hot chocolate effect – Bean Thinking

ripples on coffee at Rosslyn, the City — From ripples on the surface, to listening to the sound your coffee makes. What links a coffee to an earthquake?

What do you hear when you listen to your coffee? Or a related question, what links your coffee to earthquakes and seismology?

In recent weeks I have been making coffee with milk, not often, but enough to notice something slightly strange. While heating the milk in a small saucepan, I have accidentally tapped the side of the pan while the milk was in it. The tap, perhaps unsurprisingly, produced a ripple on the surface of the milk propagating away from the point of tapping. But what was surprising was that a very short time later, a second ripple was generated, this time from the other side of the pan propagating back towards the original wave.

The first ripple had not yet travelled across the milk surface before the second ripple had been generated and travelled back towards it. Something was causing a vibration on the other side of the pan before the first ripple had had a chance to get there. Was the pan acting like a type of bell which, as I tapped it, started to resonate all around its circumference?

Assuming that the vibration of the tap travels at the speed of sound through the metal of the pan, it would take about 50 μs for the vibration to travel half way around the circumference of the pan (diameter 14cm, with a speed of sound in steel ~ 4500 m/s). But then, if the pan were resonating, the resonance frequency would depend on the speed of sound in the milk filling the pan, which would increase as the milk was warmed. Would we see evidence for this if we video’d tapping the pan as we heated the milk?

coronal hole, Sun — Observing periodic changes to the luminosity of stars can indicate the elements within them. Image credit and copyright NASA/AIA

Rather than watching the liquid within, we could also learn about the interior of a cup of coffee by listening to it. The “hot chocolate effect” is the classic example of this. The effect occurs when hot chocolate powder is added to warm water or milk and stirred. Think about the pitch of a sound made by tapping gently on the base of your mug while you make a cup of hot chocolate. Initially, adding the powder and stirring it will introduce air bubbles into the liquid. As you stop stirring the hot chocolate but continue to tap the base of the cup the air bubbles leave the drink. The cup is acting as a resonator, so the sound that you hear (the resonance of the cup) is proportional to the speed of sound in the liquid in the cup. As the speed of sound in hot water containing lots of air bubbles is lower than the speed of sound in hot water without the air bubbles, the note that you hear increases in pitch as the bubbles leave the drink. You can read more about the hot chocolate effect in an (instant) coffee here.

It is here that we find the first connection between coffee and earthquakes. Seismologists have been listening to the vibrations of the Earth for years in order to learn more about its interior. By observing how, and how fast, waves travel through the earth, we can start to understand not only whether the inside is solid or liquid, but also what the earth is made from. This is similar to learning about the air bubbles in our hot chocolate by listening to the sound of the mug. More recently, the seismologists have shown the effect of the Covid-19 related “lockdowns” on reducing seismic noise. Something that does not have an obvious coffee cup analogy.

But seismology is not just confined to the Earth. Vibrations of a different kind have also been used recently to learn more about the interior of stars, although here it is a mix of seeing and ‘listening’. Generally, when the surface of an object vibrates, it leads to compressions and expansions of the medium within the object. This is the essence of what sound is. But in a star, these compressions and expansions also result in changes to the luminosity of the star. So, by looking carefully at the frequency of the variation in brightness of different stars, it should be possible to work out what is going on inside them. It is a branch of physics now known as “Astroseismology”. Recent astroseismology results from NASA’s Kepler satellite have been used to challenge theories about how stars form and evolve. It had been thought that as a star develops, the outer layers expand while the core gets smaller. The theories proposed that this would result in a certain change to the rotation speed of the core of the star. The astroseismology observations have revealed that, while the gist of the theory seems right, the core rotates between 10 and 100 times slower than the theories would predict. As one astroseismologist said “We hadn’t anticipated that our theory could be so wrong…. For me, finding that problem was the biggest achievement of the field in the last ten years.”.

We now use strain gauges in electronic measuring scales. They were originally invented for an entirely different purpose.

