Waves

What you'll learn

This revision guide covers all aspects of waves required for Edexcel GCSE Physics. You'll understand the properties and behaviours of transverse and longitudinal waves, master wave calculations, explore the electromagnetic spectrum and its applications, and learn about reflection, refraction, and sound waves. These concepts form a significant portion of Paper 1 and are frequently tested through both calculation and explanation questions.

Key terms and definitions

Wavelength (λ) — the distance from one point on a wave to the equivalent point on the next wave (e.g. crest to crest), measured in metres (m)

Frequency (f) — the number of complete waves passing a point per second, measured in hertz (Hz)

Amplitude — the maximum displacement of a point on a wave from its rest position, measured in metres (m)

Period (T) — the time taken for one complete wave to pass a point, measured in seconds (s)

Transverse wave — a wave in which the oscillations are perpendicular to the direction of energy transfer (e.g. electromagnetic waves, water waves)

Longitudinal wave — a wave in which the oscillations are parallel to the direction of energy transfer (e.g. sound waves)

Reflection — when a wave bounces off a boundary between two media, obeying the law that angle of incidence equals angle of reflection

Refraction — the change in direction of a wave when it passes from one medium to another due to a change in wave speed

Core concepts

Types of waves and their properties

Waves transfer energy from one place to another without transferring matter. All waves have amplitude, wavelength, frequency, and period.

Transverse waves:

• Oscillations perpendicular to energy transfer direction
• Examples: all electromagnetic waves, water ripples, waves on strings
• Can be polarised (oscillations restricted to one plane only)
• Show peaks (crests) and troughs

Longitudinal waves:

• Oscillations parallel to energy transfer direction
• Examples: sound waves, primary seismic waves (P-waves)
• Cannot be polarised
• Show compressions (regions of high pressure) and rarefactions (regions of low pressure)

Wave equations and calculations

The wave equation relates wave speed, frequency, and wavelength:

wave speed (v) = frequency (f) × wavelength (λ)

v = f × λ

Where:

• v is in metres per second (m/s)
• f is in hertz (Hz)
• λ is in metres (m)

The relationship between period and frequency:

period (T) = 1 ÷ frequency (f)

T = 1/f

Where:

• T is in seconds (s)
• f is in hertz (Hz)

The electromagnetic spectrum

All electromagnetic waves are transverse waves that travel at the same speed in a vacuum: 3.0 × 10⁸ m/s (the speed of light).

The electromagnetic spectrum in order of increasing wavelength (decreasing frequency and energy):

1. Gamma rays — shortest wavelength, highest frequency
2. X-rays
3. Ultraviolet
4. Visible light (violet → red)
5. Infrared
6. Microwaves
7. Radio waves — longest wavelength, lowest frequency

Key applications and hazards:

Radio waves:

• Applications: television, radio broadcasting, communications
• No significant hazards at normal exposure levels

Microwaves:

• Applications: satellite communications, cooking, mobile phones
• Hazards: internal heating of body tissue

Infrared:

• Applications: cooking, thermal imaging cameras, remote controls, optical fibres
• Hazards: skin burns

Visible light:

• Applications: vision, photography, illumination, optical fibres
• Hazards: bright light can damage eyes

Ultraviolet:

• Applications: fluorescent lamps, detecting forged bank notes, disinfection
• Hazards: skin cancer, premature skin aging, eye damage

X-rays:

• Applications: medical imaging, airport security scanners
• Hazards: mutation and cancer from ionising radiation

Gamma rays:

• Applications: sterilising medical equipment, cancer treatment (radiotherapy), tracers
• Hazards: mutation and cancer from ionising radiation

Reflection and refraction

Reflection:

The law of reflection states that the angle of incidence equals the angle of reflection, measured from the normal (a line perpendicular to the surface).

• Applies to all waves
• Specular reflection: smooth surfaces produce clear reflections
• Diffuse reflection: rough surfaces scatter light in many directions
• Used in: mirrors, radar, sonar, ultrasound imaging

Refraction:

When waves pass from one medium to another at an angle:

• Speed changes
• Wavelength changes
• Frequency remains constant
• Direction changes (unless entering perpendicular to boundary)

Light travelling from air into glass or water:

• Slows down
• Bends towards the normal
• Wavelength decreases

Light travelling from glass or water into air:

• Speeds up
• Bends away from the normal
• Wavelength increases

Applications include: lenses (glasses, cameras, telescopes), prisms, optical fibres.

Sound waves

Sound waves are longitudinal mechanical waves that require a medium (cannot travel through a vacuum).

Properties:

• Frequency range of human hearing: approximately 20 Hz to 20,000 Hz
• Ultrasound: frequencies above 20,000 Hz
• Typical speed in air: approximately 330 m/s (faster in solids and liquids)
• Caused by vibrating objects creating compressions and rarefactions

Ultrasound applications:

Medical imaging:

• Prenatal scans of fetuses
• Detecting tumours and kidney stones
• Partially reflected at boundaries between different tissues
• Non-ionising (safer than X-rays)

Industrial uses:

• Cleaning delicate equipment
• Detecting flaws in materials
• Measuring distances and depths (sonar)

Echo calculations:

Distance to reflector = (speed × time) ÷ 2

The division by 2 accounts for the sound travelling to the reflector and back.

