MadSci Network: Physics

Re: why does the sound made by a spoon 'clinking' a cup of coffee rise in pitch

Date: Tue Jun 16 08:53:55 1998
Posted By: Uli Dammer, Secondary School Teacher, -, Gymnasium Liestal
Area of science: Physics
ID: 892158974.Ph

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 

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). 

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