acousticsheat
I had some old flowers in a vase and noticed the water had become really stagnant, causing the whole room to smell like a fart. So I tipped out the flowers and the old water, and poured some boiling water into the vase to help clean off all the slime. To my surprise the vase started ringing like a bell! The sound was quite loud, similar to when you run your finger around the tip of a wine glass. I believe the vase is ceramic, I'll attach a picture of it below.
How is this possible?
(source: engineeringtoolbox.com)
The graph(blue lines are what you want) only goes till $50^o C$, but we can extrapolate and say that the oxygen level will become a fifth or so by the time the water reaches its boiling point.
The solubility comes from Henry's law, but I don't know the temperature dependance of the proportionality constant $k_H$--I'll check it out tomorrow and edit it in..
I think the question is too complex to give a satisfactory answer without deep study of the problem. The biggest problem is that there are several ways how vibrations (sound waves) travel from the source to the receiver. The path of the excitation: the source - glass - fluid - glass - the receiver you've described is only one one possible path. Some of the excitation shall travell through glass only, e.g. bottom or side of the glass.
So if you want to have exact solution you should find standing sound wave (eigenfunction) solution of the whole system glass + fluid, which is far from being trivial. Of course, in this case you must also consider dissipation, because you have constant excitation and without the dissipation the vibrations would continue to grow to infinity.
The second possible, more engineering way to get the answer is to disregard sidepaths of excitations and calculate in terms of traveling sound wave. At one end you have the source, excitations first travel through glass, then difract on the border between glass and liquid, travel throught liquid, again difract on the border between glass and liquid and finally travel through the glass to the receiver, where all of the wave energy is absorbed.
In both cases you need speed of sound in medium, which is not hard to obtain:
$$v^2 = \frac{E}{\rho} = \frac{K}{\rho},$$
where $\rho$ is density of the medium, while $E$ is Young's modulus (solid) and $K$ is bulk modulus (liquid). In the second case you also need transmitivity, which is of course dependent on the incident angle and you can find the right equations by peaking at Fresnel equations.
I hope I understood you right and that my answer helps.
Best Answer
I'm not sure, but it's possible that the ceramic material was relieving stress. That is, the material had many defects in it's structure (like the ones described in this wiki page), and the heat from the water gave the structure enough energy to relax and heal them. I've witnessed a ceramic cup that started to make bell like noises when I poured myself a tea in it, an. According to a ceramist I know, they "sing" like this when the ceramic pieces are new, and not when they are very old, so that is consistent with the idea that they are due to defects relaxing: once there are few defects left, they can't make more noises.