DIAGNOSIS This is coil whine from the camera's internal power supply circuitry. It is a known hardware issue with some units.
FIX Contact Nanit Support directly through the app. Provide your camera's serial number and a recording of the sound. This is a recognized defect, and they will typically initiate a warranty replacement for units producing audible coil whine.
IF THAT DIDN'T WORK If support denies a replacement, the noise may be exacerbated by electrical current. Try plugging the camera into a different outlet, preferably on a different circuit, to see if the pitch or volume changes.
HEADS UP Do not attempt to open the camera or dampen the sound physically. This will void the warranty and presents a serious electrical hazard.