I couldn't find anything online about this, so that meant I was going to write this blog post when I fixed it to help others out. I called the Samsung settlement line and they said this high pitched noise was not one of the symptoms of a blown capictor.
I took the back panel off and there was a popped capacitor, right next to an inductor, some transistors and a heat sink. The capacitor is presumably used in an LC circuit before as part of a SMPS (switched mode power supply). Initially, I tried hot gluing the inductor to quiet the oscillations down, because it didn't look too blown. The sound changed in pitch, but remained.
The next day I replaced the capacitor and the sound went away. I used my multimeter and the capacitor was measuring 0 farad. I tested some known good ones, so I was using the multimeter it correctly. I didn't have the right size capacitor handy, so I replaced the 2200uF 10v capacitor with a 220uF 50v capacitor. It's not tuned to the right frequency (I think it's allowing the square root of 10 (3.16) higher frequencies than the initial design), but the sound went away entirely, so I'm happy.
I called the samsung line back and told them it was a blown cap and they said I'm still not eligible for anything because it wasn't exhibiting any of the known symptoms. I dont know if it is worth pursuing, but it's annoying that there is a class action lawsuit to fix this issue, yet Samsung says I'm not covered.
The Fix
So in short, the fix (what you probably came here for) is to remove the back panel, look for a popped capacitor (the top will be lifted and there will be residue on it). This capacitor will probably be in the position my screwdriver is pointing to, then replace the capacitor with one of the same size. I only used a solder iron, solder, and a replacement capacitor. You will probably want a 2200uF 10v (or greater) capacitor, which you can find thator something similar at RadioShack.
Let me know if you are having the same issue or if this helped. Just curious how widespread this is.
