Re: Wave Intensity vs Energy

[Leigh Palmer <palmer@SFU.CA>]

> I was reading about Richter scales and how the scale is logarithmic. Which
> implies that a single digit increase on the scale means the intensity is 10
> times stronger with about 32 times more energy.
>
> What is the mathematical relationship between wave intensity and energy?

A logarithmic scale is one on which a single digit increment corresponds
to a change in the represented quantity by a constant factor, not
necessarily ten. Several examples come to mind:

Musical pitch is quantified in *semitones* on the logarithmic scale of
even temperament, each of which represents an increase in fundamental
frequency by a factor of the twelfth root of two.

The apparent brightness of stars is quantified on a logarithmic scale of
*stellar magnitudes*. Each increment in this scale corresponds to a
decrease in flux measured through a cononical spectral filter by a factor
of the fifth root of one hundred.

Sound intensity is quantified on a logarithmic scale of *decibels*, each
of which represents an increase in intensity by a factor of the tenth root
of ten. The unit is derivative, but the underlying unit (the bel) is never
used in practice, and "deci-" is a somewhat disreputable SI prefix anyway.

The list goes on and on, but I don't have the Richter scale at hand (I'm
sure it can be found easily on the web), but it is a similar scale. I just
wanted to dispel that misconception about what a logarithmic scale is.

In many waves (light, sound) energy intensity is proportional to the
square of the wave amplitude. This is true of earthquakes as well.

Leigh