No, the Moon does not make a ringing sound when it's in its full phase or at any other time. Sound requires a medium to propagate, such as air, water, or a solid material. However, in space, where the Moon is located, there is a vacuum, meaning there is no air or any other medium through which sound can travel.
Even if we were to imagine a scenario where the Moon had a solid surface and an atmosphere, the sound produced by the Moon would not reach us on Earth due to the vast distances involved. Sound waves would attenuate over such a long distance and become extremely faint or completely dissipate before reaching our ears.
So, in summary, the Moon does not generate sound or produce any audible vibrations that we could perceive, regardless of its phase.