# Why does the sound pitch increase on every consecutive tick at the bottom of a filled cup of coffee?

Since I don't know the proper physical terms for this, I describe it in everyday English. The following has kept me wondering for quite some time and so far I haven't found a reasonable explanation.

When you fill a ceramic cup with coffee and you click with the spoon at the bottom (from the top, through the coffee), each following tick, even when you pause for some seconds, will have a higher pitch. The following I've observed so far:

• works better with coffee than with tea (works hardly at all with tea)
• works better with cappuccino than with normal coffee
• doesn't work with just cold water
• works best with ceramic cups, but some plastic cups seem to have the same, yet weaker, behavior
• doesn't work on all types of cups, taller cups seem to work better
• must have a substantive amount of liquid (just a drop doesn't make it sing).

It must be something with the type of fluid, or the milk. I just poured water in a cup that had only a little bit fluffy left from a previous cappuccino, and it still worked. Then I cleaned it and filled it again with tap water and now it didn't work anymore.

Can someone explain this behavior?

• I'm a little confused about what's happening here. You're tapping the bottom of the coffee cup with a spoon? At the same place each time? – flies Mar 30 '12 at 14:08
• @flies: exactly that. But "same place" can be as wide as the whole bottom of the coffee cup, but seems to work best closed to the middle. You need to wait relatively long for the pitch not to increase. – Abel Mar 30 '12 at 14:18
• I believe I understand what you're saying now. You're saying that, if you pick one spot on the bottom and tap only there, you'll see this effect, but the effect is strongest when you you're close to the middle. The reason I'm asking is that if you move the spoon, tapping the coffee cup in different places, you would expect a change in pitches. (For instance, if you hit a drum in the center of the skin you get a deeper sound than if you hit the drum near the rim. The same principle applies to rigid bodies.) – flies Mar 30 '12 at 14:23
• @flies: I see your point. But the pitch gets higher — and altogether quite a bit higher! — each time you hit the bottom in (roughly) the same spot and I have no idea why. When you wait a while and click again, the original low pitch is back. – Abel Mar 30 '12 at 14:26
• Well, I think you described phenomena very well - good physics does not have to come in equations, remember Faraday. As for problem at hand, I'd say that difference of densities of fluids is accounting for different dumping properties. As for why are you able to excite higher harmonics of fluids container - I'll go make myself a cup of coffee and check it out. – Stipe Galić Mar 30 '12 at 15:58

I think you are observing "the hot chocolate effect" or something similar. See Crawford, Am. J. Phys. 50, 398 (1982). I have to confess I haven't read through the paper in enough detail to adequately summarize it.

Abstract:

The ’’hot chocolate effect’’ was investigated quantitatively, using water. If a tall glass cylinder is filled nearly completely with water and tapped on the bottom with a softened mallet one can detect the lowest longitudinal mode of the water column, for which the height of the water column is one‐quarter wavelength. If the cylinder is rapidly filled with hot tap water containing dissolved air the pitch of that mode may descend by nearly three octaves during the first few seconds as the air comes out of solution and forms bubbles. Then the pitch gradually rises as the bubbles float to the top. A simple theoretical expression for the pitch ratio is derived and compared with experiment. The agreement is good to within the 10% accuracy of the experiments.

• After doing some reading with those keywords, it seems indeed the same thing. Wikipedia has a nice link to this Powerpoint presentation by B.W. Carroll and M.B. More. – Abel Mar 30 '12 at 16:55
• Fantastic, I always wanted to know how it works!! – Slaviks Mar 30 '12 at 16:58

I first noticed this in a hot cup of Horlicks, made with milk. I would stir in the powder vigorously, then tap the bottom of the cup with the spoon to check that all the powder had dissolved. Even two taps, one second apart is enough to detect the rising pitch. It continues rising and rising over the course of, perhaps, 20 seconds.

The interesting thing is that you can make the pitch drop again by stirring it up again. It seems that the pitch is directly related to the rate at which the milk is spinning.

• If I don't stir and tap the bottom, the pitch rises. If I stir a lot and start tapping, the pitch is low and then rises. When I wait long enough and tap, the pitch is low and then rises. I don't really see a relation as the fluid can be both moving and still when the pitch is low. – Abel Apr 12 '12 at 2:48
• The wavelengths of sound produced are related to the dimensions of the cup and how much of it is filled. The bubbles in the fluid lower the speed of sound, thus lowering the frequency. The rising and lowering of the pitch is related to the production and destruction of the tiny bubbles. – Noah Apr 13 '12 at 11:49

I made this animation to explain this concept.

• works better with coffee than with tea (works hardly at all with tea) works better with cappuccino than with normal coffee

Since the effect is caused from air trapped in the powder, the reason why you won't always get the same effect, is because of how much air is trapped in the powder under production and how fast it is released when it's mixed with hot water.

• doesn't work with just cold water

Cold water won't dissolve the powder. At least not fast enough, and thus the air wont dissolve into the system. You can see if you pour in cold water on coffee powder, big chunks of coffee floats around.

• doesn't work on all types of cups, taller cups seem to work better

Not too sure about this one, but the equation that describes the frequency in the system is: $f = \frac{1}{4} \cdot \frac{v}{h}$ where v is the speed of propagation, and h is the height of the cup. I think it's just easier to distinguish this effect with a lower frequency (big cup) since the frequency is already quite high for cups already.

• Very nice animation! You might be interested in this answer – Floris Oct 7 '17 at 18:45
• Thank you @Floris that was a very interesting read! Well done sir. – nammerkage Oct 7 '17 at 18:58

My assumption has always been related to the amount of dissolved solids. I don't think it is just milk. I have noted the same phenomena with dissolving jello in hot water. Pitch increases in relation to how homogenous the mixture has become. Try it using water and jello per the directions on the box, but in a clear pyrex mixing container...you can see the two products becoming a solution and the bottom of the measuring cop is fairly uniform. It "seems" that the pitch stops increasing once the mixture has become very uniform.