Archive for the ‘Personal’ Category

Talking about the SI

June 24, 2018

In just a few days, we will be setting up our stand about the International System of Units, the SI, at the Royal Society Summer Science Exhibition (RSSSE).

In May 2019 the world plans to redefine four of the base units of the SI. The re-definition represents a profound change in our concept of measurement.

And it involves quantities with which most people are familiar, such as ‘a kilogram’, or ‘a degree Celsius’.

So we have thought long and hard about how to communicate this at RSSSE.

Where to start?

The geographical theory of knowledge  suggests that ‘explanations of concepts’ are like ‘directions from one place to another’.

And thus, when people visit our stand, we are obliged to start giving ‘directions’ from where they actually ‘are’.

Although we want to talk about the re-definition of the SI, we have to acknowledge that most people don’t actually know much about the SI.

So if we want to ‘start from where people are’, we first need to explain what the SI is now, and why it matters. And that is what we have done.

It’s about Measurement.

In the ‘orientation’ for colleagues who will be helping at the RSSSE, we have stressed three starting points to help orient visitors to the stand.

  • At the heart of science and engineering, there is measurement.
  • Measurement is the comparison of an unknown thing against a standard.
  • In the International System of Units there are seven standard things against which all physical quantities are compared.

We then have seven hands-on demonstrations – one for each of the seven standard quantities (called ‘base units’)- which will hopefully serve as starting points for conversations.

Keep it simple!

In developing the ‘hands-on demonstrations we worked with the magical people at Science Projects to build apparatus that was robust and simple.

They have years of experience developing hands-on kit for museums and interactive science centres.

As we honed our initial ideas, Science Projects staff constantly challenged us to ‘keep it simple’. And in (almost) every case, their instincts were sound.

A demonstration which is engaging and which can be immediately grasped is a dramatically better starting point for a conversation than one which is beautifully sophisticated, but only elicits the Ah-yes,-I-see-now-moment after 5 minutes.

NPL Stands for the RSSSE exhibition

Stands for the RSSSE exhibition

NPL tweaks!

We developed the demonstrations and tried them out on NPL’s Open Day in May. The stands all survived and people seemed happy with the demonstrations.

But because we are NPL, and because at RSSSE we also need to interact with Fellows of the Royal Society, we had to add some truly complex and amazing features that are right at the forefront of science.

  • The ‘time team’ decided to develop an app that would allow people to compare the time on their own phones with the time from NPL’s Caesium atomic clock.
  • The ‘length team’ decided they wanted to develop a laser interferometer that would measure the height of SI-bots in terms of the wavelength of light.
  • The ‘mass team’ wanted to put an actual working Kibble balance on the stand at the Royal Society.

As I write this on Sunday 24th June, – none of these demonstrations are ready! But my colleagues are working hard and I am cautiously confident they will succeed.

If you get a chance to visit, the RSSSE is FREE and runs from Monday 2nd July 2018 until Sunday 9th July 2018.




Work-life balance

June 23, 2018
It is possible to do lots of things at the same time. (Picture Credit: Dr Seuss)

Figure 1: It is possible to do lots of things at the same time. (Picture Credit: Dr Seuss)

One of my favourite management consultants is Dr. Seuss.

In his guide to optimising productivity, amusingly titled, “The Cat in the Hat“, (TCITH) the good doctor shows us that it is indeed possible to ‘do it all’.

I find it interesting that this book – which uses short words and a restricted vocabulary because it was written for busy managers – is now widely used with children.

I see this as a really positive development. It is after all essential that our children learn what is possible with practice. But this has not reduced the impact of TCITH in modern management.

So while “standing on a ball in the hall”, a metaphor for day-to-day work, children learn that they can also do many other things at the same time without there being any negative consequences.

In Dr Seuss’s guide, the eponymous hero also balances a cake and a rake, a fish and a dish, a fan and a man! These wittily-chosen tasks are of course merely placeholders for specific tasks that we can all learn to do simultaneously.

