I wanted to post this because it's an obscure problem and may have
happened to other people. I have been using an AKG CK80 phantom-powered
microphone for some time in a PA system with no problems. Recently we
started recording the audio using a PC, but the recordings from the AKG
have a low-level whistle at about 4KHz. All our other sources do not show
this problem (SM58, piano, DI etc)

I've found out what the problem is: the AKG is generating a low level
signal at about 43.8KHz which is aliasing in the soundcard down to audio.
It is likely that the AKG has a switching DC/DC converter running at
43.8KHz.

Actually IMO it's not the AKG which is at fault- really the soundcard ADC
should have a good enough antialias filter to eliminate everything above
half the sample rate, but in this case it doesn't. To solve the problem it
is necessary to add extra lowpass filtering at 43.8KHz.

Hope this posting will help if anyone else is getting this problem...