I bought an XPS 13 DE (9360) with Ubuntu 16.04 LTS and I thought the whine I heard through my headphones was related to the coil whine issue. I updated my BIOS to 2.1 today and I noticed that my laptop was considerably quieter (re the coil whine) until I unplugged it from AC. When using battery power, the coil whine is very noticeable again (mainly through my headphones) especially when using a mouse or the trackpad.
I also installed Windows 10 (dual boot) and didn't notice _any_ whine whatsoever unplugged or plugged in, with my headphones and without.
So now I'm wondering whether what I'm hearing in Linux is coil whine at all... Might this be instead related to audio somehow?
Same machine and almost same configuration here. Differences are: BIOS 2.2.1 (released last week), and kernel 4.10.0-33-generic (after installing the kernel and the xorg server from the hwe ubuntu kernel stack (https://wiki.ubuntu.com/Kernel/LTSEnablementStack).
As for coil whine my machine is almost silent all the time. Practically dead silent when unplugged. A slight electric noise is only appreciable sometimes when plugged.
I never play music on the laptop, but I have tried, playing some youtube music, with low-quality headphones. I haven't perceived anything weird, except the typical background noise before the music begins.
I would try in this order (just in case you haven't already done it):
1) Update Ubuntu from Ubuntu Software. The factory software contains the initial LTS release, 16.04.0. Current LTS realease is 16.04.3.
2) Try with another headphones so that you can discard issues with your current device.
3) Try with different music players.
4) If the problem persists, take a look at this arch wiki page: