Bringing together two sets of constraints

Focusing on the learners:

Distinguishing–eliciting–connecting. How will you:

• keep the different radiating mechanisms separate
• separate the phenomena from the explanations
• explore the full range of behaviours of each family of radiations
• identify and demonstrate the phenomena
• account for the reduction of intensity with increasing separation of detector from source
• build on what is known from earlier work in light and sound
• exploit a full range of applications to draw out the wave character of radiations

Teacher Tip: These are all related to findings about children's ideas from research. The teaching activities will provide some suggestions. So will colleagues, near and far.

Focusing on the physics:

Representing–noticing–recording. How will you:

• separate the lived-in world of phenomena from the models that account for those phenomena
• introduce amplitude and frequency as fundamental
• characterise a wave as delayed mimicry, without making the idea of a wave too complex
• introduce the idea of the trip time, as an essential corollary of radiations travelling
• develop model-based explanations with real power, rather than give homely analogies
• develop accounts of increasingly complex situations, relating these to simpler situations
• present the central ideas of radiating as a unifying theme

Teacher Tip: Connecting what is experienced with what is written and drawn is essential to making sense of the connections between the theoretical world of physics and the lived-in world of the children. Don't forget to exemplify this action.

Students' views about light travelling through space

When we teach about sound, light and other radiations in school, it is well worth remembering that these are familiar things within our everyday lives, whether talking about sound systems, different kinds of lighting and so on.

Some 10-year-old boys were overheard recently having a conversation about, How long it takes a beam of light to travel from England to America.

This is a very good question. It is also a question that begs further probing.

For example:

What do the boys imagine a beam of light is?

What is it that actually travels from England to America?

How could this particular journey be timed?

Insights into how young people respond to questions such as these are very helpful in identifying teaching starting points. So we asked some 13–15-year-old students a set of probing questions.

Question 1: Our nearest star

It's a well known fact that it takes light about 4.5 years to travel from Alpha Centauri, our nearest star (apart from the Sun), to the surface of the Earth.

What does it mean to say that it takes 4.5 years for light to travel from Alpha Centauri to Earth? Explain in your own words.

Some student responses:

1: If you shine a very bright light in the direction of Alpha Centauri it will take 4.5 years for the light rays to reach the star.

2: Like if you put a light bulb on the nearest star and the light switch of that bulb on Earth and flick the switch it will take 4.5 years to travel.

3: If you imagine light is a group of men it takes 4.5 years for them to walk to Earth.

4: As light is emitted from Alpha Centauri it travels through the vacuum of space all the way to the surface of Earth.

Thinking about the teaching

All four of these responses involve something moving from Alpha Centauri to Earth. This is very clear in response 3, which draws an analogy with a group of men walking to Earth. At the same time student 4 refers to the vacuum of space. So, if we have nothing in space, the question arises as to what is doing the travelling?

This is a challenging question for both teacher and learners (see the Challenge: Light passing through nothing).

Students' views about how sound travels

Question 2: Explosion!

The sound of the explosion in the city centre arrived at Steve's ears on the edge of town. What does it mean to say that the sound travelled from the city centre to Steve's ears? Explain in your own words.

Some student responses:

1: Sound just can't magically go into your ears, it needs to travel.

2: When the explosion happened it made sound waves. These sound waves then travelled to Steve's ears.

3: When the explosion happened it gave off a sound. Sound is lots of vibrations. They travelled from the explosion to his ears.

4: It means that the noise had to travel to Steve's ear like a car but it takes a bit quicker.

5: It means that the sound travelled outwards from the explosion. For example a pool of water. If you dropped a stone in a pool of water the waves travel outwards from the point at which the stone hits the water to a point at the edge of the pool.

Thinking about the teaching

Each of the responses involves something travelling from the explosion to Steve's ears. This something is: sound, sound waves, vibrations, noise.

There is a strong sense of something, like a car, starting at the explosion and travelling to Steve's ear. In fact, this is not the case. Nothing of substance travels in a sound wave as the vibration is passed on from each chunk of air to the adjacent chunks.

Establishing this fundamental property of waves is a challenge to be addressed in teaching as it goes against the common-sense ideas illustrated by these responses.

