

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 ...