acoustics – Bean Thinking

Amoret coffee Hammersmith — Amoret, so new it still didn’t have its name on the outside.

Amoret is a new addition to the coffee scene over in Hammersmith. Just up the road from the Hammersmith & City line entrance of Hammersmith tube station, I nearly missed this cute cafe when I walked past as it had no name on its frontage, nor did it have the chalk board that is characteristic of many cafes. Fortunately however, I had the address and so double backed to find a great little cafe. It appears that that majority of Amoret’s business comes from take-away orders although there is a small seating area at the back (it is small, when we visited in February, there were two chairs and a couple of tables/stools). If you are fortunate enough though to be able to take a seat at the back of the cafe, I would thoroughly recommend doing so. Not only can you enjoy good coffee in a nice environment, the friendly people behind the bar were very happy to chat about their coffee and cafe. Moreover, there is plenty to notice from this observation post at the back of the cafe.

When we visited, the espresso based coffee was by Campbell and Syme, with V60s that featured different guest roasters (though it seems that other roasters also regularly feature for the espressos). I had a coffee from Panama, roasted by Union, which featured the word “caramel” in its tasting notes. I have simple tastes (‘caramel’ or ‘chocolate’ descriptions always go down well) but it was a great coffee. Complementary water was available at the counter with take-away cups (and water ‘glasses’ ) that were compostable and biodegradable*. As the very friendly staff brought my coffee to the table, I noticed that the ‘table’ that I had put my water on was in fact a metal drum that sounded ‘clang’ as the cup was put down. The sound of the drum immediately suggested that the drum was hollow. We all recognise the sound of a hollow drum, it is partly about the pitch of the sound, but partly about the echoes that we hear as the sound reverberates inside the metal.

Kettle drum at Amoret — After I had enjoyed my filter! The table-drum at Amoret. Does the drum sound the same in summer?

Although it appears simple, the sound made by the drum is influenced by many aspects of the drum’s construction and surroundings. The stiffness of the metal and the atmospheric pressure affect the way that the drum’s surface vibrates, while the size of the drum and the speed of sound in air also affect the note, or pitch, that we hear. How is the sound of the drum affected by a change in its surroundings? For example, if the atmosphere in Amoret got much warmer, the speed of sound would increase, how would that affect the sound of the table-drum?

A few years ago, Professor Timothy Leighton was wondering how the properties of the atmosphere affected the sounds of musical instruments. Specifically, he wondered what instruments would sound like on other planets. Take Venus. Venus is a planet with a very dense, very hot atmosphere. The surface temperature on Venus is 457C (Earth’s average is approx 14C) while the atmospheric pressure is 90 Bar (Earth’s average: 1 Bar). As it gets hotter, the speed of sound increases and so, to a first approximation, the note made by the drum-table at Amoret will sound higher as the air gets warmer. However, the metal of the drum is also hotter on Venus (so less stiff) and the density and pressure of Venus’ atmosphere will act to further complicate things. So to start thinking about how things sound on Venus, we would be more sensible to think about a simpler instrument, such as an organ, which is only affected by the change of the speed of sound†. Take the famous case of Bach’s Toccata and Fugue in D minor. Played on Venus, the researchers found that, rather than be in D minor (293.66 Hz), it would have the pitch of F minor (at 349.23 Hz). You can hear Bach’s Toccata on Venus (Mars and Titan) here.

What about a human voice, how would a person sound on Venus (were they able to survive)? In humans, the pitch of the voice is determined by the rate of vibration of the vocal cords. So it is possible to construct a speech synthesiser to imitate human speech by modelling such a voice ‘box’. Erasmus Darwin, (grandfather to Charles) made such a device in around 1770 with wood, leather and silk‡. Darwin’s voice synthesiser could pronouce the sounds ‘p’, ‘m’, ‘b’ and ‘a’ and so ‘mama’, ‘papa’, ‘map’ and ‘pam’, which by some accounts was convincing enough to fool people into thinking there was a small child in the room. Why did people think that Erasmus’ ‘child’ was small? It turns out that just as with the drum, when we listen to people speak, we do not just register their pitch but also the echoes on their voice. Each time we make a sound, the sound travels from the vocal cords down to the lungs (where it gets reflected upwards) and up to the mouth (where it gets reflected downwards). We subconsciously listen for these echoes and, if they take a long time to appear, we deduce that the person is large (there is a greater distance between their voice box and their lungs). If the echo comes back quickly, clearly the distance between the voice box and the lungs is smaller and hence the person is smaller. Just like the drum at Amoret, the human voice is a bit more tricky to model on Venus than Erasmus Darwin’s device allowed for.

Leighton and co-author Andi Petulescu considered the question of the sound of the human voice on Venus in their 2009 paper. Firstly they said, the density of Venus’ atmosphere would make the vocal cords vibrate more slowly, so the person speaking would sound as if they had a deeper voice. But secondly, the high speed of sound on Venus would mean that those echoes that we listen for would come back very quickly, so we would perceive the speaker as being small. What does this sound like? A few years ago, a Dutch TV show set this very topic as a question for their annual quiz and answered it by one of the co-hosts singing Banarama’s “Venus” with, and without, the Venus voice changing software of Leighton. If you understand Dutch, the full clip is below. If you don’t understand Dutch but would just like to find out how you would sound on Venus while singing Banarama, forward to 7 minutes in for the version on Earth and 7m46 in for the Venus version.

