Why are we able to produce a tone when we rub our finger around the lip of a crystal glass?

Rubbing your finger around the rim of the glass is much like taking a bow to a violin string.

Why are we able to produce a tone when we rub our finger around the lip of a crystal glass?

The atoms in a crystal glass are arranged in a very regular pattern, a structure resembling a honeycomb or a chain-link fence. In contrast, the atoms in normal glass are connected irregularly, more like the veg-etables in vegetable soup. The pattern of the atoms in crystal ensures that the glass vibrates in only one way, with one single frequency.

Compare this to a tuning fork or a violin string. When you tap the fork or pluck the string, it only vibrates in a certain way, and only one single note is produced. So a crystal glass, like a violin string, will only produce one note when you tap it. When you try this, you should hear a pleasant pinging sound, not a dull clink like you would hear with a wineglass that's not made of crystal.

Rubbing your finger around the rim of the glass is much like taking
a bow to a violin string. Your finger slightly sticks to the glass, bending it by the tiniest amount, and then slides across the rim, letting the glass relax back into place. Your finger then sticks again, and the pro-cess is repeated hundreds of times
a second. This produces the vibrations (at just the right frequency) that lead to the warm tone.

It takes a bit of dexterity and a light touch to get a crystal glass to respond in this way. Pressing the rim too softly will never bend the glass enough to vibrate it, and pressing it too hard prevents the glass from relaxing back into place properly.