Sound of a Cup With and Without Instant Coffee:
A Foam-Filled Acoustics Demonstration

Andrew Morrison - Morrison@physics.niu.edu
Thomas D. Rossing - Rossing@physics.niu.edu
Physics Department, Northern Illinois University
DeKalb, IL 60115

Popular version of paper 3aMU3
Presented Wednesday morning, June 5, 2002
143rd ASA Meeting, Pittsburgh, PA

The breakfast table is an excellent place to observe some interesting acoustical effects. An empty coffee cup, like an ancient Chinese two-tone bell, emits two distinctly different tones depending upon where it is tapped. When it is filled with hot water and some instant coffee is added, however, a whole new set sounds are heard when the cup is tapped. The pitch rises by an octave or more as the foam clears, due to the dramatic change in the speed of sound in the bubble-filled liquid.

To study the vibrations of a coffee cup, we have used holographic interferometry, which produces a map of each mode of vibration in simple or complex structures (see one map in the illustration). In its fundamental mode of vibration, the mouth of the coffee cup changes from circular to elliptical many times a second, so that four nodes (points of minimum motion) occur around the mouth. Actually, in a cup with a handle two such modes occur, since the mass of the handle upsets the circular symmetry of the cup. If one of the nodes occurs at the handle, the cup vibrates at a slightly higher natural frequency than if the nodes occur on either side of the handle so that the handle moves with maximum amplitude of motion. So tapping a coffee cup on, or near, the handle produces a lower pitch (frequency) than tapping it, say, one eighth of the way around.

More acoustical surprises await us when we fill the cup with hot water and add some instant coffee. Before adding the instant coffee we tap the bottom of cup with a spoon to sort of "tune" ours ears. Then we add the powder. The sound of the spoon tap on the bottom will usually sound at least an octave lower than before, and it will rise again as the foam clears.

Physicist Frank Crawford noticed this same effect in hot chocolate (American Journal of Physics, May 1982), and explained it as being due to the dependence of the speed of sound in water on the bubble density. What we are hearing are longitudinal oscillations of the water column. Crawford heard pitch changes of nearly three octaves in a tall glass cylinder. Gas bubbles reduce the speed of sound in the liquid, which lowers the fundamental mode of the liquid column. As the foam clears, the speed of sound rises and so does the pitch. Crawford called this "the hot chocolate effect."

Coffee and hot chocolate are not the only liquids that show the effect. In his book "The World of Sound" (Dover, 1968), Sir William Bragg observes the effect in cold beer. In a note on the Internet, Kevin Kilty mentions that he has observed the effect with a hot chocolate mix, sugar in hot tea, salt in beer, and instant tea in cold water as well as in instant coffee. ASA president Bill Hartmann mentioned it to us while drinking coffee at an ASA meeting.

Whether this has a practical application in studying ocean acoustics, we do not know. Perhaps a changing bubble density in seawater would create a similar pitch change. However, it serves as an eye-opener at the breakfast table.