Sound propagates according to the "inverse square law", that is well defined here:
So the intensity equals 1/distance^2
Like the image in the above link shows clearly, when the intensity at the distance r is 1, then the intensity at the distance 2r is 1/4
Now, my doubts started after my sound engineering teacher said that by "doubling the distance, the sound pressure become half".
that doesn't agree with the above "inverse square law". In fact, according to my teacher, the intensity at r is 1 and the intensity at r2 is 0.5.
Then, I looked a the formula for DBSpl, and that's what I found:
DBspl = 20*log(I1/I2)
Using my teacher numbers, that would be:
DBspl = 20*log(0.5/1) = 20*0.3 = 6 db
Now, I checked to some sound engineering textbooks and actually they confirm what my teacher says. In fact they say the sound decrease 6 db every time we double the distance.
But this is not the "inverse square law", isn't it?
Where is the error? I'm doing something wrong? Or is the teacher doing something wrong? Or is the textbook saying something wrong?
When I asked this same question to my teacher he couldn't help me neither, and seemed to be puzzled by the question too.