Possible Solution for under $2.00: Plug the display into one of those ground eliminating plugs that allow you to plug grounded cords into old style two prong receptacles.
I took my display to the Apple Store. They could not reproduce the sound, so they were unable to do anything to fix it. While the Thunderbolt display was on vacation at the Apple Store, I thought more about what MAD SCI described as the possible source of the problem ["THAT MEANs that all these devices are now connected. Problem being is that the audio is not protected from ground noise…"]. The fact that the display worked fine at the Apple Store, lead me to think the problem was with the electricity in my office, since it is in a historic building in an old downtown area. I suspect my electricity may have ground noise since I have to plug everything (Wi-Fi modems, phone modem, external network drives, copier, printer, lamps, etc.) into the same circuit.
When I got my display back I decided to try plugging the display's power cord into one of those little plugs that converts a three prong into a 2 prong, by eliminating the ground prong. I plugged the display into the ground-eliminating plug, then into the surge protector. While I confess it has only been a few days that the display has been functioning under these conditions, there is no hiss sound. Last time I thought I found a solution, I performed experiments to recreate the hiss and it never went away; so this time I have decided to be superstitious rather than scientific. So you should take this report as an anecdote only.
Additionally, I do not recommend this solution, because eliminating the ground may cause problems. [As described by MAD SCI: "It is only protection against lightening really. So if you wonder why apple has done this and not fixed it yet, it’s more political than you think…."] With this in mind, I believe there is a risk the described fix could turn your display into a useless piece of junk, if there was a power surge from a lightening strike that was not eliminated by the expensive surge protector it is probably plugged into. Of course, since my noise was so loud, the display was already a useless piece of junk (until I eliminated the hiss with this "kludgy" fix), I figure I have nothing to loose.
I have the same issue with my TB Display. It does improve a lot when the display is Daisy Chained to a LaCie Raid TB HD. http://www.lacie.com/products/range.htm?id=10061. Sometimes the noise come back but I would say it does impeove to a 70% less noise.
I had the same problem with my monitor apple 27 " that suddenly after a few years of purchase started to hum/buzz/fry.
The noise was directly proportional to the intensity of illumination.
The cause of this problem is due to spiral contained into the hemi filter monitor that lacks lacquer anti vibration resonance.
I solved this way: open the monitor, I removed the card power, and removed the center speaker, until you reach the EMI filter, place internally at the input of the power cord. This EMI filter is a metal box which I disassembled from the chassis and opened (with difficulty with the use of a soldering tin to remove the fixing points.
Inside it is clearly visible a copper IUD, which in my case was devoid of protective lacquer anti-resonance.
I took the ordinary nail polish transparent and have flooded the spiral up to cover it as much as possible. The same thing I've done for safety even with spirals that are visible on the power card.
Reassembled all the buzz is gone for good.
Problem solved with 1 € of enamel and 1 or 2 hours of work.
Avevo lo stesso problema con il mio monitor apple 27" che improvvisamente dopo un paio di anni dall'acquisto ha iniziato a ronzare/friggere.
Il rumore era direttamente proporzionale alla intensità di illuminazione.
La causa è da attribuire alla spirale contenuta nell'EMI filtro del monitor che è priva di lacca di protezione anti vibrazione risonanza.
Ho risolto in questo modo: aperto il monitor, ho tolto la scheda power, e smontato l'altoparlante centrale, fino a raggiungere l'EMI Filtro, posto internamente in corrispondenza con l'ingresso del cavo di alimentazione. Questo Emi Filtro è una scatolina metallica che ho smontato dallo chassis ed ho aperto (a fatica con l'utilizzo di un saldatore stagno per rimuovere punti di fissaggio.
All'interno è ben visibile una spirale di rame, la quale nel mio caso era priva della lacca di protezione antirisonanza.
Ho preso del banale smalto per unghie trasparente ed ho inondato la spirale fino a ricoprirla il più possibile. La stessa cosa per sicurezza ho fatto anche con le spirali che sono visibili sulla scheda power.
Rimontato il tutto il ronzio è sparito definitivamente.
Problema risolto con 1 euro di smalto e 1 o 2 ore di lavoro.