Seismology and astroseismology offer clear links between listening to your coffee cup and earthquakes (or star quakes). But there is one more earthquake related connection to the coffee cup and it could be noticed by any of us who want to improve our home brewing technique.

To brew better coffee, we need to measure the mass of the coffee beans that we are using. Typically we will use a set of electric scales for this. Inside the scales is a device, called a strain gauge, that shows a change in its electrical resistance as a result of the pressure on it (from a mass of coffee for example). The scales translate this change in the electrical resistance to a mass that is shown on the display. One of the inventors of the strain gauge however was not thinking about measuring the mass of coffee at all. His interest was in earthquakes and specifically, how to measure the effect of the stresses induced by earthquakes on elevated water tanks. In order to do that he needed a strain gauge which led to the devices that you can now find in your measuring scales.

Two links between your coffee cup and earthquakes or seismology. Are there more? Do let me know of the connections that you find, either in the comments below or on Twitter or Facebook.

hot chocolate effect, Raphas — A ready prepared hot chocolate

This is an effect that reveals how sound travels in liquids. It enables us to understand the milk steaming process involved in making lattes and yet, it can be studied in your kitchen. It has an alternative name, “The instant coffee effect”, but we won’t mention that on this website any further. To study it you will need,

1) a mug (cylindrical is preferable),
2) some hot chocolate powder (no, instant coffee really will not do even if it does work)
3) a teaspoon
4) a wooden chopstick (optional, you can use your knuckle)

Make the hot chocolate as you usually would and stir. Then, remove the spoon and repeatedly tap on the bottom of the mug with the wooden chopstick (you could instead use your knuckle). Over the course of about a minute, you will hear the note made by the chopstick rise (not having a musical ear, I will have to trust that this can be by as much as three octaves).

resonator, mouth organ — The length of the pipes in this mouth organ determine the note heard. Photo © The Trustees of the British Museum

What is happening? Well, just like an organ pipe, the hot chocolate mug acts as a resonator. As the bottom surface of the hot chocolate is fixed in the mug and the top surface is open to the air, the lowest frequency of sound wave that the hot chocolate resonator sustains is a quarter wavelength. The note that you hear depends not just on the wavelength, but also on the speed of sound in the hot chocolate, and it is this last bit that is changing. When you put in the water and stir, you introduce air bubbles into the drink. With time (and with tapping the bottom surface), the air bubbles leave the hot chocolate. The speed of sound in a hot chocolate/air bubble mixture is lower than the speed of sound in hot chocolate without air bubbles. Consequently, the frequency of the note you hear is higher in the hot chocolate without bubbles than in the former case.

Let’s use this to make a prediction about what happens when a barista steams milk ready for a latte. At first, the steam wand introduces air and bubbles into the mixture but it is not yet warming the milk considerably. From above, we expect that the speed of sound will decrease as the bubbles are introduced. This will have the effect of making the ‘note’ that you hear on steaming the milk, lower. At the same time the resonator size is increasing (as the new bubbles push the liquid up the sides of the pitcher). This too will act to decrease the note that is heard as you steam (though the froth will also act to damp the vibration, we’ll neglect this effect for the first approximation). At a certain point, the steam wand will start to heat the milk. The speed of sound increases with the temperature of the milk and so the note will get higher as the milk gets warmer.

So this is my prediction, musically inclined baristas can tell me if there is any truth in this:

1) On initially putting the steam wand into the cold milk, the tone of the note heard as the milk is steamed, will decrease.
2) This decrease will continue for some time until the milk starts to get warm when the note increases again.
3) Towards the end of the process, the note heard on steaming the milk will continue to increase until you stop frothing.
4) It should be possible, by listening to the milk being steamed, to know when the milk is ready for your latte just by listening to it (if you are experienced and always use similar amounts of milk per latte drink).

So, let me know if this is right and, if it is wrong, why not let me know what you think is happening instead. I’d be interested to know your insights into the hot chocolate effect in a milk pitcher.