Archive for the ‘Simple Science’ Category


February 18, 2018


After writing about ‘singing glasses’ previously, I was discussing the effect with my friend and colleague Andrew Hanson.

Have you done the mug thing?” he asked. And proceeded to hit the rim of a mug with a spoon.

As he moved the location at which he struck the mug, the pitch of the note changed.

And then he explained. Looking from the top, if the handle of the mug is at 12 O’clock, then:

  • Striking the mug at 3, 6, 9, or 12 produces one note – a lower note.
  • Striking the mug between 1 & 2, between 4 & 5, between 7 & 8 and between 10 & 11 produced a second note – a higher note.

Mug Vibrations 01

Andrew said the explanation was that in a mug, there are two types of flexural oscillations, and the frequency of the oscillations depends on whether the handle moves or not.

I was fascinated. How had I never noticed that before? And why was the note that sounded when the mug was struck ‘on the quarter hours’ lower?

This is a very long article, and I apologise. But the physics of this phenomenon is complex and it took me a long time to get to the bottom of it.


I picked 5 mugs from our domestic collection which were as straight-sided as possible, and which had walls which were as thin as possible. I thought these choices would make the vibrational spectrum simple.

First I measured the mugs: their diameter and the wall thickness, and then I picked a wooden striker and started hitting the mugs. (Speadsheet)

The place where one strikes the mug produces an oscillation with the striking location as a local maximum of the oscillation.

For a glass, it wouldn’t matter where one struck – any location on the rim is equivalent to any other. But for mugs, the striking position matters because of the handle.

Mug Vibrations 02

To see if I could understand what was going on I arranged the mugs in size order, from the smallest radius to the largest and struck each one three times at each location.

You can hear the sound here.

I also recorded the ‘spectrogram’ using the wonderful Spectrum View app for the iPhone. A screenshot from the app is shown below together with the mugs which made the noise.Mug Vibrations 03.png

A spectrogram shows:

  • time along the horizontal axis
  • frequency along the vertical axis
  • and the loudness of a sound at a particular frequency and time is shown by the colour: blue is quiet and yellow and red are loud.

On the spectrogram above one can see vertical lines which result from the ‘impulse’ sound of me hitting the mugs. This dies away quickly and one is just left with the ‘ringing’ of the mugs which I have outlined with dotted lines.

One can see that each mug rings at two closely-spaced frequencies. The two notes differ in frequency by between 5% and 15%.

Hitting the rim at either location produces mainly one mode of oscillation, but also a little of the other.

Let’s get numerical!

I used the app to locate the frequency of each note and plotted it on a graph of the frequency versus the mug diameter. I plotted each ringing note as a red dot, and their average as a black dot.


There was a general trend to lower frequency for the larger mugs, but the Toronto mug didn’t fit that trend.

I noticed that the walls of the Toronto mug were much thicker than the other mugs. So I wondered whether I could compensate for this by dividing the frequency by the thickness of the wall.

I did this based on the idea that the speed of the wave would be proportional to the  rigidity of the mug wall against bending. And that rigidity might be roughly proportional to the wall thickness. This seemed to be confirmed because the formerly ‘anomalous’ mug frequency now sat quite sweetly on a smooth trend.

Mug Vibrations 05

Now that the data seemed to fit a trend, I felt I was getting a handle on this problem. Could I understand the dependence of the resonance frequency on diameter?


All waves obey the wave formula v = f λ. That is, the speed of the wave, v, is the product of the frequency of the wave, f, and its wavelength  λ.

For the waves on these mugs, the wavelength of the wave which runs around the rim of the cup is just half the perimeter i.e.  λ = π D/ 2 where D is the diameter of the mug.

  • So if all the waves travel with the same speed, then the resonance frequency should vary with diameter as f = 2 v / (π D) i.e. inversely proportional to the diameter.
  • However, for flexural waves, the material supporting the wave becomes floppier at longer wavelengths, and the speed of a flexural wave should fall with increasing wavelength. If this were the case we would expect the resonance frequency to vary inversely as the diameter squared.

