This reply is in no way helpful for which I apologize, but I am curious as to how you have determined that the noise is 1Khz. 1Khz isn't very high pitched, in audio it's considered mid-range.

Does the pitch stay constant? Does it vary at all? Does it sound like a mechanical noise or could it be coming from some sort of buzzer?


Just curious. That is a strange problem. Do you have crickets in your neck of the woods?