[Physics] How and why does the height of water in a glass affect it’s resonance? (resonant frequency)

Question

Why does the resonance frequency of a vibrating wine glass changes with the level of water in the wine glass?

Answer 1

The resonant frequency will be made lower the more water is in the glass, because the glass must vibrate against the water, increasing the effective inertia in the glass. Resonant frequency always looks like the square root of some kind of restoring force divided by some kind of inertia, so increasing inertia reduces resonant frequency. Or another way to look at it is, the resonant frequency is inversely proportional to the time it takes a wave to pass down the glass and bounce back up again, and contact with dense water slows down that wave.

Note this is the opposite effect that you get when you blow over the top of a wine bottle-- there the wave is in the air, not the glass, and the resonant frequency is inversely proportional to the time for sound waves in air to propagate down through the air and bounce back up again. That will be a very obvious effect, increasing the water level raises the resonant frequency in the air dramatically. But it doesn't sound like that is what you are talking about.

Note that the other answer raises the possibility that the vibration in the glass might actually bounce when it reaches the water level, much like the sound waves in the air, in which case raising the water level would raise the frequency. So your experiment will tell which of these effects is actually happening, because if the wave has to still go all the way to the bottom of the glass before coming back up, then raising the water level will lower the resonant frequency.