Students' views about the similarities and differences between visible light and X-rays

Question 3: Light and X-rays

Ian is arguing with Neil. He reckons that light from the Sun is the same kind of thing as X-rays. Neil thinks this is daft: We can see using light; we can't see with X-rays… it would go straight through us!

Who do you agree with: Ian or Neil?

Ian: Light is the same kind of thing as X-rays.

Neil: Light and X-rays are quite different.

Explain in your own words your reasons for agreeing with Ian or Neil.

Many of the younger students agreed with Neil:

1: X-rays don't use the same light as the Sun because the light from the Sun is so strong and that's from far away, but an X-ray is taken from close and is nowhere near as strong.

2: X-rays use radiation to see inside people's bodies rather than sunlight which is not for looking through you.

3: X-rays use radiation but light is completely different.

Thinking about the teaching

The main line of argument here is that X-rays are different from light because they can do different things, such as see inside people's bodies.

Responses 2 and 3 refer to X-rays as using radiation, whilst light seems to be taken as something completely different.

Some older students argued that light and X-rays are different, because:

4: They have different wavelengths and frequencies.

5: They are different points on the electromagnetic spectrum.

6: Visible light is in a completely different part of the electromagnetic spectrum so it is different to X-rays.

Thinking about the teaching

Interestingly, these students are aware of the electromagnetic spectrum but use it as a way of arguing that the radiations of the spectrum are different. It is clear that further work is needed for them to begin to see the radiations of the electromagnetic spectrum as belonging to the same family.

Some older students agreed with Ian:

7: They're just different places in the light spectrum.

8: They are quite similar as the wave speed is the same.

9: They are both part of the electromagnetic spectrum.

Thinking about the teaching

Response 8 raises the key point that all of the radiations of the electromagnetic spectrum travel at the speed of light.

Students' views about a familiar phenomenon involving sound

Question 4: Wheeeeyyyyyyaaaaaa!

The Stig (II) drives his test car down the long straight of the racing circuit. Why do you think the car makes that familiar wheeeeyyyyyyaaaaaa sound as it hurtles by? Explain in your own words.

Students gave various reasons for the distinctive sound:

1: Sound waves spread the farther away you are and so sound quieter. As the car gets closer they spread less and so sound louder.

2: It's the sound of the engine and it gets louder because it gets nearer and quiets down when it gets further away.

3: The friction of the tyres sticks to the tarmac it will make the wheeeyyyaaaa sound.

4: The car will make a sound which builds up and goes down again as the sound firstly travels towards the man. But the sound waves decrease as they travel away from him making the wheeeyyyyaaaa sound.

5: As the car approaches at speed it is moving in the same direction as the sound waves we hear. Because it is moving with the sound there is a higher concentration of sound waves. As the car passes it is the opposite.

6: The faster the engine goes the more explosions occur per minute in the engine, producing higher pitched sound (high frequency).

7: The sound waves given off by the car when it is at a distance away are slightly distorted. But as it gets closer the sound waves heard are much clearer as they don't have to travel as far.

Thinking about the learning

From these answers the change in sound might be due to: a change in loudness; the friction of the tyres; the sound building up and going down; a change in concentration of sound waves; the engine speed; or distortion of sound waves. It is clear that there are plenty of alternative common-sense ways of explaining this familiar effect.

Older students may have met the Doppler effect

Some of the older students had been taught about the Doppler effect and were able to give very good responses:

8: The sound waves squash up when coming towards us giving them a higher frequency and when travelling away the opposite happens.

9: As the car approaches all the air gets squashed and as it goes away the air is expanded: Doppler effect.

Thinking about the teaching

You'll nevertheless want to probe what lies behind these words to ensure that the ideas are connected up as you'd hope. Responses 8 and 9 are both on the right lines.

Being precise when talking about velocity

Wrong Track: The velocity of a wave is how quick it is.

Right Lines: The velocity of a wave is a measure of the speed of travel of a fixed point on the wave (maybe a wave crest) in metre/second, in the direction of travel of the wave.

Being precise when talking about frequency

Wrong Track: The frequency of a sound is how quickly it vibrates.

Right Lines: The frequency of a sound is measured in terms of the number of complete oscillations per second or hertz.

Encouraging precision when talking about waves

Thinking about the learning

When students are first introduced to these terms, there is a tendency for them to use the terms in a less than precise way.