Which of the above cases described the data best? I have plotted the two predictions on the graph below.

Mug Vibrations 06

I adjusted the speeds of the waves to match the data for large mugs and then calculated how it should vary for smaller diameter mugs.

Overall I think it is the theory in which the  speed of the flexural wave changes with wavelength that matches the data best.


So now I had a theory that the speed of a flexural wave that runs around the rim of a mug is:

  • Proportional to the wall thickness
  • Inversely proportional to the diameter
    • So the resonance frequencies are inversely proportional to the diameter squared.

After I had finished all these measurements I came across another mug that I could have included in the study – my wife’s ‘Do more of what makes you happy‘ mug.

I decided to see if I could predict its resonant frequency from measurements of its wall thickness and diameter.

I have plotted data on this mug as crosses (×) on the graphs above and I think that overall it fits the trends rather well.

The two notes

If you belong to the minority who have read this far, then well done. It is only you who get to understand the final point about why the ‘quarter hour’ notes are lower.

What is the role of the handle? There are two possibilities.

  • Does it act as an extra mass which slows down the wave?
  • Or does it provide extra stiffness, which would speed up the wave?

Since the quarter hour notes are lower, it seems that it is the extra mass which appears to dominate in the mugs I have examined.


Wonder and Science

January 31, 2018

Recipes for Wonder

My good friend Alom Shaha has a new book out!

And discussing it over dinner the other evening I was struck by an analogy.

Talking and listening and reading and writing 

Children have no problem learning to understand and speak their mother tongue.

All they require is to be exposed to people speaking and they will learn to speak

But this ability does not make them ‘good at languages’.

In contrast with the ease with which children learn to speak, is the great difficulty they have in learning to read and write.

A web search tells me that 15% of the UK population are ‘functionally illiterate’ – a figure which I think has not changed much in recent years.

Reading and writing are hard: they take practice:

  • learning letter shapes.
  • learning the relationship between shapes and sounds.

And it can be a long time before all this becomes automatic and there is a payback on the effort expended.

Nonetheless, widespread literacy is considered essential for a functioning democracy.

And most people who have been taught to read and write are happy with the extra possibilities their new skills enable.

Wonder and Science

Similarly, I think children have an intrinsic sense of wonder.

Or at least they can acquire the sense with ease if they are exposed to adults who express interest in the world around them.

But going beyond the simple pleasure of “Wow!” is hard work.

However, it is that step – from ‘Wow!” to “How?” that is the step from wonder into science.

Why is it hard?

Firstly, imagine how well parents would teach their children to read and write if they were themselves illiterate.

Similarly, scientifically illiterate parents – or more commonly parents lacking confidence in their own abilities – can find teaching science hard.

And secondly, everything is complicated. So it is easy to spread confusion rather than enlightenment.

Consider a ‘simple’ experiment – the kind of activity that people recommend for kids – such as making a wine glass ‘sing’.

Just managing to make this happen is pleasurable – it is intriguing and surprising to hear. It is, literally, wonder-ful.

But when one begins to ‘step beyond’ wonder, it all becomes difficult. I have just spent a happy thirty minutes with my wife investigating. And even with two PhDs, an iPhone equipped with a slow motion camera, and spectrogram software we found it difficult!

For example:

  • Is it the glass or the air in the glass which is vibrating?
  • Why can one see very fine waves running on the surface of water in the glass?

If you search for clues as to what is happening you will find a dearth of answers on the web.

Alom’s book?

As I understand it,  Alom’s aim in writing his ‘recipes for wonder’ is to hold hands with parents and children so that their first steps beyond wonder into science are beguiling and delightful rather than bewildering and demoralising.

Such a book is sorely needed. I hope it does well.

By the way, if you would like to hear Alom talk, he will be appearing at the Royal Institution on March 8th .

P.S. What is happening with the ‘singing’ glass?

I am afraid, the physics is too complicated to explain in full, so here is a summary.

Firstly, the fundamental mode of vibration being excited is a ‘flexural’ oscillation of the glass rim and bowl.


Normally if one calculated the resonant frequency of a sound wave in a glass object of similar dimensions to a wine glass, one might expect a resonance at a very high frequency – perhaps 10 kHz or higher.

This is because the speed of sound in glass is over 4000 metres per second‚ more than 10 times higher than the speed of sound in air.

However, when a material is formed into a ring, it has a ‘soft’ mode of flexing illustrated in the animation above. (The bowl of the glass is not quite a ring, but the upper part of the bowl is ‘almost’ a ring.)

Even if the speed of sound in the material is very high, as the material of the ring becomes thinner, then it becomes easier to flex, and the restoring force pulling the ring back into shape becomes weaker.

This causes the speed a flexural wave in a glass ring to be much lower than the speed of a sound wave in glass. Thus the resonant frequency falls as well.

Once the vibration is established, it vibrates the air around the glass which is what we hear.

But note that this is not a resonance of the air in the glass. If it were, then adding water to the glass would reduce the size of the resonant cavity and cause an increase in the resonant frequency. In fact adding water lowers the resonant frequency.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

Note also that the gravity capillary waves that can be observed on the surface of the water are also a red herring.


These waves have a very low speed – about 30 centimetres a second, and so at few hundred hertz, they have a wavelength of much less than 1 millimetre.

Finally, there is also a connection between the noise made by a glass and that made by a xylophone. Xylophone

The vibrations excited by hitting the xylophone keys are not sound waves in the metal but flexural waves.

The speed of flexural waves falls in long thin (floppy) bars – getting less and less for longer bars. So for thin materials, the flexural wave can have a low speed leading to a low resonance frequency.

The fact that a xylophone uses flexural waves explains the relative sizes of the keys.

To make a key for a note one octave lower (i.e. half the frequency) of the top key, one does not have to double the length of the key. In fact one only needs to lengthen the bar by a factor of the square root of two (i.e. make about 41% longer).

Like I said: everything is complicated!





Candles at Christmas Revisited

December 21, 2017

Last week I gave a presentation at NPL on the physics of candles.

Above is a video of the slightly chaotic 32 minute presentation and if you are so inclined, you can download the PowerPoint file here.

I have spoken before about the wonderful physics of candles. But in revisiting the subject I learned that wax is basically not flammable and I felt obliged to mention this inconvenient truth!

The highlight of the talk is using a candle to power a thermo-electric generator, which in turn powers a USB port, which in turn powers a torch, which is brighter than the candle.


Sadly, in the rush at the end of the talk I forgot to actually measure the brightness of the torch!

Next time!

And by the way, here is the slow-motion candle-relighting movie that is embedded in the PowerPoint but which doesn’t show up well in the lecture theatre view.

Thanks to Brian Madzima for the videography and editing, and Nikita Mezhnyakov for the photograph.

How do we know anything?

November 18, 2017

How do we know Anything MdeP-NPL

This is an edited video of a talk I gave recently to the NPL Postgraduate Institute about the forthcoming changes to the International System of Units, the SI.

It’s 36 minutes long and you can download the PowerPoint slides here.

It features the first ever public display of the Standard Michael – the artefact defining length in the SM, le systeme de moi, or My System of Units. (It’s shown at about 6 minutes 40 seconds into the video).

The central thesis of the talk is summarised in the slide below:


In the talk I explain how the forthcoming changes to the SI will improve future measurements.

I hope you enjoy it.


Before understanding comes familiarity

November 14, 2017

Averil Horton

It is tough being an adult. Hey. We all know that.

But is especially tough if you realise as an adult that science fascinates you. There are relatively few places where you can go and learn about science  without being condescended to, or treated like a child.

I tried to create such an environment when I ran Protons for Breakfast and my friend Averil Horton is now trialling her ‘Science Club’ with adults.

I am attending as a helper – which is delightfully low stress compared to running a class!

