resonance
In this video https://www.youtube.com/watch?v=hWwM7F-zaHs, Professor Lewin showed that for the tube, the less water there is, the longer the effective length of the tube and therefore, the lower the frequency.
He then demonstrates an opposite effect for a wine glass. Namely, an empty wine glass resonates at a higher frequency than a filled one. Why is that so?
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.
I think that you may find this similar question of interest.
The frequency of oscillation is determined by the equation: $$f = 2\pi \sqrt{\frac{k}{m}} $$ Where $k$ is the spring constant and $m$ is the mass. The spring constant of a material is a value that increases with 'stiffness' or rigidity. The more inflexible the material, the higher the value, the more flexible the material, the lower the value.
As a quick google search yields, the addition of corn syrup to water caused the frequency to decrease:
(source: k12.or.us)
http://tuhsphysics.ttsd.k12.or.us/Research/IB12/AlbeKastGard/index.htm
This makes sense. A denser material would obviously increase the mass. Furthermore, a more viscous material would impede the oscillation of the glass. Since viscous materials are usually denser that less viscous materials, it follows that higher viscosity fluids would resonate at lower frequencies.
Furthermore, in terms of sound waves specifically, the speed of sound through a material is reflected by the frequency it resonates at. Simple equations exist for calculating the resonance within tubes of uniform density. Wine glasses are not as simple, but the relationship holds. The slower sound moves through a material, the lower it's resonance frequency.
Having said all of this, there is probably a point where the tones will stop sounding lower and start sounding higher. This is because, at one point, the resonant frequency will become too low to be audible. At this point, the first audible resonant frequency will be the second harmonic (2x the resonant). This probably won't happen with wine glasses, but if it does, you'll know why.
Best Answer
For the pipe, it is the air that is vibrating. When the column of air is shorter the frequency is higher.
In the case of the wine glass, the glass (not the air) is vibrating. Add water and you increase the inertia of the glass, which lowers the frequency of the resonance. The air may also resonate - but for something the size of a wine glass the frequency is very high - inaudible compared to the vibration of the glass.