Sound and light belong to different families of radiation and the members of those families are specified in terms of their velocity, frequency and amplitude.

Thinking about the teaching

It's worth making a fuss about getting definitions such as these correct.

We'd suggest encouraging students to take pride in being precise:

Teacher: Frequency! What do we mean by frequency? Remind us, Lucas!

Lucas: Errr, the number of complete oscillations made by any point on the wave each second.

Teacher: Perfect! Music to my ears! Well done, Lucas!

Being precise when talking about amplitude

Wrong Track: The amplitude of a sound wave is how big it is.

Right Lines: The amplitude of a sound wave is the difference in density at the points of zero and maximum displacement of any point on the wave.

A very short biography of Heinrich Hertz

It's always worth bringing physics to life by introducing some of the characters behind the names. Rather than just stating that frequencies are measured in hertz, let's hear a bit about the man himself. Heinrich Hertz was born in Hamburg, Germany, on 22 February 1857. In 1880 he obtained a PhD in physics from the University of Berlin before taking up a post as a lecturer in theoretical physics at the University of Kiel in 1883.

In 1865, Maxwell's theory of electromagnetism was published and predicted the existence of electromagnetic waves moving at the speed of light, concluding that light was just such a wave. This challenged experimentalists to generate and detect electromagnetic radiation using some form of electrical apparatus.

The first clearly successful attempt was made by Hertz in 1886. For his radio wave transmitter he used a high-voltage induction coil, a condenser (capacitor, Leyden jar) and a spark gap. The sides of the gap terminated in spheres of 2 cm radius, between which there would be a spark: oscillating at a frequency determined by the values of the capacitor and the induction coil.

To prove there really was radiation emitted, it had to be detected. Hertz used a piece of copper wire, 1 millimetre thick, bent into a circle of 7.5 cm diameter, with a small brass sphere on one end, and the other end of the wire was pointed, with the point near the sphere. He added a screw mechanism so that the point could be moved very close to the sphere in a controlled fashion. This receiver was designed so that current oscillating back and forth in the wire would have a natural period close to that of the transmitter described above. The presence of oscillating charge in the receiver would be signalled by sparks across the (tiny) gap between the point and the sphere (typically, this gap was hundredths of a millimetre).

In more advanced experiments, Hertz measured the velocity of electromagnetic radiation and found it to be the same as that of light. He also showed that the nature of radio wave reflection and refraction was the same as that of light and established beyond any doubt that light is a form of electromagnetic radiation described by the Maxwell equations.

In recognition of his work, the unit of frequency – one cycle per second – is named the hertz in his honour.

Heinrich Hertz died on 1 January 1894 aged 36.

Thinking about radiation from the Sun in terms of energy in stores and power in pathways

Think of a car left in a Mediterranean beach car park, where there is no shade. You get back to the car at the end of the day and open the doors. The metal of the car is too hot to touch: You could fry an egg on the bonnet! The air inside is stifling hot.

This familiar event is not too difficult to account for. The Sun has been shining on the car.

Now try to build in more links – that's what physics is all about. Can you give a good account in terms of energy in stores and power in pathways?

Richer descriptions

Thinking about stores

In trying to provide a deeper explanation, you can go back to the energy ideas of the SPT: Energy topic. Using these you can think of the Sun as a nuclear store and the car as a thermal store, with the two connected through a heating-by-radiation pathway.

As the long hot summer day progresses, the Sun's nuclear store is gradually depleted (not by very much!) and the thermal store of the car fills as energy is shifted from one to the other. The quantity of energy in the Sun's nuclear store is reduced: some of that energy ends up in the thermal stores of the car (of course, most of the energy from the Sun's store ends up in other stores).

In energy terms, that's the full story.

Thinking about pathways

You may wish to go a step further by thinking more deeply about the radiation pathway. In this case of the Sun heating the car, no physical material travels from the Sun to car. The heating-by-radiation pathway works through electromagnetic radiation. Electromagnetic oscillations, changing electric and magnetic fields, which are created in the Sun travel to Earth and set matter (such as the stuff that the car is made from) oscillating as they are absorbed by it. In this way energy is shifted by the heating-by-radiation pathway.

The speed of sound in solids and gases

Wrong Track: Sounds travel more slowly in solids because they are denser than gases and so it's harder for the sound to get through.

