If a hot beverage in a cup gets stirred, the sound of the spoon changes. You can easily hear this if you repeatedly cling the spoon to the cup ground after stirring. The cling sound will raise in tune for quite a long time.

This even happens if the fluid motion is (almost) stopped after stirring, eg. by using the spoon to do so.

What is the reason for this effect? Why it last so long after stirring?

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    $\begingroup$ So do you think it's due to something in the fluid, or due to the spoon being hotter? Have you tried heating the spoon some other way (running under hot water, or holding -- carefully -- over a stove to heat it up) and checking the sound it makes? $\endgroup$ – tpg2114 Sep 25 '15 at 11:29
  • $\begingroup$ Or what about using a hot spoon in different temperatured cups? $\endgroup$ – Kyle Kanos Sep 25 '15 at 12:17
  • $\begingroup$ The spoon actually stays in the fluid, so it doesn't change temperature that much. The experiment can be repeated again and again without cooling the spoon. $\endgroup$ – dronus Sep 26 '15 at 9:47
  • $\begingroup$ Two plausible explanations so far. $\endgroup$ – dronus Sep 26 '15 at 9:52

This is a well known effect, and most clearly happens with hot instant cocoa which has just been mixed. Stir the cocoa while tapping the spoon on the mug, and you'll hear the pitch of the tapped spoon go down. Now start tapping while not stirring; the pitch will gradually go up by an octave or more. But, if you stir again, the pitch will go back down again.

The cause is microscopic bubbles of air, which lower the speed of sound in the cocoa and thus lower the resonant frequency of the mug. Heated tap water is supersaturated with air; add cocoa or sugar and the air will come out of solution into those microscopic bubbles, lowering the resonant frequency. Let the cocoa sit, and the bubbles will rise, leaving the bulk of the mug with fewer bubbles and a higher sound velocity, raising the resonant frequency of the mug. Stir, and you'll bring the bubbles back down, reversing the effect and lowering the pitch.

  • $\begingroup$ I will try this with water only, but there may still be air bubbles inside. How to get an gas free hot fluid at home? $\endgroup$ – dronus Sep 26 '15 at 9:55
  • $\begingroup$ I believe heated tap water won't show this effect, as there's nothing to nucleate the air on (hence the references to adding sugar in the linked articles). But, if you heat the water to boiling, let it sit for a few hours, and then heat it again, you should have fairly air-free water. Let us know how it goes. $\endgroup$ – Daniel Griscom Sep 26 '15 at 11:04

I enjoy listening to this phenomenon as I wait for my teabag to brew.

What is happening is that parts of the the ceramic cup heat up and expand. Because its shape is constrained (assuming it doesn't break), this produces a stress in the material that increases its resonant frequency (like tightening a guitar string).

When it gets to Middle C, my tea's ready.

  • $\begingroup$ I suspect the magnitude of this phenomenon depends not only on the material type but on the quality of the cup -- different amounts of strain, different resonance ranges, etc. $\endgroup$ – Carl Witthoft Sep 25 '15 at 12:54
  • $\begingroup$ @Carl: Exactly. Just like any musical instrument :-) $\endgroup$ – Oscar Bravo Sep 25 '15 at 13:07
  • $\begingroup$ This is incorrect. The pitch in this situation can change by a half octave or more. But, a heated ceramic cup changes size by at most a few percent, which would at most change the resonance by a fraction of a semitone. $\endgroup$ – Daniel Griscom Sep 26 '15 at 2:21
  • $\begingroup$ The sound of the cup depends on it's shape but also it's stiftness, so an irregulary heating the cup (hot inside, could on the outside) could change the material stress by magnitudes (lower or raise) and thus the tone. The stirring adds more of this heat to the cup as the cup surface layer of the fluid gradually cools down with the cup. Sounds quite plausible. $\endgroup$ – dronus Sep 26 '15 at 9:52
  • $\begingroup$ Ah; I thought the answer was about the size of the cup changing with temperature. However, if the stiffness of the cup were significant, then you could see this effect in an empty cup. It would be easy to test: let us know if you see the effect. (My guess is that you won't.) $\endgroup$ – Daniel Griscom Sep 26 '15 at 12:00

I would suggest the surface of the stirred fluid has more area as it is in rotation. The expanded conal shaped surface area is resonating at a lower frequency driven by the sharp pings generated by the spoon against the hard bottom of the cup. As the rotation slows the fluid has less surface and the pitch rises as the level of the fluid drops at the edge of the cup, and rises in the center of the fluid vortex. This may also explain the super low frequency audible incidents during a tornado where "train engine rumble" caused by low pressure is "amplified" by the vortex of the air column. This was first observed and questioned by me 49 years ago and the answer eluded me until today. Excelsior ! Clem


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