And the key insight of which I have been reminded repeatedly is that experience has to come to before understanding. And for adults, just gaining exposure to the experiential pleasure of hands-on experimentation is so difficult!

I won’t describe the classes in detail, but below I will just post a couple of pictures showing the kinds of things people do. And with the exception of a couple of potentially dangerous things – everyone does everything!

Cutting Potassium…

This slideshow requires JavaScript.



Growing Silver…


Burning Magnesium…


Experiments with density…


Burning hydrocarbons…


And we are not even half way through!

Measuring Temperature with Sound

November 12, 2017


I have just given the first of a series of five talks for The Training Partnership, a company that provide ‘enrichment’ days for A level students.

Since one of my key messages is the importance of measurement in science, I feel obliged to perform some measurements during the presentation.

I find this worrisome, but I think it works well. When it works!

Anyway, with four more presentations to go I thought I would create a page with links to all the the resources I use in the talk.


The PowerPoint presentation can be found here. Please feel free to steal animations if you think they will be helpful, but please give credit to NPL.


During the presentation I use:

  • Audacity for capturing acoustic wave-forms and analysing them: it is astonishing software, and completely free.
  • Sound Card Oscilloscope for detecting the resonance within the spherical resonator: it is excellent and free for educational users. It also comes with a built in oscillator, but for the demo it is much clearer if I use a separate device. So I use…
  • Signal Generator, an app for IOS devices. There many others for both IOS and Android but this one is fine and costs £0.99.

And this is the spreadsheet I use to interpret the results from the experiment.


In my talk I use the same microphone for all the demonstrations, a commercial lapel microphone from RS Components (RS Stock No.242-8911which costs about £20. Similar devices are available from other suppliers.

I chose this particular model because it more robust than home-made contraptions and has a small head – so it fits inside tubes. Larger microphones will work but they tend to damp acoustic waves more strongly.

I hold it in place with a blob of Blutac.

The miniature loudspeaker I use for the resonator demo is quite specialised. It is from a range of products used in headphones, mobile phones and hearing aids produced by the Knowles corporation.

think the model I used is  from this ‘BK’ series. It requires wires to be soldered onto very tiny terminals, and then wired to a 4 mm jack plug that can connect to a mobile phone.

One alternative would be to dismantle a pair of in-ear headphones and just use the loudspeaker from one earphone.

Tube and Resonator

The metal tube I use in the talk is 1.1 metre long stainless steel tube approximately 9.5 mm diameter. You can also use many other types of tubing such as copper or steel plumbing tube.

In general, longer is better for more accurate measurements at room temperature, but it is obviously more difficult to heat it uniformly.

The resonator is a 3-D printed version of the copper resonator we used to measure the Boltzmann constant and make the most accurate temperature measurements in history.

I have placed the 3-D printing files in a zipped folder hereThere are files for the Northern Hemisphere, the Southern Hemisphere, and the plugs. Creating the resonator is quite complicated and I will write a separate blog post on that later.

Good luck!


The Joy of Science

October 15, 2017

For the last couple of weeks I have been a helper at Averil Horton’s Science Club.

It’s  very low key

Just a few adults doing science experiments themselves. And then discussing the results.

Helping – which requires no prior work on my part – has reminded me of the simple pleasure people experience from doing stuff for themselves.

And the pleasantness of discussing what one sees with others. It is the Joy of Science.

Here are some pictures.

Setting things on fire…


Seeing what floats in what…


Playing with colours…


Averil & Colours

And finishing with a little bit of magic…



Talking about the ‘New’ SI

July 3, 2017

I was asked to give a talk about the SI to some visitors tomorrow morning, and so I have prepared some PowerPoint slides

If you are interested, you can download them using this link (.pptx 13 Mb!): please credit me and NPL if you use them.

But I also experimentally narrated my way through the talk and recorded the result as a movie.

The result is… well, a bit dull. But if you’re interested you can view the results below.

I have split the talk into three parts, which I have called Part 1, Part 2 and Part 3.

Part 1: My System of Units

This 14 minute section is the fun part. It describes a hypothetical system of units which is a bit like the SI, but in which all the units are named after my family and friends.