Right Lines: The particles in solids are closer together and more tightly coupled. So the delay in the vibration being passed on between neighbouring volumes of particles is much less. Sound travels faster in solids than in gases.

Linking to models

Thinking about the learning

Based on everyday reasoning many students believe that sounds travel more slowly in solids than in gases.

Thinking about the teaching

Links can be made here to the masses and springs wave model introduced in the Physics Narrative.

The wave pulse travels at the highest speed through the model when low masses are held together by stiff springs. This is good for a solid, provided that you remember to include the effect of both mass and stiffness on the speed.

In fluids, this mass and spring model is not good for describing the connections between individual particles, but the bulk properties of the materials do have measures like mass (you might spot that this is simply density) and springiness that together set the wave speed.

Making links explicit: fitting representations together

One of the distinctive features of physics as a subject is that it involves representing ideas and phenomena in a whole range of different ways. This is certainly the case in the topic area of radiation.

Think, for example, about the different ways we talk and think about sound:

• Sound waves have a velocity, a frequency, and an amplitude. All three can be measured.
• Sounds need a medium to pass through.
• Sound waves consist of groups of particles oscillating back and forth.
• Sound waves belong to the family of longitudinal waves.
• Sound provides a pathway by which energy can be shifted.
• Sound waves can be represented in terms of graphs that show the variation in density of the air through which they are passing.

This list captures just some of the distinctive features of sound waves: sometimes on a macroscopic scale (the speed is 330 metre inverse second); sometimes on a sub-microscopic scale (picturing the air particles moving back and forth); sometimes in terms of energy; and sometimes graphically.

A deep understanding of sound waves involves being able to fit all of these representations together in such a way that they all make sense. This is often not easy. Students are likely to need help from their teacher in making these key links, and in drawing attention to the nature of the explanations and representations that are currently being used:

Teacher: OK! Let's get those atomic spectacles on and try to picture what is happening in the sound wave in terms of the air particles.

The next step on from making links within the topic area of sound is to start identifying the links (similarities and differences) with other radiations, such as light.

Odd as it may seem, knowing how light and sound radiations differ from each other is a big help in appreciating the key features of each.

Light can travel through a vacuum

Wrong Track: Well, light and sound waves involve something oscillating back and forth. That's what a wave is. Like the coils of the slinky spring. So there must be something, maybe small amounts of air, that is vibrating to make up the light wave.

Right Lines: In fact there is nothing, no stuff, vibrating back and forwards in a light wave. The vibrations consist of changing electric and magnetic fields.

The rise and fall of the Aether (ether)

Thinking about the learning

Following on from the reasonable-sounding fact that sound can travel through air but can't travel through nothing, it comes as a shock for some students to learn that light from the Sun does, in fact, travel through nothing.

Thinking about the teaching

The idea that there must be something vibrating to make a light wave is not a new one. In the history of physics, it was generally accepted right up to the start of the 20th century that there must be some kind of material medium – the ether – to support the passage of electromagnetic radiation.

The argument in favour of the ether went something like this:

The electric component of electromagnetic radiation consists of changing electric fields, and all such changing fields require separated and opposite electric charges. Electric charge is a fundamental property of matter, so some form of matter is required to provide the changing field that needs to exist at any point along the path of the electromagnetic wave. The passage of waves in a true vacuum would imply the existence of electric fields without associated electric charge, or of electric charge without associated matter, and this is not possible.

The concept of the ether eventually fell from favour and the path of its demise is an interesting story in the development of physics. The basic point in all of this is that if students have problems in accepting that light can travel through nothing (but how can nothing carry oscillations?), they are in good company.

What happens to light as it spreads out from a source?

Wrong Track: Light gets weaker as it travels away from a lamp just because it is gradually absorbed by air or any other material in its path.

Right Lines: Even if there are no absorbers in the way of the light, it gets dimmer, or its intensity lessens, because it is spreading out.

Bernard's butter gun

Thinking about the learning

As light spreads out from a source, its intensity decreases due to the processes of absorption and spreading.

Thinking about the teaching

The butter gun story offers an interesting approach to introducing the way in which light intensity decreases as it spreads from a source.

Bernard the inventor has a fantastic new idea. His friend, Julia, runs a sandwich shop and is always complaining that she and her staff spend all of their time buttering bread. Bernard decides that he will try to help out and comes up with his idea of a butter gun.

