If you wet the finger and rub the rim of the glass, the sound will be higher pitched. If the glass is filled with water, the pitch of the sound will shift again.
Glass cups are able to sing because of their shape and elasticity. The shape of the glass causes it to resonate. The vibrations from the finger’s friction on the glass cause it to vibrate in a pattern that produces a sound wave. The speed of the waves produced depend on the elasticity of the glass. Because of its composition and material properties, glass produces sounds in the mid-to-high frequency ranges, which are perceived by the human ear as “singings”.