(September 15, 2023 at 1:34 pm)BrianSoddingBoru4 Wrote:

(September 15, 2023 at 1:24 pm)Deesse23 Wrote: 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

(September 15, 2023 at 2:14 pm)Anomalocaris Wrote:

(September 15, 2023 at 1:34 pm)BrianSoddingBoru4 Wrote: 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

dB is a logarithmic scale,  105dB sound is 316 times more energetic than 80dB sound.   Adding 80.000 dB sound on top of 105.000dB sound yields 105.014dB sound, which rounds back down to 105db.   logarithmically the power in 80db sound is just too puny next to that in 105dB sound to register significantly on top of 105 dB.

I wish we could have avoided this rabbit hole, but here we go..

There are actually TWO db scales. 20 x log and 10x log

10x log is used for comparing energies, 20x log for units that are the sqrt of energies (or db-wise 1/2).
For sound this is the energy of the sound as opposed to the pressure, because the energy is equal to pressure squared (x2 in dbs) thus you just use x10 instead of x20.
I was assuming his device measures air pressure, not sound energy.

(September 15, 2023 at 2:14 pm)Anomalocaris Wrote:

(September 15, 2023 at 1:34 pm)BrianSoddingBoru4 Wrote: 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

dB is a logarithmic scale,  105dB sound is 316 times more energetic than 80dB sound.   Adding 80.000 dB sound on top of 105.000dB sound yields 105.014dB sound, which rounds back down to 105db.   logarithmically the power in 80db sound is just too puny next to that in 105dB sound to register significantly on top of 105 dB.

Which is what I said earlier. At least I think that’s what I said - that you can’t simply add decibels. xdB + xdB doesn’t equal 2xdB.

Boru

(September 15, 2023 at 2:32 pm)Deesse23 Wrote:

(September 15, 2023 at 1:34 pm)BrianSoddingBoru4 Wrote: 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

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

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

Boru

(September 15, 2023 at 2:49 pm)BrianSoddingBoru4 Wrote:

(September 15, 2023 at 2:14 pm)Anomalocaris Wrote: dB is a logarithmic scale,  105dB sound is 316 times more energetic than 80dB sound.   Adding 80.000 dB sound on top of 105.000dB sound yields 105.014dB sound, which rounds back down to 105db.   logarithmically the power in 80db sound is just too puny next to that in 105dB sound to register significantly on top of 105 dB.

Which is what I said earlier. At least I think that’s what I said - that you can’t simply add decibels. xdB + xdB doesn’t equal 2xdB.

Boru

You cant add dbs direclty, but the values add, and depending on the result your resulting db values ads numerically less.
dbs arent numbers but factors. You dont add factors. You convert to numbers and then go back to total factor.

Heres a good source if you want to understand the topic

http://www.sengpielaudio.com/calculator-db.htm

(September 15, 2023 at 1:35 pm)Foxaèr Wrote: I still don't know all the things I don't know.

I am even worse.  I know none of the things I don’t know.

(September 15, 2023 at 2:55 pm)Deesse23 Wrote:

(September 15, 2023 at 2:49 pm)BrianSoddingBoru4 Wrote: Which is what I said earlier. At least I think that’s what I said - that you can’t simply add decibels. xdB + xdB doesn’t equal 2xdB.

Boru

You cant add dbs direclty, but the values add, and depending on the result your resulting db values ads numerically less.
dbs arent numbers but factors. You dont add factors. You convert to numbers and then go back to total factor.

Heres a good source if you want to understand the topic

http://www.sengpielaudio.com/calculator-db.htm

I really don’t.

Boru

(September 15, 2023 at 2:52 pm)BrianSoddingBoru4 Wrote:

(September 15, 2023 at 2:32 pm)Deesse23 Wrote: 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.

All I said was that 80dB + 105dB isn’t 185dB. That’s true as far as it goes, even if it’s drastically over simplified. It’s not an invitation to teach me math. I’m 53 years old and you can’t make me do math!! I won’t I won’t I won’t!! Neener neener!

Boru

I wasn't going to say anything. You can add db but since it is logarithmic instead of linear, you will not get results comparable to if the measures were linear.