Stirring sugar into a cup of coffee
the "hot chocolate effect"
Have you ever noticed that the sound that you get from a cup of coffee changes as you stir in sugar? Listen to / watch the experiemnts below.
(best watched full screen)
Also discussed on The Naked Scientists
15 Feb 2009 Musical Milk - Why does the sound of steaming milk change?;
( mp3 clip
, transcript text )
Adding sugar to hot water
Take a CLEAN cup and fill it with cold water from the tap (it MUST be cold) and put it in the microwave for a minute or two. Don't boil it - just
bring it up to 70C or so. A good drinking temperature.
Now add a teaspoon of sugar, stirring as you do it. Make sure you use a metal teaspoon. Listen to the tinkling noise it makes. Notice
that the pitch drops. Now stop stirring, but keep tapping the outside of the cup. Notice that the pitch rises again?
Here are some spectrograms (with sound) that show what is happening:
Air is more soluble in cold water than in hot water. Cold water out of the tap has lots of dissolved air. When you heat it up in the microwave
the air-in-water solution becomes supersaturated. Adding sugar (or any granular material) very quickly nucleates lots of tiny air bubbles out of solution.
Now, water has a density of around 1000kg/m3 and the presence of tiny air bubbles doesn't change this much. But its stiffness (or better, the Bulk Modulus)
is around 10^9 GPa, whereas it drops to about 10^5 GPa with only 0.01% of its volume taken up by air bubbles (these are round figures for illustration).
This massive reduction in stiffness causes some of the vibration modes of the water-filled coffee cup to drop in frequency. But as the bubbles rise to the surface then
the volume fraction of air drops below 0.01% and the frequency goes back to "normal".
A fuller explanation can be found under the heading "The hot chocolate effect" in the American Journal of Physics -- May 1982 -- Volume 50, Issue 5, pp. 398-404
and there is a nice acoustic holography image of the vibrating walls of a coffee cup done at the
Physics Department, Northern Illinois University
and there's more on the "cheap instant coffee effect"