Do we need to know the amplitude of the first noise source to answer the question, teach?

gswitz
Do we need to know the amplitude of the first noise source to answer the question, teach?

No. You just need to know that they're ratios and the formula to calculate the RMS for this situation (which is the only part that hasn't been discussed here yet - it's the square root of the sum of the squares).
 
You just regard the larger one as 0dB (a ratio of 1:1). The idea is to find the ratio between the two added together and just the larger one alone.
 
 

∞

Let's say you have 2 numbers x and y and y is expressed as a ratio compared to x:
 
y = .1 * x
 
The .1 was randomly chosen in this case - all you need to do is convert -16dB (or whatever) into a ratio. Then:
 
What is x + y if x = 1? (x = 1 because 0dB = 1:1 ratio)
 
That's peak.
 
What is the square root of (x squared + y squared)?
 
That's RMS.
 
 
 
But the point of all of this is that if you have 2 similar noise sources, the quieter one simply becomes completely and absolutely irrelevant once it falls a perhaps surprisingly small amount below the louder one - it contributes so very little to the overall noise that's it's simply meaningless if you get rid of it or nor. You will hear the exact same amount of noise even if you get rid of it completely.

And we were talking about a 1dB difference before.
 
If you solve for "how many dB's y is below x to result in a 1 dB difference" you'll find that by the time the quieter noise is -6dB getting rid of it completely will only reduce the overall noise by about 1dB RMS.
 

Drew,

I'm now wondering about the case of 2 mics on one acoustic guitar...

Both will have
random noise from the pres and dac (+3).
Room noise will be shared. (+6)
Guitar shared (+6) in phase

So the signal to noise ratio might improve enough to notice? Maybe?

Practice says I don't notice. My pres and dac are mighty quiet.

In part I'm asking if this is a proper application of the learning.

Original Pranksta
...It has been many decades since I slid a log...
 

And it's been decades since I've heard anyone use that expression!
 
Geoff, my kneejerk reaction - without actually thinking about it much - is that two mics on a source would worsen the overall S/N ratio. But not by a lot, because though their noise is additive, so is their signal. Of course, the signals will likely not be identical (e.g. a Mid/Side mic setup) and therefore not a straight up 1+1=2 scenario. Noise, being random, could be far more cumulative.

gswitz
Drew,

I'm now wondering about the case of 2 mics on one acoustic guitar...

Both will have
random noise from the pres and dac (+3).
Room noise will be shared. (+6)
Guitar shared (+6) in phase

So the signal to noise ratio might improve enough to notice? Maybe?

Practice says I don't notice. My pres and dac are mighty quiet.

In part I'm asking if this is a proper application of the learning.

First thought:
 
Let's say you had one mic and split it into 2 channels. What would that do?
 
If the mic pre/dac's noise floor is low enough then that part would be irrelevant based on the exercise above, so it's really no change. You can't change SNR by just splitting and recombining things, right?
 
Which leads us to the question of whether phase addition vs. cancellation with two mics would be different for the signal vs. room noise.
 
Most significant case I can think of - micing a tuning fork (because it's a very pure tone). 
 
Mics in phase at tuning fork's frequency = much better SNR
 
Mics (mostly) out of phase at fork frequency = much worse SNR
 
For anything else than something like a tuning fork, I'd think it'd be a contest for relative phase cancellation/reinforcement between the noise and signal. If you can get your signal largely in phase I'd expect to see a little better SNR.

∞

You need to convert the -16dB to a ratio first.
 
And at the end, you need to convert the answer back into dB's.