A-level Physics (Advancing Physics)/What is a wave?

At this point in the course, it is easy to get bogged down in the complex theories and equations surrounding 'waves'. However, a better understanding of waves can be gained by going back to basics, and explaining what a wave is in the first place.

Definitions
A wave, at its most basic level, is a repeated disturbance that spreads out and transfers energy as it moves forwards. Water ripples, light and sound all do this.

The image below shows a waveform. It plots distance through the medium on the x-axis (e.g. distance along the surface of water), and the amount of disturbance on the y-axis (e.g. distance from where the surface would be if the water was not disturbed by ripples). The amount of disturbance is known as the displacement. Waves tend to keep the same maximum displacement. This is known as the amplitude.

The distance between two equivalent points in a wave, along the direction in which the wave travels, is known as the wavelength. The 'peaks' or 'troughs' (where displacement is at a maximum or minimum) are usually chosen as these are the best points of a wave to measure. This is the distance a wave needs to travel in order to repeat itself, or the distance of one oscillation.

The nature of a wave
This raises the question "How can the disturbance itself move?" In some cases, this is easy to answer. Lots of waves travel through a material, in which case it is the material of the medium that is being disturbed. Such waves are called "mechanical waves", which require a material medium to travel in in order to exist. The easiest example to think about is a water wave. One area moves up, pulling the next one up with it. The water in this area gains potential energy. Eventually, pressure and gravity pull the water back down, and they gain kinetic energy which is again passed onto the next area. This allows the process to repeat, spread out and keep passing energy on.

The nature of electromagnetic waves, which includes light, is much more difficult to explain. There is a section below that discusses this.

Velocity, frequency and wavelength
You should remember the equation v = fλ from earlier in this course, or from GCSE. v is the velocity at which the wave travels through the medium, in ms−1, f (or nu, ν) is the frequency of the wave, in Hz (how many waves pass through a point each second), and λ is the wavelength, in m.

This is analogous to walking. Frequency would be the number of steps taken in a unit of time, equivalent to how many times the wave oscillates in a unit of time. The wavelength is equivalent to how long each step is. As most waves have a set speed (e.g. the speed of light or speed of sound), as wavelength goes up the frequency goes down, and vice versa. They are inversely proportional. When walking, if you take steps more often, each step must make you travel less distance if you are to continue walking at the same speed.

This equation applies to electromagnetic waves, but you should remember that there are different wavelengths of electromagnetic radiation, and that different colours of visible light have different wavelengths. You also need to know the wavelengths of the different types of electromagnetic radiation:



The problem of explaining the nature of light
Until relatively recently, scientists struggled to explain what light was. In the past they could only look at what light could do and make educated guesses. Developing ideas from evidence is extremely important in science. Using ideas and to make to explain evidence is extremely important in science. Models are ideas that represent reality. Often, models are developed to explain existing evidence. A good model will predict unobserved behaviour.

Could light be made of particles?

Some scientists have historically suggested that light is a stream of particles. This would explain away the need for a medium to travel through. It would explain why light travels more slowly in denser materials, unlike sound. It also explains why light can travel in straight lines, as well the angle of incidence is equal to the angle of reflection when light "bounces" off a surface. However, there are some behaviours that a particle model does not explain well.

Light as a wave?

Light was observed to have some properties of waves, e.g. being able to spread out. This behaviour seemed to be best explained by waves. As such, a lot of scientists historically liked to think of light as a wave. However, waves were thought of as disturbances. The proponents of a wave model struggled to explain how light could move through a vacuum. This is a place with no material to disturb. Sound cannot pass through a vacuum at all because there is no material to disturb and pass energy onto. The fact light could move through a vacuum was very problematic to using waves as an explanation.

In order to get around this, some scientists came up with the idea of 'ether'. They said there must be a mysterious and undetectable substance that exists everywhere for light to disturb in order to move in. However, the ether theory had problems, including being unable to detect any. It is not a theory accepted by modern physicists.

The evidence

New experiments kept showing light to have more and more behaviour unique to waves. The most important was perhaps interference. This made physicists accept that it must be a wave. Despite not being able to explain what light was a wave in, accepting this was the only way to explain its behaviour.

Types of Waves
Waves can be categorised based on how the disturbance moves relative to the wave. A wave which causes disturbance parallel to the direction of its travel is known as a longitudinal wave, whereas a wave which causes disturbance perpendicular to the direction of its travel is known as a transverse wave.

Superposition / Interference
Note that disturbance is often described as a displacement, which is a vector quantity. Vectors at any point simply add up.

One feature of waves is that they superpose. When they are travelling in the same place in the medium at the same time, they both affect the medium independently. The vector quantities of displacement simply add up and the material is displaced by the vector sum. If two waves do this whilst moving in opposite directions, after passing through one another, they will carry on unaffected.

This is often referred to as as "interference". Some physicists do not like this word as it implies any wave interfering is unwanted, or "noise". However, this effect can be extremely useful e.g. when heating food in a microwave oven.

Consider two identical waveforms being superposed on each other. The resultant waveform will be like the two other waveforms, except its amplitude at every point will be twice as much. This is known as constructive interference. Alternatively, if one waveform moves on by half a wavelength, but the other does not, the resultant waveform will have no amplitude, as the two waveforms will cancel each other out. This is known as destructive interference. Both these effects are shown in the diagram below:



These effects occur because the wavefronts are travelling through a medium, but electromagnetic radiation also behaves like this, even though it does not travel through a medium.

Questions
1. What is a wave?

2. Through what medium are sound waves propagated?

3. What aspects of the behaviour of light make it look like a wave?

4. What aspects of the behaviour of light make it look like a particle?

5. Consider the diagram on the right. White light is partially reflected by the transparent material. Some of the light, however, is refracted into the transparent material and reflected back by the opaque material. The result is two waves travelling in the same place at the same time at the same polarisation(the light is not a single beam). Why does, say, the red light disappear? (Variations on this question are popular with examiners.)

6. What is the wavelength of green light?

7. The lowest frequency sound wave humans can hear has a frequency of approximately 20 Hz. Given that the speed of sound in air is 343ms−1, what is the wavelength of the lowest frequency human-audible sound?

/Worked Solutions/