alt.sci.physics.acoustics

Keith Carlson wrote:
> The definition I know is:
>
> SPL = 20 log (p1/p0), or 10 log (p1/p0)^2 (where "^2" means to the
> power of 2)
>
> I understand that the factor of 10 is because it's expressed in decibels as
> opposed to bels. My specific question, though, is why is the ratio squared?
> If p0 is the reference pressure level, and p1 is the measured pressure
> level, why isn't SPL just the log of that ratio, similar to the way sound
> power level is the log of power level ratio?

For some years, I puzzled over the same thing. After all, a foot is a
foot, and a horsepower is a horsepower; what could be simpler? Then
along came acoustics with its occurrence in 3D space, and electrical
engineering, and things were not so simple anymore.

At one time, I compared it to dollars; what happened if your salary
went up one decibel. Would that be ten percent more? Or is it 20, or more?

A quandary.

Suppose we decide that it should relate to energy (e.g. horsepower).
Dollars would have to be like that, so a 1 dB increase in salary has to
be over 20%.

Then there is the inverse "square" law... For a doubling of distance
from a source, the energy intensity is 1/4 that before. For acoustics we
then have a coherent set of metrics.

Similarly, in electrical engineering, we can speak of voltage or of
power. For double voltage, we have four times the power. For a given
signal, one can refer to its level as being in relation to a fixed
quantity such as a volt or a watt. We should want consistency if at all
possible.

Some consistency has been found in acoustics by noting that the
intensity, DEFINED here as the power incident on a unit area, is
proportional to pressure squared. The decibel level is then defined as
ten times the logarithm of the pressure ratio squared (the ratio of the
subject acoustic pressure to a reference acoustic pressure).

If one only knows the pressure in linear units (pounds per square inch,
or pascals), then the same acoustic level expression is obtained by
moving the exponent two outside the log function where it becomes just a
factor of 2, making the multiplier to be 20 instead of 10. Nothing has
changed except for the position of the factor 2.

To settle all questions of it being 10 or 20, resolution of the
reference quantity and the measurement quantity needs to be settled;
i.e. the foot vs the horsepower.

In the case of computer software writing, there is no alternative to
the fact that the programmer MUST have some knowledge of the acoustics
and physics of the phenomenon for which he is composing software to
represent. To not do so will place his software products in great
jeopardy, aandoften they will be useless.

Angelo Campanella