What do you know today that you didn't know yesterday?

[Deesse23]

Not really

To be precise: db = 20 log (a1/a2)
+20db = x10
+3db =   x1.4 (sqrt(2) to be precise)
-20db = x 0.1 (1/10)
-3db =   x0.7 (1/1.4, or 1/sqrt(2)to be precise)

Thus something +3db bigger than something else is 40% bigger!
Thus something -3db smaller than something else is 30% smaller!
Adding two EQUAL things is doubling them. 20x log(2) = +6db, or x sqrt(2)^2

The log is the reason why you cant just add dbs. Adding dbs would be multiplying values. You have to convert to "normal" numbers, then add, then convert back to dbs. Dbs arent good for adding numbers, but for MULTIPLYNG.  adb + bdb = a x b (old fashioned slide rules used this, before we had electronic calculators).
Dbs are good for showing any multiplicative effects
Dbs are good for estimating dominant and negligible effects (because of the multiplicative nature)

Now, as i previously said, your table saw is actually x10 times louder than the dust extractor. Or, the dust extractor ads just 10% (1/10) of the table saw to the total sound. The total sound is 1,1 the table saw. The big question is: How many db is x1.1 (see above)?
db is 20 x log (a1/a2), a1/a2= 1,1, thus both devices combined are  +0.8db louder than the table saw. Be careful when taking measurements. Air pressure decreases with the square of the distance. So make sure to

#1 measure both devices from the same distance individually
#2 put them next to each other (or place your meter exaclt yhalfway between both devices) and measure with same distance FROM BOTH

If you do it properly, and if your meter is sensitive enough (10% should be easily possible), you should see a total just short of +1db more than your table saw.

Your homework for today: Check it out and report back to class, ASAP :-P

Then I wasn’t actually wrong when I said, ‘Decibels are not additive’?

I reject the homework assignment. I’ll take the fail.

Boru

dbs are counter intuitive to untraine dpeople. It takes a little bit of time (and understanding the math) to get used to this.

Lots of effects in nature (like acoustic fields, or any other fields) work with the 1/r or 1/r^2 rule. These fields don tget weaker with an additive effect, but a multiplicative/divisive one. So converting to dbs and adding is much easier. Also the 1/r curve gets transformed into a LINE with the slope being the exponent.
Another view of this whole idea is like this: You have + x and ^ (addition, multiplication and potency, "levels 1-3" so to speak). Writing stuff down in dbs basically converts potencies to multiplication and multiplication to addition. You go down one level!

Adding dbs is actually multiplying --> if you wanna multiply, just add dbs
Multiplying dbs is actually potentiating --> if you wanna potentiate, just multiply dbs
Now for your "problem" again: "less than adding" * dbs is actually adding --> if you wanna add (sound pressure or energy), you need to "less than add" (level 0 so to speak) dbs, :-P thats why 105db + 85db is just WAY LESS than 185db

*there is no word for the operation one level below addition.....not that i know of

A very powerful way to juggle around numbers.........before we had pocket claculators.