[ot] Decibels and the ear (was: Re: [plug] Hot and bothered CPU hankers for cool breeze)

[James Devenish]

In message <20031216150328.GA11572 at erdos.home>
on Tue, Dec 16, 2003 at 11:03:28PM +0800, Cameron Patrick wrote:
> On Tue, Dec 16, 2003 at 10:25:51PM +0800, James Devenish wrote:
> 
> | Okay then, I have no reason to think you're right or wrong (in fact, I'd
> | forgotten that decibels may be closely related to aural perceptions,
> | since they're also used for general signal analysis). But I'm going to
> | stick to good-old 10log(f) for now. So, let's say one machine is 50dbA
> | (hey, isn't rounding nifty!). That's 10^{-8}Wm^{-2} (is it?). So 400
> | times that would be...60--70dbA?? So that would be, say, 30% louder in
> | perception? Well, that would seem to match Derek's story! :)
> 
> Yep :-)  You're probably right-er than my original calculations...

Geez. I got the calculation wrong. Let me try again with a calculator:

50db = 10^{-7}Wm^{-2}
400 * 10^{-7} = 4 * 10^{-5}
L = 10 * log_{10}(4 * 10^{-5} / 10^{-12})
= 10 * log_{10}(4 * 10^{7})
= 76dB
76 / 50 = 1.52

So the difference is a factor of 0.52??

> Presumably Derek wouldn't necessarily be in the middle of the room
> surrounded by these machines and the closer ones would be a good deal
> louder than those further away.

Assuming he's no closer than 1m to the nearest machine, then the
contribution from the other machines would be less, and 400x or
52% would be overestimations??

> (And had a better memory!)

I am like a goldfish.