Investigating waves

Required practical: Investigating waves in water and strings

Water waves (ripple tank):

• Use a ripple tank with a vibrating dipper or bar
• Measure wavelength using a ruler on the screen below
• Count oscillations in a known time to find frequency
• Calculate wave speed using v = f × λ

Waves on a string:

• Attach string to a vibration generator
• Adjust frequency or length to produce standing waves
• Measure wavelength between nodes (points of zero displacement)
• Calculate wave speed

Required practical: Investigating reflection and refraction

Reflection:

• Direct a ray of light at a plane mirror
• Measure angle of incidence and angle of reflection from the normal
• Verify that they are equal

Refraction:

• Direct a ray of light through a rectangular glass or perspex block
• Trace the incident ray, refracted ray, and emergent ray
• Measure angles to the normal
• Observe bending towards normal on entry, away from normal on exit

Worked examples

Example 1: Wave calculation

Question: A water wave has a frequency of 2.5 Hz and a wavelength of 0.8 m. Calculate the speed of the wave. [3 marks]

Solution:

• Select the correct equation: v = f × λ [1 mark]
• Substitute values: v = 2.5 Hz × 0.8 m [1 mark]
• Calculate and state units: v = 2.0 m/s [1 mark]

Example 2: Electromagnetic spectrum application

Question: Explain why gamma rays are used to sterilise medical instruments rather than infrared radiation. [3 marks]

Solution:

• Gamma rays are ionising radiation / have much higher energy than infrared [1 mark]
• Gamma rays can penetrate through the instruments and packaging [1 mark]
• Gamma rays kill bacteria/microorganisms by damaging their DNA/cells [1 mark]

Example 3: Refraction calculation with period

Question: A ray of light has a frequency of 5.0 × 10¹⁴ Hz in air where it travels at 3.0 × 10⁸ m/s.

(a) Calculate the wavelength of the light in air. [3 marks]

(b) Calculate the period of the wave. [2 marks]

Solution:

(a)

• Rearrange v = f × λ to λ = v ÷ f [1 mark]
• Substitute: λ = (3.0 × 10⁸) ÷ (5.0 × 10¹⁴) [1 mark]
• λ = 6.0 × 10⁻⁷ m (or 600 nm) [1 mark]

(b)

• Use T = 1 ÷ f [1 mark]
• T = 1 ÷ (5.0 × 10¹⁴) = 2.0 × 10⁻¹⁵ s [1 mark]

Example 4: Ultrasound echo

Question: A ship uses ultrasound to measure the depth of water beneath it. An ultrasound pulse is sent out and the echo is detected 0.30 seconds later. The speed of sound in water is 1500 m/s. Calculate the depth of the water. [3 marks]

Solution:

• Calculate total distance travelled: distance = speed × time = 1500 m/s × 0.30 s = 450 m [1 mark]
• Recognise the pulse travels down and back (double the depth) [1 mark]
• Depth = 450 m ÷ 2 = 225 m [1 mark]

Common mistakes and how to avoid them

• Confusing wavelength with amplitude — wavelength is the distance between repeating points (crest to crest), while amplitude is the maximum displacement from rest position. Draw clear diagrams labelling both.

• Forgetting to halve distances in echo calculations — sound travels to the reflector and back, so the total distance must be divided by 2. Always write "distance to object = total distance ÷ 2" in your working.

• Mixing up the angle of incidence and angle of refraction — the angle of incidence equals the angle of reflection (not refraction). In refraction, the ray bends towards the normal when entering a denser medium.

• Stating that frequency changes during refraction — when waves refract, only speed and wavelength change; frequency remains constant. Remember: the wave oscillates at the same rate throughout its journey.

• Claiming electromagnetic waves need a medium — electromagnetic waves can travel through a vacuum; only mechanical waves (like sound) require a medium.

• Not using the correct units — always check: wavelength in metres (m), frequency in hertz (Hz), speed in m/s, period in seconds (s). Convert if necessary (e.g. cm to m, kHz to Hz).

Exam technique for "Waves"

• "Calculate" questions — always show the formula, substitution with units, and final answer with correct units. Even if your final answer is wrong, you can earn method marks. Each step typically earns 1 mark.

• "Explain" and "Describe" command words — "Explain" requires you to give reasons why something happens (earn marks for cause and effect). "Describe" requires you to state what happens without necessarily explaining why. Read the command word carefully.

• Drawing ray diagrams — use a ruler and sharp pencil. Always draw and label the normal (perpendicular to the surface). Mark angles clearly from the normal, not the surface.

• Using data from graphs or tables — in practical questions, you may need to read wavelength from diagrams or count wave oscillations from traces. Take care with scales and show your method clearly for calculation marks.

Quick revision summary

Waves transfer energy without transferring matter. Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel. Use v = f × λ for all wave speed calculations. The electromagnetic spectrum ranges from gamma rays (shortest wavelength) to radio waves (longest wavelength), all travelling at 3.0 × 10⁸ m/s in a vacuum. Reflection obeys angle of incidence = angle of reflection. Refraction occurs when waves change speed between media, bending towards the normal when slowing down. Sound waves are longitudinal, requiring a medium, with ultrasound used in medical imaging and industrial applications.