The idea is to show the structure of any system of units and to highlight some potential shortcomings.

It also emphasises the fact that systems of units are not ‘natural’. They have been created by people to meet our needs.

Part 2: The International System of Units

This 22 minute section – the dullest and most rambling part of the talk – explains the subtle rationale for the changes in the SI upon which we have embarked.

There are two key ideas in this part of the talk:

  • Firstly there is a description of the separation of the concepts of the definition of a unit from the way in which copies of the unit are ‘realised‘.
  • And secondly, there is a description of the role of natural constants in the new definitions of the units of the SI.

Part 3: The Kilogram Problem

This 11 minute section is a description of one of the two ways of solving the kilogram problem: the Kibble balance. It has three highlights!

  • It features a description of the balance by none other than Bryan Kibble himself.
  • There is an animation of a Kibble balance which takes just seconds to play but which took hours to create!
  • And there are also some nice pictures of the Mark II Kibble Balance installed in its new home in Canada, including a short movie of the coil going up and down.


This is all a bit dull, and I apologise. It’s an experiment and please don’t feel obliged to listen to all or any of it.

When I talk to a live audience I hope it will all be a little punchier – and that the 2800 seconds it took to record this will be reduced to something nearer to its target 2100 seconds.




How would you take a dinosaur’s temperature?

March 15, 2017
A tooth from a tyrannosaurus rex.

A tooth from a tyrannosaurus rex.

Were dinosaurs warm-blooded or cold-blooded?

That is an interesting question. And one might imagine that we could infer an answer by looking at fossil skeletons and drawing inferences from analogies with modern animals.

But with dinosaurs all being dead these last 66 million years or so, a direct temperature measurement is obviously impossible.

Or so I thought until earlier today when I visited the isotope facilities at the Scottish Universities Environmental Research Centre in East Kilbride.

There they have a plan to make direct physical measurements on dinosaur remains, and from these measurements work out the temperature of the dinosaur during its life.

Their cunning three-step plan goes like this:

  1. Find some dinosaur remains: They have chosen to study the teeth from tyrannosaurs because it transpires that there are plenty of these available and so museums will let them carry out experiments on samples.
  2. Analyse the isotopic composition of carbonate compounds in the teeth. It turns out that the detailed isotopic composition of carbonates changes systematically with the temperature at which the carbonate was formed. Studying the isotopic composition of the carbon dioxide gas given off when the teeth are dissolved reveals that subtle change in carbonate composition, and hence the temperature at which the carbonate was formed.
  3. Study the ‘formation temperature’ of the carbonate in dinosaur teeth discovered in a range of different climates. If dinosaurs were cold-blooded, (i.e. unable to control their own body temperature) then the temperature ought to vary systematically with climate. But if dinosaurs were warm-blooded, then the formation temperature should be the same no matter where they lived (in the same way that human body temperature doesn’t vary with latitude).
A 'paleo-thermometer'

A ‘paleo-thermometer’

I have written out the three step plan above, and I hope it sort of made sense.

So contrary to what I said at the start of this article, it is possible – at least in principle – to measure the temperature of a dinosaur that died at least 66 million years ago.

But in fact work like this is right on the edge of ‘the possible’. It ought to work. And the people doing the work think it will work.

But the complexities of the measurement in Step 2 appeared to me to be so many that it must be possible that it won’t work. Or not as well as hoped.

However I don’t say that as a criticism: I say it with admiration.

To be able to even imagine making such a measurement seems to me to be on a par with measuring the cosmic microwave background, or gravitational waves.

It involves stretching everything we can do to its limits and then studying the faint structures and patterns that we detect. Ghosts from the past, whispering to us through time.

I was inspired.


Thanks to Adrian Boyce and Darren Mark for their time today, and apologies to them both if I have mangled this story!

Do you really want to know if global warming is real?

January 28, 2017

About a year ago, I thought that Climate Change Deniers had lost the argument.

