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Understanding science: what we cannot know
Understanding science: what we cannot know

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2.4 Wave motion

How can we capture both the heights of the wave crests and troughs as well as the undulation of the wave, without using complex mathematics? It can be done! Let’s say we have a wave of a certain amplitude. Now think of the wave as being represented by an arrow of a length that equals the amplitude and which rotates in a circle as the wave progresses, such that it points up at a crest and points down in a trough.

This diagram shows a wave diagram with several points marked with dots. There’s an orange dot where the wave meets the baseline. Next, there’s a green dot where the wave reaches its highest point. Next, there’s a blue dot where the wave meets the baseline again. Finally, there’s a purple dot where the wave reaches its lowest point. Each of these coloured dots corresponds to a simple coloured circle containing an arrow pointing in a particular direction. The orange circle (wave meets baseline) has an arrow pointing to the right. The green circle (highest point) has an arrow pointing up. The blue circle (wave meets baseline again) has an arrow pointing left. The purple circle (lowest point) has an arrow pointing down.
Figure 6 Wave represented by an arrow

You may be wondering how this picture is useful. It helps us to understand what happens when two waves meet. If you throw two stones into a pond, you can see circular waves emanating from both impact sites. Eventually these waves will overlap. In fact, they’ll essentially pass through each other, with the heights of the two waves combining to form the resulting wave pattern.

Let us consider a situation with two waves in terms of our arrow picture. For simplicity, let’s also assume that the amplitudes are the same, so there are two arrows of equal length. As the waves progress, our arrows rotate around. How do the waves add up? If at any place and time both arrows point up, the waves add together and produce a crest of double the height. If both point down, this produces a trough of double the depth. However, if both arrows point in opposite directions, the waves cancel out. The way the two waves interact is determined by the angle between the two arrows. This is often referred to as the ‘phase’ or ‘phase difference’.

This diagram shows two combinations of waves and the results. It does this using the circles containing arrows from Figure 6. Both situations are depicted as simple mathematical sums, i.e. wave 1 + wave 2 = result. Figure (a) shows one circle containing an arrow that points up, and one circle containing an arrow that points down. circle 1 + circle 2 = one circle containing both arrows equal in size and pointing in opposite directions = no circle remaining, as the waves have cancelled out. Figure (b) shows two circles containing arrows that point up. circle 1 + circle 2 = one double-size circle containing both arrows stacked together = one double-size circle with one double-size arrow.
Figure 7 (a) Waves cancelling out (b) waves adding together

So, in the right circumstances – with the correct phase difference – waves can cancel out. There are modern electronic devices that make use of this fact: noise-cancelling headphones. They are in fact making noise that cancels out the noise around you!

These kinds of interactions between waves are described with specific terms: the most common being ‘interference’ and ‘superposition’. The former is commonly used for sound waves or electromagnetic waves. Superposition is a term that is more commonly applied to quantum waves. This type of interaction is characteristic of waves.

Observing an interference pattern is seen as clear evidence of wave motion. A typical setup for observing such a pattern is the double-slit experiment.

The double-slit experiment is an experiment where light is projected onto a screen. An opaque barrier with two thin slits cut into it is then placed between the light source and the screen. When this experiment is performed correctly, an interference pattern of light and dark stripes appears on the screen.

This is a diagram of the double-slit experiment. A light source (represented by a light bulb) sits on the left hand side. The light waves are then depicted as they approach a barrier on the right, which has two slits in it. The waves pass through these slits and continue to travel until they hit the screen. A rectangular strip notated with ‘appearance of screen’ shows a pattern of black and white stripes, with patches of grey blending the space between them.
Figure 8 The double-slit experiment

If we think in terms of light, the interference pattern consists of bright and dark stripes (or if we just consider a two-dimensional slice, bright and dark spots). The reason that these stripes form is due to the phase difference. This result comes from the difference in the path lengths of light that travelled through one slit compared with light that travelled through the other slit. Whenever the phase difference causes the waves to cancel, it produces a dark stripe. When they point in the same direction, it produces a bright stripe.

Note that the phase difference is all that matters here. The brightness of the light itself does not impact the direction of our arrow. Note that in order to observe this interference effect, the double-slit setup must have a size that is comparable with the wavelength of the light – so it has to be very small for visible light. Also, you will need a nice beam of light, which consists of a single wave rather than a mixture of many waves. Such light is provided by a laser as a light source.

Having covered these concepts, it’s time to ask how things work in the realm of quantum physics.