Hi there,
I have the exact same problem... I have a MBA (June 2009) SSD which experiences a high pitched noise out of my audio port. I connect a mini video port to a dvi-hdmi cable adapter. I previously used this same setup on my MBP. So, I answered your questions. I'm pretty sure I need to service the unit.
What if you try connecting some headphones into the port? Does everything work normally or are you getting the high pitched sound there as well?
Yes, same noise. Harder to hear cause the MBA amplifier *****, but its there. My Shure heapdhones don't lie.
What sort of audio cable are you using?
1/8 Stereo to RCA, with a recessed iphone (1g) adapter. Also tried the adapter from my headphones.
It's plugged directly into the TV or some sort of speaker system?
Into my speakers, but same when I tried the TV