[LAD] Circular Reasoning

Lars Luthman lars.luthman at gmail.com
Fri Aug 31 13:07:49 UTC 2007

On Fri, 2007-08-31 at 14:59 +0200, Jens M Andreasen wrote:
> 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.

At a lower frequency the magnet has to work against the tension of the
membrane for a longer time - I'm sure a speaker cone doesn't obey a
perfect Hooke's law, but it may have something to do with it.

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