Key Stage 4 science · Physics – Wave motion

GCSE waves: wavelength, frequency, wave speed and refraction

This GCSE physics topic gives students a precise language for waves. They define amplitude, wavelength and frequency, use the wave equation to link them to wave speed, distinguish transverse waves from longitudinal ones, and explain what happens when a wave meets a new material: it may be absorbed, reflected, transmitted or refracted, because waves travel at different speeds in different media.

Properties of waves, explained

A wave transfers energy, and often information, from one place to another without transferring matter. Ripples spreading across a pond are a good example: a floating leaf bobs up and down but is not carried to the shore. Students describe waves using four measurements. Amplitude is the maximum displacement of a point on the wave from its rest position. Wavelength is the distance from a point on one wave to the same point on the next, such as crest to crest. Frequency is the number of waves passing a point each second, measured in hertz. The time for one wave is the period, which is one divided by the frequency.

These are tied together by the wave equation: wave speed (in metres per second) equals frequency (in hertz) multiplied by wavelength (in metres). Students rearrange it to find any of the three, and should be comfortable with answers in standard form for very small or very large values. For sound, a higher frequency is heard as a higher pitch and a larger amplitude as a louder sound. Human hearing is usually quoted as about 20 hertz to 20 kilohertz.

In a transverse wave, the oscillations are at right angles to the direction the energy travels. Light and all other electromagnetic waves, ripples on water and waves on a rope are transverse. In a longitudinal wave, the oscillations are along the direction of travel, forming regions where the particles are squashed together (compressions) and spread apart (rarefactions). Sound is longitudinal, and so are some seismic waves. Because sound is a vibration of particles, it needs a medium and cannot travel through a vacuum.

When a wave meets a boundary between two materials, it can be absorbed, reflected or transmitted, in different amounts. Reflection follows a simple rule: the angle of incidence equals the angle of reflection, both measured from the normal, a line drawn at right angles to the surface. A transmitted wave often changes speed, because the speed depends on the medium. Light slows down when it enters glass or water; sound speeds up when it passes from air into a liquid or solid, travelling about 330 metres per second in air, around 1,500 in water and faster still in most solids. If the wave meets the boundary at an angle, the change of speed makes it change direction, which is called refraction. During refraction the frequency stays the same, so a change in speed shows up as a change in wavelength.

Words your child will hear

Amplitude: The maximum distance a point on the wave moves from its rest position.
Wavelength: The distance from one point on a wave to the same point on the next wave.
Frequency: How many complete waves pass a point each second. Measured in hertz (Hz).
Transverse: A wave whose vibrations are at right angles to the direction of travel.
Longitudinal: A wave whose vibrations are in the same direction as its travel, like sound.
Refraction: A change in a wave’s direction when its speed changes as it enters a new medium.
Normal: An imaginary line at right angles to a surface, used to measure angles in ray diagrams.

What the National Curriculum says

The programme of study for Key Stage 4 says:

Students should be taught about amplitude, wavelength, frequency, relating velocity to frequency and wavelength
Students should be taught about transverse and longitudinal waves
Students should be taught about velocities differing between media: absorption, reflection, refraction effects

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

In a tank of water, a paddle makes ripples with a frequency of 5 Hz. In the deep part of the tank the wavelength is 0.040 m. The ripples then move into a shallow part, where the wavelength is 0.025 m. Find the wave speed in each part and explain what has happened.

Choose the wave equation: wave speed = frequency × wavelength. Check that the wavelength is in metres.
Deep water.
```
v = f × λ
  = 5 × 0.040
  = 0.20 m/s
```
The frequency is set by the paddle, so it stays at 5 Hz when the ripples cross the boundary. Use the new wavelength for the shallow water.
```
v = 5 × 0.025
  = 0.125 m/s
```
Compare. The ripples travel more slowly in shallow water, since the speed has dropped from 0.20 to 0.125 m/s. With frequency unchanged, the wavelength must be shorter, which matches the measurements.
If the ripples reached the boundary at an angle, the change of speed would also change their direction. That is refraction, and the waves would bend towards the normal in the slower region.

The speed is 0.20 m/s in deep water and 0.125 m/s in shallow water. The frequency stays at 5 Hz, so the slower waves have a shorter wavelength.

Common mistakes and how to help

Thinking the water or air itself travels along with the wave

A wave’s energy visibly moves across the pond, so it seems that something must be moving with it.

What helps: Float a cork or rubber duck on ripples and watch it bob up and down in place. The medium oscillates around a fixed position while the energy travels on.

Confusing amplitude, wavelength and frequency

All three describe the shape of a wave, and a taller wave looks as if it should also be more frequent.

What helps: Sketch the same wave three times: once taller, once with the crests further apart, once with more waves in the same time. Name which measurement changed each time. Amplitude is about height, wavelength about distance, frequency about count.

Saying that the frequency changes when a wave is refracted

Speed and wavelength both change at a boundary, so frequency is assumed to change too.

What helps: Think of the source as a metronome. The number of waves leaving the source each second is fixed, and they cannot pile up at the boundary, so the frequency is unchanged.

Believing sound travels faster in air than in water or solids, because it is “thinner”

Light slows down in denser materials, so students assume sound does the same.

What helps: Sound is a vibration passed from particle to particle. In liquids and solids the particles are much closer together and more strongly linked, so the vibration is passed on more quickly. Use the figures: about 330 m/s in air and about 1,500 m/s in water, with most solids faster still.

How to help at home

Make transverse and longitudinal waves. Stretch a skipping rope or a coiled spring toy gently along the floor with a partner. Flick it sideways for a transverse wave, and push and pull along its length for a longitudinal one. Ask which direction the coils move compared with the wave.
Make ripples in a washing-up bowl. Tap the surface at a steady rate and watch the ripples, then tap faster. Float a cork or small toy and see that it bobs rather than travels. Ask how the wavelength changes when the frequency increases.
Bend a pencil. Place a pencil in a clear glass of water and look from the side. It appears to bend at the surface. Ask your child to explain it using the idea that light changes speed and direction when it passes between water and air.
Hear pitch and volume. Hold a ruler over the edge of a table and twang it. A shorter overhanging length gives a higher pitch, and a bigger flick gives a louder sound. Which of these changes the frequency and which the amplitude?
Compare sound through a solid. Rest an ear on a table and ask someone to tap lightly at the far end, then listen with your ear lifted. The sound through the table is louder and clearer. Discuss what this shows about how well sound travels through solids compared with air. (The difference in speed is too small to notice over a table.)

Builds on

Key Stage 3: Water waves and sound waves
Key Stage 3: Hearing, microphones and ultrasound
Key Stage 3: Light waves and reflection
Key Stage 3: Mirrors, lenses, the eye and colour