Is the magnetic field preventing the metal atoms from vibrating and
producing sound? Or is something else going on?
No, planet Earth is the biggest magnet that we are attached to; and
it cannot stop atoms vibrations. The ringing of an anvil has to do
with acoustic wave phenomena.
When hammer strikes an anvil, it sets up an acoustic wave, which
travels up and down along axis of symmetry of the anvil, very
similar to a guitar strings (or any other string instrument). By
attaching a magnet, you creating an acoustic wave trap. Because
magnet connection with the anvil is loose, the wave dissipates a lot
of energy on crossing from anvil to magnet. The magnet becomes an
Another thing that is going on is because mass of the magnet is very
small compared to mass of the anvil, the magnet will vibrate at
frequency of anvil times mass ratio. if mass of anvil is 100 times of
mass of magnet and anvil vibrates at 2000 Hz, the magnet frequency
will be 2000 * 100 = 200000 Hz, which is way above human hearing