Notes on a cup

Ritzenhoff Mugs

Experimental apparatus

An opportunity for an experiment with a cup of coffee. Sadly though, for the experiment itself, it would probably help if the mug were empty, so there are two choices: Either grab a coffee and drink it so that you have the empty cup next to you, or get an empty cup and wait for your coffee until later. There is though, perhaps a third choice, get two cups, one with coffee in it, one empty, that sounds a much better idea.

Now, get a pen or pencil and start to tap the rim of the cup, make note of the sound that the cup makes as you tap at a point next to the handle, moving around to 45º from the handle, 90º from the handle etc. Perhaps compare the sound of different mugs but, on going around any particular cup, what do you hear? The note that you will hear when you tap the mug just next to the handle, or at 90º intervals from the handle should be lower than the note that you hear at 45º angles to the handle. Why is that?

wobbly bridge, Millennium Bridge

“Couple at St Pauls”, photograph © Artemisworks Photography. The ‘wobbly bridge’ is in the background.

Before answering that question, and to give you some time to think about it, it may be time to consider a (related) anecdote. Back at the turn of the millennium, a new ‘shard of light’ was built across the Thames. The Millennium Bridge takes pedestrians from the Tate Modern on the South bank towards St Paul’s on the North bank (or vice versa). It opened on 10th June 2000 and then closed, two days later, owing to problems that left it labelled the ‘wobbly bridge’. Along with many people, I had been taken in by the newspaper headlines of the time saying that we had built a terrible and wobbly bridge. It wasn’t until I was researching St Katherine’s Docks for the White Mulberries cafe-physics review that I found David Blockley’s book, ‘Bridges, the science and art of the world’s most inspiring structures’ and learned the true story. It turns out that the reason the bridge wobbled was because of a previously unknown phenomenon. Dubbed ‘synchronous lateral excitation’, it is a human crowd response to a platform swaying under their feet. Apparently in response to a swaying platform, people will widen their gait slightly to compensate for the wobble, only this acts to increase the sideways force on the platform itself and so can amplify the wobble. This bit had been known, what had not been appreciated was how the ‘wobble’ would grow if a crowd were present. The reason that the wobbly bridge surprised everyone was that never before had the critical mass of pedestrians been walking on a susceptible bridge. According to Blockley, 156 people walking along a particular section of the (original) Millennium Bridge did not cause a problem, but 166 walking in a group along the bridge caused the wobble to quickly become very appreciable.

hitting Zorro

Poor Zorro being experimented upon.

The solution, of course, was to damp the structure, to add shock absorbers and weights to the bridge so that the oscillation decreased. The cup is behaving similarly. Each time you tap the cup, you are exciting a standing wave around the rim of the mug, this is what is exciting the sound. This vibration has four points of maximum oscillation (called anti-nodes) and four stationary points (nodes) around the mug spaced at equal intervals. If the cup is hit so that the handle (which adds a relative weight to one side of the cup) is at a point of maximum oscillation, the mass that is being moved is greater than if there is a node at the handle so it does not have to move. This change of mass shifts the frequency of the oscillation and so the note is lower than when the handle is at a point of zero movement. For more information on the standing waves in your cup click here.

So it’s not just science in your coffee cup, a world of engineering is mirrored in your brew too.

Bridges – the science and art of the world’s most inspiring structures, by David Blockley was published by Oxford University Press in 2010, it is well worth a read as it is a very accessible and informative guide to bridges as well as being entertaining.

If you notice any engineering in your coffee cup, why not let me know via the comments section below or by contacting me via email.

Bridging worlds at White Mulberries, St Katherine’s Docks

chalkboard at White Mulberries

Sign board at White Mulberries.

Five minutes walk from the Tower of London is an area that feels far removed, physically and metaphorically, from the crowds swarming around the central tourist sights. St Katherine’s Docks offer a peaceful retreat a stone’s throw away from the bustle of the Tower. And if you are in this area, there is no better place to have a coffee (and potentially a cake) than White Mulberries. This café looks over the central basin of the three docks in St Katherine’s and is, seemingly, in the only 19th century warehouse still standing in the docks. On each occasion I have visited White Mulberries the coffee has been very good. As a black coffee drinker, the taste of the coffee has to be great as there is no hiding a bitter espresso with the milk of a latte and White Mulberries has passed every time (their website says that they rotate the coffee roasters, so I can only assume that they have a great relationship with their suppliers). If Latte Art is your thing though, White Mulberries also has that. It was an example of the latte art at White Mulberries that accompanied my recent article in Physics World.

Bascule Bridge, St Katherine's Docks

A moving bridge at the entrance to St Katherine’s Docks. There are youtube videos of this opening.

The point of a “café-physics” review on Bean Thinking though is only partly about the great coffee on offer (all cafes that are featured in the Daily Grind have great coffee). Part of the point of a café-physics review is to look around, slow down and notice things and see what physics there is around the café in question. There is always something to notice, always something science-like to appreciate. White Mulberries is no different, with an enormous number of things to notice, from the water in the docks to the Aeolian harps made by the rigging on the yachts moored nearby. What I would like to concentrate on today though are the bridges. Bridges are often used in scientific outreach with children. I think it is partly because so many concepts in physics can be communicated by practising making bridges. Forces need to be balanced (Newton), stress and strain needs to be considered, the properties of materials are unconsciously learned. And this, I think is another reason that bridges are a great ‘outreach’ tool, because bridges are inherently multidisciplinary. To make a good bridge requires elements from physics, chemistry, mechanical and civil engineering and art to name just a few. A bridge needs to satisfy the aesthetic demands of the public that use it as well as the structural demands of the people that will stand on it. And the bridges in the docks required yet more work and more understanding, for these aren’t just bridges that span a waterway, these bridges need to move somehow to allow boats to pass, either by having a platform that rises up (as with the nearby Tower Bridge), or platforms that swing around (which was the design of some of the original bridges at St Katherine’s Docks). Great thought and understanding went into the design and building of these mechanisms for moving the bridges. There is much to be gained by contemplating bridge design.

Microcord image of Tower Bridge with tourist in foreground

Tower Bridge, Photo © Artemisworks Photography,

Which brings us to another bridge, this time a metaphorical one between White Mulberries and the Coffee Houses of the past. The designer of St Katherine’s Docks was Thomas Telford (1757-1834). As well as specifying the design of the docks, he was responsible for some of the original bridges in the docks themselves, particularly a swing bridge that was built in 1828. St Katherine’s Docks was Telford’s only London project but that didn’t stop him from being a regular in a Coffee House near (what is now) Trafalgar Square. For many years Telford drank coffee in the Salopian Coffee House (most likely in Spring Gardens, just behind Cockspur St). This was where he stayed when in London and, as he was a famous engineer by that point, he started to attract crowds of engineers and admirers to the Salopian in the hope of meeting him. So important was Telford to the business of this central London coffee house that, when he left to live in Abingdon St, the new landlord of the Salopian complained to him “What, leave the house? Why sir, I have just paid £750 for you!”.

Fortunately, White Mulberries has far more to attract customers to it than one illustrious coffee drinker, though perhaps it has those as well.


White Mulberries is at St Katherine’s Docks, E1W 1AT,

A good book on bridges is: “Bridges – the science and art of the world’s most inspiring structures”, David Blockley, Oxford University Press (2010)

Coffee House anecdotes from “London Coffee Houses”, Bryant Lillywhite (1963)