[Keith Carlson]

Well, I know what the definition is, but I'm trying to understand where it
comes from to help me remember it. I tend to get SPL vs sound power level
mixed up (as well as when it's 3db or 6db that represents a doubling).

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?