What you'll learn
This revision guide covers all the essential wave concepts you need for WJEC GCSE Physics. You'll explore the properties and behaviours of mechanical and electromagnetic waves, including reflection, refraction, diffraction and interference. Understanding waves is crucial as they account for approximately 15-20% of your final GCSE Physics examination.
Key terms and definitions
Wavelength (λ) — the distance from one point on a wave to the equivalent point on the next wave, 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 wave from its rest position, measured in metres (m)
Transverse wave — a wave where the oscillations are perpendicular to the direction of energy transfer (e.g. light, water waves)
Longitudinal wave — a wave where the oscillations are parallel to the direction of energy transfer (e.g. sound waves)
Electromagnetic spectrum — the family of electromagnetic waves ranging from radio waves to gamma rays, all travelling at the speed of light in a vacuum
Reflection — the change in direction of a wave at a boundary, where the angle of incidence equals the angle of reflection
Refraction — the change in direction of a wave as it passes from one medium to another due to a change in wave speed
Core concepts
Wave properties and the wave equation
All waves transfer energy without transferring matter. Waves are described by their amplitude, wavelength, frequency and speed.
The wave equation connects these properties:
wave speed (m/s) = frequency (Hz) × wavelength (m)
or v = f × λ
This equation applies to all waves and is essential for calculations. If frequency increases, wavelength must decrease (if speed remains constant), showing their inverse relationship.
The period (T) of a wave is the time taken for one complete wave to pass a point, measured in seconds. Period and frequency are related:
T = 1/f or f = 1/T
Wave speed depends on the medium through which the wave travels. Light travels fastest in a vacuum (3 × 10⁸ m/s), while sound travels at approximately 330 m/s in air at room temperature.
Transverse and longitudinal waves
Transverse waves have oscillations perpendicular to the direction of energy transfer. Examples include:
- All electromagnetic waves (light, radio waves, microwaves, etc.)
- Water waves (ripples on a pond)
- Waves on strings
- S-waves (secondary seismic waves)
In transverse waves, you can identify crests (peaks) and troughs (lowest points).
Longitudinal waves have oscillations parallel to the direction of energy transfer. Examples include:
- Sound waves in air, liquids and solids
- P-waves (primary seismic waves)
- Compression waves in springs
Longitudinal waves consist of compressions (regions where particles are closer together) and rarefactions (regions where particles are further apart). The wavelength is measured from the centre of one compression to the centre of the next compression.
The electromagnetic spectrum
All electromagnetic waves are transverse waves that can travel through a vacuum. They all travel at the same speed in a vacuum: 3 × 10⁸ m/s (300,000,000 m/s or 300,000 km/s).
The electromagnetic spectrum in order of increasing frequency (and decreasing wavelength):
- Radio waves — longest wavelength, lowest frequency
- Microwaves
- Infrared radiation
- Visible light (red to violet)
- Ultraviolet radiation
- X-rays
- Gamma rays — shortest wavelength, highest frequency
Key applications of electromagnetic waves:
- Radio waves: television and radio broadcasting, communications
- Microwaves: satellite communications, mobile phones, cooking food
- Infrared: thermal imaging, remote controls, cooking, heaters
- Visible light: vision, photography, fibre optic communications
- Ultraviolet: security marking, fluorescent lamps, sterilisation
- X-rays: medical imaging, airport security scanners
- Gamma rays: sterilising medical equipment, cancer treatment (radiotherapy)
Hazards increase with frequency. Ultraviolet radiation can cause skin cancer and eye damage. X-rays and gamma rays are ionising radiation that can damage cells and DNA, potentially causing cancer. Microwaves can cause internal heating of body tissue.
Reflection of waves
Reflection occurs when a wave bounces off a surface. The law of reflection states:
angle of incidence = angle of reflection
Both angles are measured from the normal (an imaginary line perpendicular to the surface). This law applies to all types of waves.
Smooth surfaces produce specular reflection where parallel rays remain parallel after reflection, producing a clear image. Rough surfaces produce diffuse reflection where parallel rays scatter in many directions, producing no clear image.
Plane mirrors form virtual images that are:
- The same size as the object
- The same distance behind the mirror as the object is in front
- Laterally inverted (left and right reversed)
- Upright
Sound waves reflect off hard surfaces, producing echoes. This principle is used in ultrasound imaging and sonar.
Refraction of waves
Refraction occurs when a wave changes speed as it enters a different medium, causing a change in direction (unless the wave enters along the normal).
Key principles of refraction:
- When waves slow down, they bend towards the normal
- When waves speed up, they bend away from the normal
- Frequency remains constant during refraction
- Wavelength changes (shorter when speed decreases, longer when speed increases)
Light travels slower in denser media. When light enters glass from air:
- It slows down
- Wavelength decreases
- The light bends towards the normal
When light exits glass into air, the reverse occurs.
Optical density describes how much a material slows down light. Glass is optically denser than air, so light travels more slowly in glass.
The refractive index of a material indicates how much light slows down in that material compared to a vacuum.
White light can be dispersed by a prism because different colours (frequencies) of light refract by different amounts. Violet light bends most, red light bends least, producing a spectrum.
Wave phenomena: diffraction and interference
Diffraction is the spreading out of waves when they pass through a gap or around an obstacle.
Diffraction is most significant when:
- The gap is similar in size to the wavelength
- The gap is smaller than the wavelength
Longer wavelength waves diffract more than shorter wavelength waves. This explains why long-wavelength radio waves can be received behind hills, while shorter wavelength microwaves cannot.