I thought that we were all moving on to answering more interesting questions, such as what to do about it.

But it seems I was wrong. It seems that in this post-truth world, climate change deniers are uninterested in reality – preferring instead alternative facts.

I am left speechless in the face of this kind of intellectual dishonesty.

Actually I am only almost speechless. I intend to continue trying to empower people by fighting this kind deception.

Rather than trying to woo people over to my view, my aim is simply to offer people the chance to come to their own informed opinion.

See for yourself

As part of my FREE University of Chicago Course on Global Warming, I have been using some astonishing FREE software. And its FREE!


The ‘Time Series Browser’ allows one to browse a 7000 station subset of our historical temperature records from meteorological stations around the world.

  • The data are the local station temperatures averaged over 1 month, 1 year or 1 decade. Whichever you choose you can also download this data into a spreadsheet to have fun with on your own!
  • One can select sets of data based on a variety of criteria – such as country, latitude band, altitude, or type of geographical location – desert, maritime, tropical etc. Or you can simply pick a single station – maybe the one nearest you.

Already this is enormously empowering: this is the pretty much the same data set that leading climate scientists have used.

For this article I randomly chose a set of stations with latitudes between 20°N and 50°N.


The bold dots on the map show the station locations, and the grey dots (merging into a continuous fill in parts) are the available locations that I could have chosen.

The data from the selected stations is shown below.  Notice the scale on the left hand side runs from -10 °C to + 30 °C.


In this form it is not obvious if the data is warming or cooling: And notice that only a few data sets span the full time range.

So how do we discover if there are trends in the data?

The first step

Once you have selected a set of stations one can see that some stations are warm and others cool. In order to be able to compare these data fairly, we subtract off the average value of each data set between 1900 and 1950.

This is called normalisation and allows us to look in detail at changes from the 1900-1950 average independent of whether the station was in a warm place or a cold place.


Notice that the scale on the left-hand side is now just ± 3.5 °C.

The second step

One can then average all the data together. This is has the effect of reducing the fluctuations in the data.

One can then fit a trend-line to see if there is a recent warming or cooling trend.


For this particular set of stations its pretty clear that since 1970, there is a warming trend. The software tells me it is approximately 0.31 ± 0.09 °C per decade.

What I have found is that for any reasonably diverse set of stations a warming trend always emerges. I haven’t investigated this thoroughly, but the trend actually seems to emerge quite clearly above the fluctuations.

But you can check that for yourself if you want!

Is it a cheat? No!

You can check the maths of the software by downloading the data and checking it for yourself.

Maybe the data is fixed? You download the source data yourself – it comes from the US Global Historical Climatology Network-Monthly (GHCN-M) temperature data-set.

But accessing the raw data is quite hard work. If you are a newbie, it will probably take you days to figure out how to do it.

There is more!

This ability to browse, normalise, average and fit trends to data is cool. But – at the risk of sounding like a shopping channel advertorial – there is more!

It can also access the calculations of eleven different climate models.

For the particular set of stations that you have selected, the software will select the climate model predictions (a) including the effect of human climate change and (b) without including human-induced climate change.

For my data selection I chose to compare the data with the predictions of the CCSM4 Climate model. The results are shown below


You can judge for yourself whether you think the trend in the observed data is consistent with the idea of human-induced climate change.

For the particular set of stations I chose, it seems the CCSM4 climate model can only explain the data by including the effect of human-induced climate change.

But Michael: this is just too much like hard work!

Yes and no. This analysis is conceptually challenging. But it is not crazily difficult. For example:

  • Schoolchildren could do this with help from a teacher.
  • Friends could do it as a group and ask each other for help.
  • University students could do this.
  • Scout groups could do it collectively.

It isn’t easy, but ultimately, if you really want to know for yourself, it will take some work. But then you will know.

So why not have a go?  The software is described in more detail here, and you can view a video explaining how to use the software here.

[January 28th 2017: Weight this morning 71.2 kg: Anxiety: Sick to my stomach: never felt worse]

%d bloggers like this: