VIBRATION

 Answer 

First of all, when you hear the coathanger hitting an object in the air, the lack of surface area in the hanger prevents its mainly low frequency vibrations from transferring to the air, and instead, you just hear mainly high frequencies that result from the impact.
Then you bypass the air conduction route, and substitute bone conduction through the bones of the skull by coupling the hanger to the string, your fingers and finally to the bones of the head via the usual "plugging your ears" gesture. The amazing low frequencies of the hanger now go directly to your inner ear and it probably sounds more like Big Ben chiming!
A great party trick, and also popular (and quiet) with kids.