Interference occurs when two waves meet and superpose (add together).
Constructive interference occurs when two crests (or two troughs) meet. The waves combine to produce a larger amplitude.
Destructive interference occurs when a crest meets a trough. The waves cancel each other out, producing zero amplitude if they have equal amplitude.
Interference patterns demonstrate that waves can add and subtract. This produces regions of loud and quiet sound, or bright and dark fringes with light waves.
Sound waves
Sound waves are longitudinal mechanical waves that require a medium (solid, liquid or gas) to travel. Sound cannot travel through a vacuum.
Sound travels at different speeds in different materials:
- Fastest in solids (~5000 m/s in steel)
- Slower in liquids (~1500 m/s in water)
- Slowest in gases (~330 m/s in air)
The speed of sound in air increases slightly with temperature.
Pitch is related to frequency:
- High frequency = high pitch
- Low frequency = low pitch
The human hearing range is approximately 20 Hz to 20,000 Hz (20 kHz).
Ultrasound refers to sound waves with frequencies above 20 kHz (above human hearing). Uses include:
- Medical imaging (pregnancy scans)
- Breaking down kidney stones
- Quality control (detecting cracks in materials)
- Sonar for measuring depth
Loudness is related to amplitude:
- Large amplitude = loud sound
- Small amplitude = quiet sound
The decibel scale measures sound intensity. Prolonged exposure to sounds above 85 dB can damage hearing. Sounds above 120 dB cause immediate pain and damage.
Worked examples
Example 1: Wave equation calculation
Question: A radio station broadcasts at a frequency of 95.8 MHz. Calculate the wavelength of these radio waves. (Speed of electromagnetic waves = 3 × 10⁸ m/s) [3 marks]
Solution:
- Convert frequency to Hz: 95.8 MHz = 95.8 × 10⁶ Hz [1]
- Rearrange wave equation: λ = v/f [1]
- λ = (3 × 10⁸)/(95.8 × 10⁶) = 3.13 m [1]
Mark scheme tip: Always show unit conversions clearly and rearrange equations before substituting values.
Example 2: Refraction
Question: Explain why a swimming pool appears shallower than it actually is. [3 marks]
Solution:
- Light from the bottom of the pool travels from water (denser) to air (less dense) [1]
- The light refracts (bends) away from the normal as it speeds up [1]
- The refracted rays appear to come from a position higher than they actually do, making the pool look shallower [1]
Mark scheme tip: Use correct terminology (refract, normal, optically dense) and explain the consequence of the physical process.
Example 3: Electromagnetic spectrum
Question: A student investigates different regions of the electromagnetic spectrum. (a) Name the region between infrared and X-rays. [1 mark] (b) Compare the wavelength of gamma rays to radio waves. [1 mark] (c) State one use of microwaves. [1 mark]
Solution: (a) Ultraviolet (or UV) [1] (b) Gamma rays have much shorter wavelengths than radio waves / gamma rays have wavelengths approximately one million times smaller [1] (c) Satellite communications / mobile phones / cooking food (any one) [1]
Common mistakes and how to avoid them
Confusing wave speed with wave frequency: Remember wave speed depends on the medium, while frequency depends on the source producing the wave. When waves refract, frequency stays constant but speed and wavelength change.
Measuring angles from the surface instead of the normal: Always measure angles of incidence and reflection from the normal (perpendicular line), not from the reflecting surface itself.
Stating sound waves are transverse: Sound waves are longitudinal. Particles oscillate parallel to the direction of energy transfer. Only describe electromagnetic waves and water waves as transverse.
Forgetting to convert units: Always convert MHz to Hz, km to m, and cm to m before using the wave equation. Show this conversion clearly in your working.
Mixing up compressions and rarefactions: In longitudinal waves, compressions are where particles are pushed together (high pressure), rarefactions are where particles are spread out (low pressure).
Assuming all electromagnetic waves are dangerous: Only the higher frequency end of the spectrum (UV, X-rays, gamma rays) causes significant harm through ionisation. Radio waves, microwaves (at low intensity), infrared and visible light are generally safe.
Exam technique for "Waves"
Command word "Explain": Provide reasons why something happens using physics principles. For refraction questions, state the change in speed, direction and relate to normal line. This typically requires 2-3 marking points for 2-3 marks.
Wave equation questions: Always write the equation, substitute values with units, then calculate. Show rearrangement clearly. Even if your final answer is incorrect, you can gain method marks. Questions worth 3 marks typically award 1 mark for equation, 1 for substitution, 1 for answer.
Diagram questions: Use a ruler for straight lines (rays, normals). Label all relevant angles and clearly mark the normal with a dashed line perpendicular to the surface. Add arrowheads to show direction.
Application questions: When asked about uses or hazards of electromagnetic waves, be specific. "Communication" is too vague—state "satellite communication" or "mobile phone signals". Link the property of the wave (e.g. wavelength) to its use where possible.
Quick revision summary
Waves transfer energy without transferring matter. Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel. Use v = fλ for all wave calculations. Electromagnetic waves form a spectrum from radio to gamma rays, all travelling at 3 × 10⁸ m/s in a vacuum. Reflection follows angle of incidence equals angle of reflection. Refraction occurs when waves change speed between media, bending towards the normal when slowing down. Diffraction is greatest when gap size matches wavelength. Sound waves are longitudinal and travel fastest through solids.