pirateat46 said:
Therefore, I propose that the perceived change in ringing pitch of a freshly poured cup of coffee tapped on its edge by a spoon is due to changes in the resonant qualities of the cup as it absorbs heat from the coffee fresh from the pot.
That makes sense.
Cups are normally fairly good insulators. When you fill the cup with a hot liquid a thermal gradient through the thickness of the cup will build up slowly. As it does that, the inside of the cup expands more than the outside.
This will result in stresses in the cup. In the tangential direction these will be compression in the hot part and tension at the cold part. These stresses are large - they are big enough to shatter the cup, if it is cracked before you fill it with hot liquid (been there, done that!)
If the cup was initally at room temperature, at first the temperature gradient will not be uniform - it will be steeper near the inside. So most of the material in the cup will be in tension. This will raise the vibration frequency of the cup in the same way as a guitar string increases frequency if the tension (i.e. the internal stress) in increased.
Some ideas for more experiments to confirm or deny this:
1) Try it with a metal container, e.g. an empty food can or a small saucepan. The temperature gradient through the metal will be small because it is a good conductor of heat, therefore the thermal stress will be small and there should be no change of pitch.
2) Try warming a cup for a while in a warm oven (set to less than 100 degC!) till it is at uniform temperature (that may take a hour or more) and then full with cold water. The pitch should drop, because this time most of the cup will be in compression not tension.
The theory about the rotation speed of liquid changing the frequency is physically sensible but the effect would be too small. The frequency of vibration (judging by the sound) is about 500 to 1000 Hz. The frequency of rotation of the coffee is only 1 or 2 rev/sec.
If the two frequencies were closer together there could be an effect - for example water flowing through a high pressure fire hose, where the flow does create dangerous vibrations in the hose unless it is handled correctly.