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

[Deesse23]

Wrong

DBs are multiplicative, in that they provide a multiplicative scale for numbers.

Adding DBs equals MULTIPLYING values.
Example: +20db = x 10, +40db = 10 x 10 = 100, +60Db = 10 x 10 x 10 = 1000, -20db = 1/10, etc

Thus the machine with +20db more noise level is TEN times louder than the other*. APPROXIMATELY the 100db machine is dominant (assuming the sound waves do not create interference, cancel each other out n stuff. Lets not go down that rabbi thole today), because the total air pressure is only x1,1 of the dominant one.

That way you can easily display wide ranges of numbers in plots, or display certain behaviours that are multiplicative, making them look "Linear" in the "multiplicative realm" of DBs.

*in terms of air pressure..... but heres the catch: With +20db the air pressure is TEN times more, but human ears work in a LOGARITHMIC scale, just like DBs and we have subjectively linear perception according to a db scale! That way we can distinguish between a sound of  a fly and a starting 747 next to us, two sound events separated by 10^12 in terms of sound pressure. We dont perceive the plane being gazillions of times louder, but only tousands of times, according to the multiplicative perception we have. We kinda perceive an event with 60+db (compared to another), which is x1000 times louder, in fact like 3x (+20db) louder.

According to my sound meter, my shop vac/dust extractor runs at 80dB, my table saw at 105dB. When I run both together, I get a reading of 105dB.

Am I looking at this wrong?

Boru

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