📏 Distance along the bottom
This is like a photograph of the whole wave at one moment. The distance from one crest to the next crest is the wavelength. The height of a crest above the rest position is the amplitude.
Properties of Waves » Describing Waves
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 3.3, 3.9
- The exact definitions of amplitude, wavelength, frequency, period and wavefront
- How to read amplitude, wavelength and period from a wave diagram or graph
- Why all waves can be reflected and refracted
- How a ripple tank shows reflection and refraction
🔒 Unlock Full Course Content
Sign up to access the complete lesson and track your progress!
Unlock This CourseFive words that describe any wave
In Transverse and Longitudinal Waves you drew a transverse wave as a smooth wavy line. Now add a straight horizontal line through the middle of it. This line is the rest position: where each point sits when no wave is passing. The highest points of the wave are the crests and the lowest points are the troughs.
Learn these five definitions word for word, with their units.
| Quantity | Definition | Unit |
|---|---|---|
| Amplitude | The maximum displacement of a point on the wave from its rest position | metre (m) |
| Wavelength (symbol λ) | The distance from one point on a wave to the same point on the next wave, for example from one crest to the next crest | metre (m) |
| Frequency (symbol f) | The number of complete waves passing a point each second | hertz (Hz) |
| Period (symbol T) | The time taken for one complete wave to pass a point | second (s) |
| Wavefront | A line joining points on a wave that are at the same stage of their vibration, for example a line drawn along one crest | (a line, so no unit) |
Remember, displacement is a distance in a given direction. Here it means how far a point on the wave is from its rest position.
A frequency of 1 Hz means one complete wave passes each second. So if 5 complete waves pass a point each second, the frequency is 5 Hz.
Key terms:
- Rest position: where a point on the wave sits when no wave is passing. It is also called the undisturbed position.
- Crest: the highest point of a transverse wave. It is also called a peak.
- Trough: the lowest point of a transverse wave.
Reading a wave diagram
Exam papers show two kinds of wave diagram that look the same at first glance. Always read the label on the horizontal axis.
🕒 Time along the bottom
This is a displacement-time graph. It follows one point as it moves up and down. The time from one crest to the next crest is the period. The height of a crest above the rest position is still the amplitude.
Worked example 1: amplitude and wavelength
Question: A diagram shows a wave on a string. The crests are 3 cm above the rest position and the troughs are 3 cm below it. The diagram is 20 cm wide and shows exactly 4 complete waves. State the amplitude and the wavelength.
Amplitude: measure from the rest position to a crest. Amplitude = 3 cm. It is not 6 cm, which is the full height from trough to crest.
Wavelength: 4 complete waves fit into 20 cm, so one wave is 20 ÷ 4 = 5 cm long. Wavelength = 5 cm.
Worked example 2: period
Question: A displacement-time graph shows the displacement of one point on a wave against time. There are crests at 0.1 s, 0.6 s and 1.1 s. State the period.
Period: it is the time from one crest to the next. 0.6 − 0.1 = 0.5 s. Period = 0.5 s.
Check: 1.1 − 0.6 = 0.5 s as well, so the answer is the same for every pair of crests.
Longitudinal waves have the same five quantities. The wavelength is the distance from the middle of one compression to the middle of the next compression. The amplitude is still the maximum displacement of a particle from its rest position.
Wavefronts and the ripple tank
A ripple tank is a shallow glass-bottomed tray of water. A straight bar just touching the surface vibrates up and down and sends out straight ripples. A lamp above the tank casts shadows of the ripples onto a white screen below, so the pattern is easy to see.
Looking down from above, each crest shows up as a long straight line. Each of these lines is a wavefront. To draw them, rule a set of parallel, equally spaced lines. Then add an arrow at right angles to the lines to show the direction the wave is travelling.
The distance from one wavefront to the next is one wavelength.
All waves can be reflected and refracted
When a wave meets a boundary, the place where one material (or one depth of water) ends and another begins, two things can happen.
- Reflection: the wave bounces off the boundary and travels back into the material it came from.
- Refraction: the wave crosses the boundary, its speed changes, and this makes it change direction.
The direction only changes if the wave meets the boundary at an angle. If it meets the boundary head-on, it changes speed but carries straight on.
Reflection in the ripple tank. Stand a straight metal barrier in the water, at an angle to the wavefronts. The wavefronts hit the barrier and bounce off, travelling away in a new direction. The reflected wavefronts are the same distance apart as before. Reflection does not change the speed, the frequency or the wavelength.
Refraction in the ripple tank. Lay a flat glass plate on the bottom of the tank so that the water above it is shallow. Water waves travel more slowly in shallow water. Send the wavefronts towards the edge of the plate at an angle. Now explain what you see in steps:
- One end of each wavefront reaches the shallow water first and slows down.
- The rest of that wavefront is still in deep water, so it is still travelling faster.
- The wavefront swings round to a new angle, so the wave travels in a new direction.
- The slower waves bunch up, so the wavefronts are closer together: the wavelength is shorter. The frequency stays the same.
Reflection and refraction are not special to water. All waves can do both, transverse or longitudinal.
| Wave | Reflection | Refraction |
|---|---|---|
| Water waves | Ripples bounce off the side of a bath or a barrier in a ripple tank | Ripples change direction when they pass from deep water into shallow water at an angle |
| Sound waves | Sound bounces off hard surfaces such as walls and cliffs | Sound changes direction when it passes between warm air and cold air, because its speed is different in each |
| Light waves | Light bounces off a mirror, which is how you see your face in it | Light changes direction when it passes between air and water or glass. Light from a straw in a glass of water changes direction as it leaves the water, which is why the straw looks bent |
Common mistakes
- Measuring amplitude from trough to crest. That is twice the amplitude. Always measure from the rest position.
- Reading wavelength from a graph with time on the horizontal axis. Crest to crest on that graph is the period. Check the axis label first.
- Counting lines, not gaps. Five wavefronts have only four wavelengths between them.
- Vague definitions. 'How many waves there are' is not frequency. You need 'the number of complete waves passing a point each second'.
- Saying refraction is just 'bending'. For full marks say the wave changes speed at the boundary, and that this causes the change of direction.
Exam-style question
A student uses a ripple tank to study water waves. A vibrating bar makes straight wavefronts. Viewed from above, the wavefronts appear as parallel lines.
(a) State what is meant by the term wavelength. [1 mark]
(b) The distance from the first wavefront to the sixth wavefront is 10 cm. Determine the wavelength of the waves. [2 marks]
(c) The bar makes 4 complete waves each second. State the frequency of the waves, with its unit. [1 mark]
(d) The student places a glass plate in the tank to make a region of shallow water. The wavefronts reach the edge of the shallow region at an angle. Describe and explain what happens to the waves as they enter the shallow water. [4 marks]
Model answer
(a) The distance from one point on a wave to the same point on the next wave, for example crest to crest (1).
(b) Six wavefronts have 5 wavelengths between them (1). Wavelength = 10 ÷ 5 = 2 cm (1).
(c) 4 Hz (1).
(d) The waves slow down in the shallow water (1). The part of each wavefront that enters the shallow water first slows down before the rest (1), so the wavefronts change direction, which is refraction (1). The wavefronts become closer together, so the wavelength is shorter (1).
Exam tip
In part (b), draw six short lines on your paper and count the gaps before you divide. In part (d), 'describe and explain' means say what happens and say why: the change of speed is the 'why'.