|MadSci Network: Physics|
Thank you for your interesting question. I am not sure if I can help you but I'll try. A ceramic cup is already an extremely complicated object if you look at it from the point of view of mechanics. It has a variety of resonance frequencies depending on its size,material,.... Not only one but several frequencies are normaly stimulated if you tap it with a spoon. Lets consider the influence of several external parameters on the "sound" of a given cup: (A) the strength and the place where you tap it with the spoon (B) the amount of liquid in it (C) the sort of liquid (density, sound velocity, maybe viscosity...) (D) the temperature of liquid and cup (E) and the shape of the liquid surface (a parabulum if you stirr it perfectly) Observations: According to my quick experiments with my cups at home (A) has only little influence on the sound. I had the impression that you get a clearer sound (with less harmonics) if you hit the cup near its upper edge. (B) has a major influence: the higher the water level is, the deeper the spound ! If you touch the cup with you finger the sound is damped very strongly. I don't think there is a difference between water and coffee (C) but the density of the fluid might make a little difference. In contradiction (?) to your observations I did not find a strong effect of the temperature (D) on the frequency (my neighbour, a violine player wasn't a home....) Explanation: If the cup is hit by the spoon it starts to oszillate, mainly in the radial direction (therefore the strong damping if you touch the cup with your finger). The water cannot stop the oszillation (different from an bottle you whistle on) and the water close to the ceramic followas the oszillation and sound wave propagates through the liquid. The extra mass of the water near the surface needs to be accelerated and this results in a deeper sound (like a thicker guitar string gives a deeper sound). Back to your main question. Why does the pitch goes up if you stirr the coffee ? Could it be that you had (milk) powder in the coffee ? The powder has a lot of air in it. This might lower the sound velocity in the air/liquid mixture. Or could it be that your cup had some structures inside. The faster you stirr, the higher the "contact noise frequency" would be. It cannot be the water level however which rises while stirring (see above).
Try the links in the MadSci Library for more information on Physics.