Hello,
 
The first fan is buzzing at about 35% speed.
This is my second card.
 
The first card also had this problem but with a second or third fan and made strange sounds.
 
By the way, i noticed that the power supply (EVGA G3 750W) has annoying coil whine/buzzing.
Previously I had the GT 710 so I did not hear anything.
 
I can still return the card, maybe I will have more luck with SC2.
In addition I must RMA my PSU, I will send it to local store.
 
Very disappointed.
 

I checked. 
But this is rather loud wind noise, whistling.
This problem occurs when the fan speed is between 34% and 38%.

When time permits please contact EVGA tech support.

Hmm I think I hear those sounds too more or less, but more at higher fan speeds of 60+.
I guess it are normal sounds for a dual-ball bearing fan, but maybe others have a better ear.
 
I think my old EVGA 460 EE and 560SC had similar fan sounds, and also those use dual-ball bearing.
 
Meanwhile while testing this I figured out that Precision XOC 6.1.14 crashes when you open hardware monitor -> change fan setting -> close hardware monitor, that'll be a bug report.

It is indeed a bit strange that it occurs in a specific range at lower speeds.
For me it just becomes noisier the faster I let them spin, no strange things like that.
 
Hopefully someone else with more indepth knowledge could answer this definitely whether it's an unexpected fan behaviour issue.

Did you resolve this? I have the same issue. Fan noise that sounds similar to when you blow air across the top of a glass bottle? Only affects my power and memory fan, and occurs around 27-32% fan speed. I've confirmed it occurs even when only one fan is running (so it's not harmonic dissonance between fans).

Incredibly annoying, wish EVGA would acknowledge this at least.

What your hearing unfortunately appears to be very common as I have the exact same issue on two 1080 Ti FTW3's that I have tried now. It's clear in your video the noise that is being made, it is a high pitched humming noise. What I find interesting is that it is affecting your GPU fan whereas it has been the MEM and PWR fans on both cards that I have tried. Are the other fans on yours affected? I find the MEM fan hums like this at 30% and then again at 60-67% being even worse at the higher rpm. 
 
It has been suggested by EVGA that the case is amplifying the fan vibrations etc, also possibly that imbalanced fans could cause this. If it was imbalanced fans I have been unlucky enough to receive another card like this. I am not sure about these assumptions as a lot of owners are coming forward about the issue.
 
Is anyone here equipped to breadboard the card? That way we could rule out the case resonance theory...

In the first card only the GPU fan was quiet.
The second card had a loud GPU fan only, and only in the range 34-38%.
Below and above these values I heard only the sound of the wind.
 
The power supply is waiting for return.
I know that the power supply can generate some sounds, but mine is very noisy, it is very annoying.
 

Graphite8five
Your first card sounds just like both of mine with bad noise on the MEM and PWR fans.
 
It's very interesting that it is the GPU fan this time and only the GPU fan making the humming noise on your second card and this suggests that it must be an issue with the fans themselves... Are you going to request another replacement? 
 
The Seasonic X series that I have are known to have a subtle constant buzzing but mine has got worse recently and I wonder if it is linked to the 1080 Ti in some way. Did you just notice the buzzing in your PSU with the addition of the 1080 Ti? 
 
If it is indeed an issue with the fans on the FTW3's I think I must request that I get a non defected card.

As I mentioned previously please contact EVGA technical support