The butter gun works so that melted butter squirts out, in pulses, from the barrel of the gun at high speed, a bit like water from a hose-pipe.

Bernard finds that if he places one slice of bread 1 metre from the gun, the bread gets a covering 1 cm deep (too thick). Alternatively, Bernard finds that he can place 4 slices of bread at a distance of 2 m, such that they are all covered by the cone of butter and each one gets a covering of 14 centimetre of butter.

Julia encourages Bernard, for the sake of economy, to move the gun just 1 metre further back.

Here they find that that they can fit 9 slices of bread into the cone and that each slice gets a covering of 19centimetre of butter.

Julia is really happy about this! Now she can cover 9 slices of bread with just one squirt of the butter gun.

Julia has spotted a pattern in these figures:

distance	number	thickness
1	1	1
2	4	14
3	9	19
4	16	116

As Julia explains:

Julia: The greater the distance of the bread from the gun, the less the thickness of the butter on each slice. This is because the butter spreads out as it travels away from the gun. So, for example, after travelling 3 metre, the butter has spread out to make a cone which will cover 9 slices. Since there is only one squirt of butter from the gun, this butter must be 19^th the thickness of the butter achieved with one slice at 1 m distance.

Julia makes a mental note that if business becomes bad she will move the butter gun to a 4 m distance.

What has Bernard's butter gun got to do with light? More than you might imagine! Light spreads out in just the same way as the butter from the gun. In other words, as light travels away from a point source its intensity is reduced simply because it is more spread out (just like the reduced thickness of butter).

If the distance from the point source to a light detector is increased:

from 1 metre to 2 metre, the intensity of light falls by 14;

from 1 metre to 3 metre, the intensity falls by 19;

and so on.

Ray diagrams as a theoretical tool

A ray diagram is a tool used by physicists to explain or predict the behaviour of beams of light as they pass through objects such as glass blocks or lenses. When ray diagrams are first introduced, students not surprisingly often assume that they show the world as it really is. This is not the case. Ray diagrams belong firmly to the world of theory – to a world where rays of light travel out from a point source, and where single rays are refracted and reflected in particular ways in relation to normal line constructions.

In the real world beams of light exist (like the beam from a car headlamp) but point sources and normal lines do not.

Ray diagrams for explaining a whole range of phenomena

The distinction between real and theoretical worlds in relation to light is important. It is worth emphasising in your teaching:

Teacher: So, ray diagrams offer us a really important tool for dealing with a whole range of phenomena related to light. These include how we see, how telescopes work, and how rainbows are made. Just as we can use a hammer to work on a range of DIY jobs, so we can use ray diagrams to explain a variety of effects. When we use a telescope, there are no individual light rays being refracted through the lenses, but these simplified ray diagrams help us understand how the telescope works.

Learning how to draw ray diagrams for particular cases, such as the reflection of light in a mirror, the refraction of light through glass blocks, and the refraction of light in lenses, is just a starting point. Students need help in moving between the world of theory and the real world. The core message here is that learning to construct ray diagrams is not an end in itself; students need practice in applying them to real world situations. Otherwise what is the point?

Teacher: OK, so we've got this diagram that shows a ray of light being refracted away from the normal as it passes from water to air. Nice diagram. Normal line clearly shown. But what has this to do with the swimming pool or river seeming shallower than it really is? Who can use the ray diagram to help explain?

There's a good chance you could improve your teaching if you were to:

Try these

• emphasising that there is movement as radiations travel from source to detector
• ensuring that radiating is presented as a unifying mechanism, across families of radiations
• using a simple, but evocative description of radiating, such as do like me, but later
• consistently characterising waves by their frequency and amplitude
• being consistent about the energy in stores and the power in pathways
• giving examples of the full range of media for each family of radiations
• explicitly modelling situations with ray diagrams

Teacher Tip: Work through the Physics Narrative to find these lines of thinking worked out and then look in the Teaching Approaches for some examples of activities.

Avoid these

• referring to light energy
• not implying that light simply runs out
• conflating rays with physical objects
• not making unifying connections between different phenomena

Teacher Tip: These difficulties are distilled from: the research findings; the practice of well-connected teachers with expertise; issues intrinsic to representing the physics well.