# Non-linearity of wattage to SPL...

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#### JoeBob

I know as wattage increases SPL increase isn't linear, but my questions is if at 1 watt there's an SPL of say 90dB, what wattage would it takke to reach 93dB?

Also, a speaker with a sensitivity of 102dB at 1 watt, what SPL would it put out at 10w, 100w and 500w?

I just don't know what the curve for the increase in SPL looks like, and it's been bothering me that I don't know...

#### hifi

1W = +0db (speaker sensitvity as it is speced at one watt)
2W = +3db
4W = +6db
8W = +9db
16W = +12db
32W = +15db
64W = +18db
128W = +21db
256W = +24db
512W = +27db
1024W = +30db

hopes this helps..

#### JoeBob

Oh, I didn't think doubling wattage caused a 3dB increase. I don't know why, I guess I heard it somerwhere. Silly question, at least it straightened me out...

#### Helix

db's are simply the log of a ratio,

so a doubling of power is 2/1

and when dealing with power we mutilply by 10 hence

10*log 2 = 3db

so an increase from 2 to 16 watts is :

10*log 16/2 = 9db

When dealing with voltage then you multiply by 20. Also you have to be careful with the sign and context of where it's quoted, because you could be talking 3dbs down (attenuated) or 3 db up (gain) or even -3db down (gain!).

If i had a filter and at a particular frequancy, on the input i had 10 volts and on the output there was 5 volts, i could calculate how many db's the signal is being attenuated :
20 *log 10/5 = 6db

*LECTURE MODE OFF*

#### PassFan

JoeBob:
Helix is right. This is a complex subject. If you care to read more on this subject do a search on the different forumns. Theres plenty in here.

#### cyclotronguy

As I remember one dB is an acoustic change that is only just discernable. Hearing is non-linear, ten dB gain is perceived as twice as loud; ten dB reduction half as loud.

Cyclotronguy

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