It is not easy for us to travel to Venus to investigate whether Prof. Leighton was correct. It is possible for us to repeatedly visit Amoret to investigate how the coffee cups sound as they are put on the drum as the temperature changes around us. This seems a fantastic excuse to revisit to me.

Amoret is at 11 Beadon Road, W6 0EA

‡”Erasmus Darwin – A life of unequalled achievement” by Desmon King-Hele was published by Giles de la Mare Publishers (1999)

* It should be noted that ‘compostable’ plastic has a very specific definition that does not mean that it can necessarily be composted in the way that you or I would understand the term, as I described in more detail here. Nonetheless, it is definitely a significant improvement from conventional plastic and I would love to see more cafes follow suit with environmentally sound packaging.

† Of course this comes with a fair few caveats, not least the fact that the organ has to have flue pipes only. I would thoroughly recommend browsing Professor Timothy Leighton’s excellent webpage on this and other aspects of acoustics which you can find here.

A post that applies equally to tea, just swap the word “tea” for “coffee” throughout!

A cusp caustic in an empty mug of coffee — Have you seen this line?

Look deep into your coffee. Do you see the secrets of the cosmos being revealed? Well, neither do I usually but there is something in your coffee that could be said to have ‘cosmic implications’ and I’m sure it’s something that you’ve seen hundreds of times.

Now, admittedly it is easier to see this effect if you put milk in your coffee. Imagine drinking your (milky) coffee with a strong light source (the Sun, a lightbulb) behind you. You see that curved line of light that meets in a cusp near the centre of the cup? You can see various photos of it on this page. Yes, it is indeed the reflection of the light from the curved mug surface but it is far from just that. It is what prompted a professor at Duke University to say “It’s amazing how what we can see in a coffee cup extends into a mathematical theorem with effects in the cosmos.” To understand why, perhaps it is worth reflecting a bit more on our coffee.

The shape of the curve is called a ‘cusp’ and the bright edge is known as a ‘caustic’. It is fairly easy to play with the angle of the cup and the light so that you can see the first cusp curve but you can go further and create caustics that are the result of multiple reflections. Such multiple reflections can give heart shaped curves or “cardioids” so, in a certain sense adding milk to your coffee is good for (seeing) the heart.

caustic in a cup of tea or coffee — A cusp reflection is just visible in a cup of (soya) milk tea

Caustics were first investigated by Huygens and Tschirnhaus in the late 17th century. Mathematically, the cusp curve is termed an epicycloid, you can draw one by tracing the shape made by a point on the circumference of a circle rotating around a second circle, as this graphic from Wolfram mathematics demonstrates. There is a lot of maths in milky coffee. But just how is it that these curves reveal the “Cosmos in a cup of coffee“? It turns out that once you start to see caustics you start to see them everywhere. Caustics are not just going to be formed on the inside of your coffee mug, they can be formed by light waves getting bent by ripples on the surface of a stream or even by gravity, in a phenomenon known as “gravitational lensing”. Gravitational lensing is when a massive object, such as a black hole or a galaxy, bends the light travelling past it so that it acts analogously to a lens in optics (but a very big one). It is this last type of caustic that prompted the headline quoted above. In a series of papers published in the Journal of Mathematical Physics, Arlie Petters of Duke University and coworkers calculated how light from distant objects was focussed through gravitational lensing and the effects of caustics. Their predictions (and in particular any exceptions to their predictions) could lead to a new way to search for the elusive dark matter, which is thought to contribute to much of the Universe’s mass. They are now waiting for the Large Synoptic Survey Telescope (LSST) to start mapping the sky in order to test their theories.

multiple caustics from multiple LEDs — Multiple light sources are being reflected in this cup.

Before concluding this discussion of cosmic coffee, it is worth taking another look at the mathematician Tschirnhaus. As well as maths, he was known for his philosophy and his chemistry. In fact, it seems that he was responsible for the invention of European porcelain. As noted elsewhere, it has been argued that it was the ability of Europeans to start making their own porcelain that explained the rapid rise in consumption of tea and coffee during the eighteenth century in Europe. Interestingly, one of the tools that allowed Tschirnhaus to succeed in manufacturing porcelain in Dresden where others elsewhere failed was his use of “burning mirrors” to focus the heat and to achieve higher furnace temperatures than were otherwise available. He was using those caustics that he and others had so thoroughly studied mathematically in order to produce the type of cup in which we most often encounter the easiest caustics. A lovely little ‘elliptical’ story on which to end this Daily Grind.

In order to see the caustics in your coffee, it is necessary that the coffee reflects the light incident on it. Meaning, you need to add milk to your coffee. I knew there had to be a good reason to add milk to coffee at some point. Please do share your photos of caustics in your coffee either here or on Facebook or Twitter.