quick one for those who know their sound level equations

[deadtom]

If you had 3 fans, each producing an intensity level of 17dB, what would the resultant intensity level of 3 fans side by side?

I have worked it out to what I think it would be, but I'm not so confident on the maths so would like to hear from other people who are smarter than I.

thanks,

Tom

[Xerstead]

IIRC 10db equates to a doubling of the percieved loudness, so 3 fans @17db would be:
17 + 10(doubles volume) +5 (half as much again) = 32? assuming constructive interference.

[deadtom]

hmm, I've always thought of it as being more complicated than that.

i got 21.76db, because:

each fan = 17dB

Intensity, I = ?
minimum intensity audible to human ear, I0 (0 is meant to be subscript) = 1x10^-12 Wm^2
Intensity level, IL = 10log(I/I0) dB

-> 17 = 10log(I/1x10^-12)

-> I = I0 x 10^(17/10)

-> I = ~5x10^-11 Wm^-2

3 fans = 3 times intensity = 3 x I = ~1.5x10^-10 Wm^-2

as noted above, intensity level = 10log(I/I0) dB

-> 10log(1.5x10^-10/10^-12) = ~21.76 dB

[Simpo Two]

Wouldn't it depend on whether the sound waves were in or out of phase? Two fans out of phase might be silent... anti-noise etc....

[mattnunn]

Ouch,

Unfortunately it's not so simple. Assuming you have three noise sources equidistant from a receiver (you're ear) and the three noise sources are in phase (this is important,) then you can expect a 3dB gain for the second noise source added (that's a doubling) and about a 4.8(ish) dB gain for the addition of the third noise source, that would be dBA or sound power which (along with variations db B and dB C are supposed to reflect for the operation of the human ear.

Unweighted pure sound pressure level or dB SPL doubles every 6dB, the third source would give you a rise of 9.6dB - but that's pure logarithmic representation of power, different from what your ear might perceive.

Basically get to Maplin and buy a cheap Noise Measuring device, use it, then take it back.

[deadtom]

ok well for the sake of simplicity, assume no interference occurs

[deadtom]

mattnunn said:

stuff

so its not as simple as, like i did, working out the intensity at the source, then tripling it and finding the subsequent intensity level?

[mattnunn]

deadtom said:

mattnunn said:

stuff

so its not as simple as, like i did, working out the intensity at the source, then tripling it and finding the subsequent intensity level?

No.

So get a calculator (with a log button) and do 10 (log(2)) That's you doubling = 3dB

10 (log(3)) that's you tripling 4.7dB

10 (log(4)) that's you quadrupling 6dB

That's your basic logarithmic, looks exponential on a log graph, rise. Used to express all sorts of power

But sound as perceived by your lugs doesn't work like that because your ears themself have a specific response, to power as well as frequency, which is why dB A,B,C are used.

Lookey here...

http://www.engineeringtoolbox.com/adding-decibel-d...

http://www.engineeringtoolbox.com/sound-power-leve...

[deadtom]

mattnunn said:

10 (log(3)) that's you tripling 4.7dB

which equals 17+4.7 = 21.7, which is what i got.

using my way, if there were just two fans, ie a doubling of intensity the result would be 10log(10^-10/10^-12) = 20 dB, which is the same as your 17+3 method.

and quadruplinh would be 10log(2x10^-10/10^-12) = 23dB = 17+6 dB

I guess the way I did it is the long hand version of the way you describe?

[mattnunn]

deadtom said:

mattnunn said:

10 (log(3)) that's you tripling 4.7dB

which equals 17+4.7 = 21.7, which is what i got.

using my way, if there were just two fans, ie a doubling of intensity the result would be 10log(10^-10/10^-12) = 20 dB, which is the same as your 17+3 method.

and quadruplinh would be 10log(2x10^-10/10^-12) = 23dB = 17+6 dB

I guess the way I did it is the long hand version of the way you describe?

Sorry, yes I wasn't saying you were wrong, I just wanted to point out that dB SPL and dB A were different.

As an aside that's a very quiet fan(s) you have, does your ear perceive the extra noise when you turn the second and third one on?

[deadtom]

ah ok, I thought you meant my answer was wrong, and i was stumped as to why my maths didnt work until i actually did the numbers your way and found that they came out the same

and its not my fans in question, it just came up on a well known imageboard that i frequent, and no one else managed to come up with the answer.

but yeah, 17dB is extremely quiet, but they are only computer cooling fans so i guess they would be

[paranoid airbag]

I think (I may be wrong - I couldn't show working to back this up) that if you're adding incoherent sound sources (i.e. just as likely to destructively interfere as constructively), the total expected sound intensity is proportional to the square root of the number of sources - so root(3) times the intensity, not 3 times. Although you could have completely in-sync fans I suppose.