For example in my life, they might represent:

  • Preparing for the Royal Society Summer Science Exhibition
  • Refereeing scientific papers.
  • Mending broken equipment.
  • Mending the gutter
  • Carrying out urgent experiments for customers
  • Giving training courses
  • Managing complex manufacturing projects with tight deadlines.
  • Collecting the children’s stuff from university.
  • Planning collaborative projects with European partners.

All in addition to “standing on a ball in the hall” i.e. carrying out my normal job.

I have to admit that I occasionally find this stressful. But when I do I turn to Dr. Seuss for re-assurance.

Looking at the charmingly-drawn illustrations (see Figure 1), I see ‘a cat’ who is ‘doing it all’ and enjoying it at the same time.

The seminal impact of TCITH can be assessed by considering our relatively recent concerns with ‘work-life balance’, a concept clearly foreseen and graphically illustrated in TCITH.

Looking at ‘cat’ in the illustrations, it is clear that if life is busy or challenging at home, one merely needs to add an equivalent challenge at work in order to maintain the work-life balance.

  • Dr. Seuss: Thank you.
  • Cat in the Hat: you are my hero.


The James Webb Space Telescope

May 10, 2018

Last week I was on holiday in Southern California. Lucky me.

Lucky me indeed. During my visit I had – by extreme good fortune – the opportunity to meet with Jon Arenberg – former engineering director of the James Webb Space Telescope (JWST).

And by even more extreme good fortune I had the opportunity to speak with him while overlooking the JWST itself – held upright in a clean room at the Northrop Grumman campus in Redondo Beach, California.

[Sadly, photography was not allowed, so I will have to paint you a picture in words and use some stock images.]


In case you don’t know, the JWST will be the successor to the Hubble Space Telescope (HST), and has been designed to exceed the operational performance of the HST in two key areas.

  • Firstly, it is designed to gather more light than the HST. This will allow the JWST to see very faint objects.
  • Secondly, it is designed to work better with infrared light than the HST. This will allow the JWST to see objects whose light has been extremely red-shifted from the visible.

A full-size model of the JWST is shown below and it is clear that the design is extraordinary, and at first sight, rather odd-looking. But the structure – and much else besides – is driven by these two requirements.

JWST and people

Requirement#1: Gather more light.

To gather more light, the main light-gathering mirror in the JWST is 6.5 metres across rather than just 2.5 metres in the HST. That means it gathers around 7 times more light than the HST and so can see fainter objects and produce sharper images.


Image courtesy of Wikipedia

But in order to launch a mirror this size from Earth on a rocket, it is necessary to use a  mirror which can be folded for launch. This is why the mirror is made in hexagonal segments.

To cope with the alignment requirements of a folding mirror, the mirror segments have actuators to enable fine-tuning of the shape of the mirror.

To reduce the weight of such a large mirror it had to be made of beryllium – a highly toxic metal which is difficult to machine. It is however 30% less dense than aluminium and also has a much lower coefficient of thermal expansion.

The ‘deployment’ or ‘unfolding’ sequence of the JWST is shown below.

Requirement#2: Improved imaging of infrared light.

The wavelength of visible light varies from roughly 0.000 4 mm for light which elicits the sensation we call violet, to 0.000 7 mm for light which elicits the sensation we call red.

Light with a wavelength longer than 0.000 7 mm does not elicit any visible sensation in humans and is called ‘infrared’ light.

Imaging so-called ‘near’ infrared light (with wavelengths from 0.000 7 mm to 0.005 mm) is relatively easy.

Hubble can ‘see’ at wavelengths as long as 0.002 5 mm. To achieve this, the detector in HST was cooled. But to work at longer wavelengths the entire telescope needs to be cold.

This is because every object emits infrared light and the amount of infrared light it emits is related to its temperature. So a warm telescope ‘glows’ and offers no chance to image dim infrared light from the edge of the universe!

The JWST is designed to ‘see’ at wavelengths as long as 0.029 mm – 10 times longer wavelengths than the HST – and that means that typically the telescope needs to be on the order of 10 times colder.

To cool the entire telescope requires a breathtaking – but logical – design. There were two parts to the solution.

  • The first part involved the design of the satellite itself.
  • The second part involved the positioning the satellite.

Cooling the telescope part#1: design

The telescope and detectors were separated from the rest of the satellite that contains elements such as the thrusters, cryo-coolers, data transmission equipment and solar cells. These parts need to be warm to operate correctly.

The telescope is separated from the ‘operational’ part of the satellite with a sun-shield roughly the size of tennis court. When shielded from the Sun, the telescope is exposed to the chilly universe, and cooled gas from the cryo-coolers cools some of the detectors to just a few degrees above absolute zero.

Cooling the telescope part#2: location

The HST is only 300 miles or so from Earth, and orbits every 97 minutes. It travels in-to and out-of full sunshine on each orbit. This type of orbit is not compatible with keeping a gigantic telescope cold.

So the second part of the cooling strategy is to position the JWST approximately 1 million miles from Earth at a location known as the second Lagrange point L2.

At L2 the gravitational attraction of the Sun is approximately 30 times greater than the gravitational attraction of the Earth and Moon.

At L2 the satellite orbits the Sun in a period of one year – and so stays in the same position relative to the Earth.

  • The advantage of orbiting at L2 is that the satellite can maintain the same orientation with respect to the Sun for long periods. And so the sun-shade can shield the telescope very effectively, allowing it to stay cool.
  • The disadvantage of orbiting at L2 is that it is beyond the orbit of the moon and no manned space-craft has ever travelled so far from Earth. So once launched, there is absolutely no possibility of a rescue mission.

The most expensive object on Earth?

I love the concept of the JWST. At an estimated cost of $8 billion, if this is not the most expensive single object on Earth, then I would be interested to know what is.

But it has not been created to make money or as an act of aggression.

Instead, it has been created to answer the simple question

I wonder what we would see if we looked into deep space at infrared wavelengths.”. 

Ultimately, we just don’t know until we look.

In a year or two, engineers will place the JWST on top of an Ariane rocket and fire it into space. And the most expensive object on Earth will then – hopefully – become the most expensive object in space.

Personally I find the mere existence of such an enterprise a bastion of hope in a world full of worry.


Many thanks to Jon Arenberg  and Stephanie Sandor-Leahy for the opportunity to see this apogee of science and engineering.


Breathtaking photographs are available in galleries linked to from this page


Error Bar

April 15, 2018

Error Bar

This picture arrived in my in box through the medium of Twitter.

The Bar

It shows the Error Bar, with 20 ± 2 beers on tap, and a neon sign in which two glasses conspire to make an uncertainty indication.

It must surely be run by a burned-out metrologist who couldn’t take the heat of cutting-edge metrology.

The modern day equivalent of Graham Greene’s ‘whisky priest’, they retired to a town with barely a single calibration laboratory.

Here, they run the Error Bar and (unheeded) give advice on uncertainty estimation to random passers by while dispensing precise doses of tequila, with amounts of ethanol traceable to the SI base unit mole .

The awning of the bar sports the logo of the BIPM – the International Bureau of Weights and Measures – where they were seconded for a summer.

Error Bar detail 2

However it was here that their true love slipped away while they worked on an impossible uncertainty budget. And they never recovered.

In memory of their lost love,  they commissioned the local blacksmith to create a railing on the disabled access ramp which reflects the uncertainty that life always entails.

Error Bar detail 1

The Restaurant

And after a drinking a glass or two of tequila, one can retire to the restaurant next door – Measurands (literally meaning “the things which are measured”).

Error Bar detail 3

Is this place real?

I doubt it. 

But the picture has been created with great care by a metrologist and (if they can ever confess to creating this picture)  I would love to shake their hand…

…and perhaps buy them a drink in this little out-of-the-way bar I have heard of…


Air Temperature

April 1, 2018

Recently, two disparate strands of my work produced publications within a week of each other.

Curiously they both concerned one of the commonest measurements made on Earth today – the measurement of air temperature.

  • One of the papers was the result of a humbling discovery I made last year concerning a common source of error in air temperature measurements. (Link to open access paper)
  • On the other  paper I was just one amongst 17 authors calling for the establishment of global reference network to monitor the climate. My guess is that most people imagine such a network already exists – but it doesn’t! (Link to open access paper)

I am writing this article because I was struck by the contrasting styles of these papers: one describing an arcane experimental detail; and the other proposing a global inter-governmental initiative.

And yet the aim of both papers was identical: to improve measurement so that we can more clearly see what is happening in the world.

Paper 1

In the middle of 2018 I was experimenting with a new device for measuring air temperature by measuring the speed of sound in air.

It’s an ingenious device, but it obviously needed to be checked. We had previously carried out tests inside environmental chambers, but the temperature stability and uniformity inside the chambers was not as good as we had hoped for.

So we decided to test the device in one of NPL’s dimensional laboratories. In these laboratories, there is a gentle, uniform flow of air from ceiling to floor, and the temperature is stable to within a hundredth of a degree Celsius (0.01 °C) indefinitely.

However, when I tried to measure the temperature of the air using conventional temperature sensors I got widely differing answers – varying by a quarter of a degree depending on where I placed the thermometer. I felt utterly depressed and humiliated.

Eventually I realised what the problem was. This involved stopping. Thinking carefully. And talking with colleagues. It was a classic case of eliminating the impossible leaving only the improbable.

After believing I understood the effect, I devised a simple experiment to test my understanding – a photograph of the apparatus is shown below.


The apparatus consisted of a set of stainless steel tubes held in a clamp stand. It was almost certainly the cheapest experiment I have ever conducted.

I placed the tubes in the laboratory, exposed to the downward air flow, and  left them for several hours to equilibrate with air.

Prior to this experience, I would have bet serious amounts of money on the ‘fact’ that all these tubes would be at the same temperature. My insight had led me to question this assumption.

And my insight was correct. Every one of the tubes was at a different temperature and none of them were at the temperature of the air! The temperature of the tubes depended on:

  • the brightness of the lights in the room – which was understandable but a larger effect than I expected, and
  • the diameter of the tubes – which was the truly surprising result.

Results 1

I was shocked. But although the reason for this is not obvious, it is also not complicated to understand.

When air flows air around a cylindrical (or spherical) sensor only a very small amount of air actually makes contact with the sensor.

Air reaching the sensor first is stopped (it ‘stagnates’ to use the jargon). At this point heat exchange is very effective. But this same air is then forced to flow around the sensor in a ‘boundary layer’ which effectively insulates the sensor from the rest of the air.

Air flow

For small sensors, the sensor acquires a temperature close to that of the air. But the air is surprisingly ineffective at changing the temperature of larger sensors.

The effect matters in two quite distinct realms.


In metrology – the science of measurement – it transpires that knowledge of the temperature of the air is important for the most accurate length measurements.

This is because we measure the dimensions of objects in terms of the wavelength of light, and this wavelength is slightly affected by the temperature of the air through which the light passes.

In a dimensional laboratory such as the one illustrated below, the thermometer will indicate a temperature which is:

  • different from the temperature of artefacts placed in the room, and
  • different from the temperature of the air.


Unless the effect is accounted for – which it generally isn’t – then length measurements will be slightly incorrect.


The effect is also important in climatology. If a sensor is changed in a meteorological station people check that the sensor is calibrated, but they rarely record its diameter.

If a calibrated sensor is replaced by another calibrated sensor with a different diameter, then there will be a systematic effect on the temperatures recorded by the station. Such effects won’t matter for weather forecasting, but they will matter for people using the stations for a climate record.

And that brings me to Paper 2

Paper 2

Hadcrut4 Global Temperature

When we see graphs of ‘global temperatures’ over time, many people assume that the data is derived from satellites or some ‘high-tech’ network of sensors. Not so.

The ‘surface’ temperature of the Earth is generally estimated in two quite distinct parts – sea surface temperature and land surface temperature. But both these terms are slight misnomers.

Considering just the land measurements, the actual temperature measured is the air temperature above the land surface. In the jargon, the measurement is called LSAT – the Land Surface Air Temperature.

LSAT is the temperature which human beings experience and satellites can’t measure it.

LSAT data is extracted from temperature measurements made in thousands of meteorological stations around the world. We have data records from some stations extending back for 150 years.

However, it is well known that data is less than ideal: it is biased and unrepresentative in many ways.

The effect described in Paper 1 is just one of many such biases which have been extensively studied. And scientists have devised many ways to check that the overall trend they have extracted – what we now call global warming – is real.

Nonetheless. It is slightly shocking that a global network of stations designed specifically with the aim of climate monitoring does not exist.

And that is what we were calling for in Paper 2. Such a climate network would consist of less than 200 stations world-wide and cost less than a modest satellite launch. But it would add confidence to the measurements extracted from meteorological stations.

Perhaps the most important reason for creating such a network is that we don’t know how meteorological technology will evolve over the coming century.

Over the last century, the technology has remained reasonably stable. But it is quite possible that the nature of data acquisition for meteorological applications will change  in ways we cannot anticipate.

It seems prudent to me that we establish a global climate reference network as soon as possible.


Paper 1

Air temperature sensors: dependence of radiative errors on sensor diameter in precision metrology and meteorology
Michael de Podesta, Stephanie Bell and Robin Underwood

Published 28 February 2018
Metrologia, Volume 55, Number 2

Paper 2

Towards a global land surface climate fiducial reference measurements network
P. W. Thorne, H. J. Diamond, B. Goodison , S. Harrigan , Z. Hausfather , N. B. Ingleby , P. D. Jones ,J. H. Lawrimore , D. H. Lister , A. Merlone , T. Oakley , M. Palecki , T. C. Peterson , M. de Podesta , C. Tassone ,  V. Venema, K. M. Willett

Published: 1 March 2018
Int. J. Climatol 2018;1–15.

Obesity Policy

March 6, 2018

BBC Story Extract

Today the BBC are reporting that:

Britain needs to go on a diet, says top health official

The article states that people should allow:

  • 400 kilo-calories for breakfast
  • 600 kilo-calories for lunch
  • 600 kilo-calories for dinner

which adds up to 1600 kilo-calories a day. With this dietary intake, most adults in sedentary occupations will lose weight or maintain a healthy weight.

However, the article then goes on to say:

It is recommended that women should eat no more than 2,000 kilo-calories a day, while men should limit their intake to 2,500 kilo-calories.

No! As I pointed out previously, this is just too many calories for both men and women with sedentary lifestyles.

Any government campaign based on these figures is bound to fail.

Calories versus Age

For someone of my height and weight, the government’s recommended dietary intake is about 30% too high.

Is weight homeostasis possible?

February 28, 2018

I am slightly obsessed with my weight. Forgive me: I am 58 and have spent many decades repeatedly putting on weight slowly, and then losing it rapidly.

For many years I have wondered why can’t I just eat modestly and trust my body to “sort itself out!”

My recent discovery of the Mifflin St Joer equations (link) has allowed me to  simulate my weight over time, and my calculations are allowing me to understanding my own experience.

But my calculations have also raised a profound question:

  • Is homeostasis of weight even possible?


Homeostasis (or Homoeostasis) is the term given to physiological systems which conspire to keep something constant.

For example, we have systems that maintain our body temperature without any conscious effort. I don’t have to berate myself for being too hot and promise myself that in the future I will try to be cooler.

No. Our bodies sort out their internal temperature. I understand the system consists of temperature sensitive cells and nervous system reflexes that control blood flow, sweat glands, shiver reflexes, and our desire to undertake activity.


And I have generally imagined that in a more perfect world, a similar kind of system would underpin my desire to eat.

In this ideal world, I would naturally maintain my weight without any obvious effort on my part – stopping eating when I had eaten ‘enough’.

I had thought such a system actually existed. One part of the system is supposed to arise from the competing actions of hormones such as ghrelin – which makes us experience hunger – and leptin – which makes us feel satiated.

Together, ghrelin and leptin are supposed to act as part of a system of energy homeostasis.

However, having run many simulations of my own weight versus time (see below) and reflected on this, I am sceptical.

“But I know a bloke who…”

We all know people who seem to be able to eat at their ease and not put on weight.

I have no explanation for that, but then I have never experienced that myself.

My experience is that my weight either increases or decreases over time. What I have never observed it to do in all my 58 years on Earth is to stay the same! (I have written about this before: story 1 or story 2.)

