This is eminently lookupable. The
NY State law says:
(b) No person shall operate a bicycle unless it is equipped with a bell or other device capable of giving a signal audible for a distance of at least one hundred feet, except that a bicycle shall not be equipped with nor shall any person use upon a bicycle any siren or whistle.
So horns are OK as are anything else as long as it's not a siren or a whistle.