Wonder and Science

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!





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