What’s the problem?

I programmed the Mifflin St Joer equations into a spreadsheet to see the predicted effect on my weight of various dietary and exercise choices.

You can download the spreadsheet here and perform calculations about yourself in the privacy of your own computer. 

I entered my current age (58.2 years) and weight (74 kg), and I used the MSJ equations to predict what would happen to my weight if I ate 1800 kiloCalories (kCal) a day.

The results are shown below together with the effect of eating 50 kCal/day more or less

Weight versus Age Projection

  • The red line suggests that if I eat 1800 kCal/day then my weight will gradually decline over the next couple of years stabilising at about 71 kg. That would be dandy.
  • However, the dotted green lines show what would happen if I got my calorific intake wrong by ± 50 kCal per day. This is plus or minus half of a small glass of wine, or a half a biscuit either eaten, or not eaten.

These ‘alternate realities’ predict that my weight in three years time might be anywhere between 64 kg and 77 kg – a range of 13 kg!

To be within a kilogram of the predicted weight, my average energy intake would need to match 1800 kCal/day within 10 kCal a day. That is less than a single mouthful of food!

I don’t believe that any autonomic system can achieve that level of control. 

Weight versus Age Projection 2

So what?

Reflecting on these simulations, I don’t believe that the systems within our bodies that mediate ‘energy homoeostasis’ operate well over many years.

At least they don’t operate well in an environment where calories are so easy to obtain.

So I think my experience of slow weight gain over time is not a fault with my autonomic nervous system, or a moral failing on my part. It is just the way things are.

Asking the thinerati

Asking several slim individuals around the coffee machine this morning confirmed my view. They all were either (a) young (b) self-conscious about fitting into clothes or (c) weighed themselves regularly.

Personally I have resolved to keep weighing myself and using this to provide manual feedback.

How is my weight doing? Thank you for asking. It’s been just about stable since Christmas and I intend to keep it that way!


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.


My Weight: Good News or Bad News?

January 5, 2018

I spent most of 2017 feeling bad about my weight.

But as I review the data now I realise I can say positive things about my weight which – if I could believe my own words – would leaving me feeling good about my weight.

Alternatively, I could say negative things which would leave me feeling bad about my weight.

In either case the data would be the same. So which view should I take?

The data

The graph below shows my weight determined first thing in the morning for almost every day throughout the last two years.

Weight 2016-2017

2016 was a good year. I lost about 14 kg and felt enormously better. And in 2017 I initially managed to lose another couple of kilos,

Weight 2017

But then, as work became a nightmare, my weight drifted back up at just 10 g per day – a weight gain equivalent to a biscuit or a glass of wine per day.

By the end of the year I managed to catch my breath enough to slowly lose some weight. And that is pretty much where I am at now.

Postive or Negative?

So how should I feel about this data? What story should I tell myself?

Should I say:

“Well done! You managed to keep control of your weight through a difficult year. And your weight is only 1 kg more than it was at the start of 2017. And still 13 kg lower than it was at the start of 2016”?

Or should I say:

“What a mess! You put on 3 kg through the year!

In either case, the data are the same. So actually I think I will just keep the graphs and refrain from telling myself any story at all. Indeed, the real storyline won’t become clear until I find out what happens next.

I will keep you informed.

2018: Here we come!

January 4, 2018

Top Cat Guide to Life

2017 was a difficult year for me, by far the worst of my 17 years at NPL.

But after a break in which I have managed to breathe, become 58 years old, spend time with my family, and read some books, I have resolved to try to focus on the positive.

At first I thought I would follow advice from the  ‘indisputable leader of the gang’, Mr. Top Cat, from New York City, who has published his ‘Guide to Life‘.

But in fact after reading Mr. Cat’s advice, I can inform you that it is not so much feline, as asinine.

However, his positivity and self-assuredness are enviable, if somewhat (respectively) mysterious and misplaced.

My plan is to reflect on the positive – of which there is plenty – while not ignoring the negative. It’s a tough balance, but nobody said life would be easy.

In any case, if you are reading this, I wish you all the best for the remaining 98.9% of 2018.


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