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 disturbance by which energy is transferred because this disturbance is a store, of sorts, of potential energy. This begs the question "How is this disturbance transferred across space?" In some cases, this is easy to answer, because some waves travel through a medium. The easiest example to think about is a water wave. One area moves up, pulling the next one up with it, and pressure and gravity pull it back to its original position.

Features of a wave

However, some waves (electro-magnetic waves) do not appear to travel through a medium. Physicists have puzzled over how light, which behaves like a wave in many situations, travels for a long time. One theory was that there was a mysterious 'ether' which pervaded all of space, and so light was just like water waves, except that the water was invisible. This theory is widely regarded to be incorrect, but, since light is assumed to be a wave, what is it a disturbance in?

Another explanation is that light is not a wave, but instead is a stream of particles. This idea would explain away the need for an 'ether' for light to travel through. This, too, has its problems, as it does not explain why light behaves as a wave.

So, we are left with a paradox. Light behaves as both a wave and a particle, but it can be shown not to be either. Quantum physics attempts to explain this paradox. However, since light behaves as both a wave and a particle, we can look at it as both, even if, when doing this, we know that we don't fully understand it yet.

The image on the right shows a waveform. This plots the distance through the medium on the x-axis, and the amount of disturbance on the y-axis. The amount of disturbance is known as the amplitude. Wave amplitudes tend to oscillate between two limits, as shown. The distance in the medium between two 'peaks' or 'troughs' (maxima and minima on the waveform) is known as the wavelength of the wave.

Types of Waves

Waves can be categorised according to the direction of the effect of the disturbance relative to the direction of travel. A wave which causes disturbance in 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.

Longitudinal wave (e.g. sound) Transverse wave (e.g. light)

Superposition

One feature of waves is that they superpose. That is to say, when they are travelling in the same place in the medium at the same time, they both affect the medium independently. So, if two waves say "go up" to the same bit of medium at the same time, the medium will rise twice as much. In general, superposition means that the amplitudes of two waves at the same point at the same time at the same polarisation add up.

Interference

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.

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 (no. of wavelengths per. second), and λ is the wavelength, in m.

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:

Questions

1. Through what medium are sound waves propagated?

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

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

4. 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.)

5. What is the wavelength of green light?

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

Worked Solutions