Waves
Explore the nature of waves, their key properties — amplitude, wavelength, and frequency — and the fundamental difference between transverse and longitudinal waves, with real-world examples.
What Is a Wave?
A wave is a transfer of energy from one place to another through a medium (or sometimes through a vacuum), without the permanent transfer of matter. The particles of the medium vibrate as the wave passes — they move about their rest position and then return, rather than travelling along with the wave.
Waves are responsible for light, sound, heat radiation, earthquakes, and even the ripples you see when you drop a stone in a pond.
Parts of a Transverse Wave
Amplitude (A)
The maximum displacement of a particle from its rest position. Measured in metres (m). A larger amplitude means a more energetic (louder/brighter) wave.
Wavelength (λ)
The distance between two successive identical points on a wave (e.g. crest to crest or trough to trough). Measured in metres (m).
Frequency (f)
The number of complete wave cycles that pass a given point per second. Measured in hertz (Hz). 1 Hz = 1 cycle per second.
Transverse vs Longitudinal Waves
The two main types of waves differ in the direction of vibration of the particles compared to the direction the wave travels.
Transverse Waves
Particles vibrate perpendicular (at right angles) to the direction the wave travels.
- Light waves (all electromagnetic waves)
- Water surface waves
- Waves on a string or rope
- Seismic S-waves (secondary waves)
Longitudinal Waves
Particles vibrate parallel (in the same direction) to the direction the wave travels, forming compressions and rarefactions.
- Sound waves in air
- Ultrasound (medical imaging)
- Seismic P-waves (primary waves)
- Slinky compressed along its length
| Feature | Transverse | Longitudinal |
|---|---|---|
| Particle vibration direction | Perpendicular to wave travel | Parallel to wave travel |
| Features | Crests and troughs | Compressions and rarefactions |
| Can travel in vacuum? | Yes (light) | No (needs a medium) |
| Examples | Light, water waves | Sound, seismic P-waves |
Wave Speed and the Wave Equation
The wave speed (v) is how fast the wave moves through a medium. It is related to the wavelength and frequency by the wave equation:
speed (m/s) = frequency (Hz) × wavelength (m)
The Electromagnetic Spectrum
All electromagnetic (EM) waves travel at the same speed in a vacuum: c = 3 × 10⁸ m/s (the speed of light). They differ in wavelength and frequency. From longest wavelength to shortest: radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays.
Speed of Sound
Sound travels at about 340 m/s in air at room temperature. It travels faster in liquids and solids than in gases because particles are closer together. Sound cannot travel through a vacuum — there are no particles to vibrate.
Frequency and Pitch / Colour
For sound waves, higher frequency = higher pitch. For light waves, higher frequency = higher energy = shorter wavelength. Violet light has a higher frequency than red light. Ultraviolet (UV) light has a higher frequency than visible light, which is why it can cause sunburn.
Key Vocabulary
Frequency (f)
The number of complete wave cycles passing a point per second, measured in hertz (Hz). Higher frequency means more energy transferred per second.
Wavelength (λ)
The distance between two successive crests (or troughs) of a wave, measured in metres. Wavelength and frequency are inversely related when wave speed is constant.
Amplitude (A)
The maximum displacement of a particle from its equilibrium (rest) position. Amplitude is related to the energy of the wave — a louder sound or brighter light has a larger amplitude.
Compression / Rarefaction
Features of longitudinal waves. A compression is a region where particles are crowded together; a rarefaction is where they are spread apart. Together they carry wave energy.
Worked Examples
A sound wave has a frequency of 440 Hz and travels at 340 m/s. What is its wavelength?
Formula: v = f × λ, so λ = v ÷ f
Substitute: λ = 340 m/s ÷ 440 Hz
Answer: λ ≈ 0.77 m (77 cm). This is the wavelength of the musical note A4 (concert A).
Explain the difference between transverse and longitudinal waves, with one example of each.
Transverse: Particles vibrate at right angles to the direction of wave travel. A crest and a trough can be identified. Example: light — the electric field oscillates perpendicular to the direction of travel.
Longitudinal: Particles vibrate parallel to the direction of wave travel, creating alternating compressions (high pressure) and rarefactions (low pressure). Example: sound in air — air molecules are pushed together and pulled apart as the sound wave passes.
A radio wave has a wavelength of 3 m. Calculate its frequency. (Speed of light = 3 × 10⁸ m/s)
Formula: v = f × λ, so f = v ÷ λ
Substitute: f = (3 × 10⁸) ÷ 3
Answer: f = 1 × 10⁸ Hz = 100 MHz. This is in the FM radio band (typical FM radio stations broadcast at 88–108 MHz).
Knowledge Check
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Key Concepts Summary
- ✓ Waves transfer energy without transferring matter. Particles vibrate about their rest position.
- ✓ Key properties: amplitude (max displacement), wavelength (distance per cycle), frequency (cycles per second, Hz).
- ✓ Transverse waves: particle vibration is perpendicular to wave travel. Examples: light, water surface.
- ✓ Longitudinal waves: particle vibration is parallel to wave travel. Example: sound. Features compressions and rarefactions.
- ✓ Wave equation: v = f × λ. Speed, frequency, and wavelength are linked.
- ✓ All EM waves travel at 3 × 10⁸ m/s in a vacuum. Sound cannot travel in a vacuum.