Travis Jordan writes:

The beeping is probably from a refrigerant leak detector. This of
course is a different 'leak' than the one that is staining your ceiling.
If your evaporator coil is leaking that is a bad sign, and probably
means that a replacement system is in order. If your current system is
over 12 years old then you should think about replacing it.

The operator can make the leak detector howl without any leak, if he cares
to. This is a great way to sell big jobs to suckers, like selling brake
jobs to biddies. A little common sense and asking for a detailed
demonstration of the leak will stop most of such casual trickery, though.
Even "honest" guys do this, as detecting leaks is fraught with false-
negative and false-positive squeals.

The safest method, short of being a testing expert yourself, is to have at
least one other tradesman do an independent check. They love to prove the
other guy was wrong.