strain gauge

Coffee quakes

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.