Wave properties: transverse, longitudinal and the wave equation
What is a wave?
A wave is a transfer of energy (and information) without the transfer of matter. The particles (or fields) oscillate but do not travel with the wave.
Key wave quantities
| Quantity | Symbol | Unit | Definition |
|---|---|---|---|
| Amplitude | A | metres (m) | Maximum displacement from rest/equilibrium position |
| Wavelength | λ | metres (m) | Distance from one point on a wave to the next identical point (e.g. crest to crest) |
| Frequency | f | hertz (Hz) | Number of complete waves passing a point per second |
| Period | T | seconds (s) | Time for one complete wave; T = 1/f |
| Wave speed | v | m/s | Speed at which the wave pattern travels |
Wave equation
$$v = f \times \lambda$$
Where v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m).
Example: A sound wave has frequency 440 Hz and wavelength 0.77 m. Calculate the speed. v = 440 × 0.77 = 338.8 m/s ≈ 340 m/s (speed of sound in air).
Rearrangements:
- f = v/λ (frequency = speed ÷ wavelength)
- λ = v/f (wavelength = speed ÷ frequency)
Transverse waves
Transverse waves: oscillation of particles (or field) is perpendicular (at right angles) to the direction of wave travel.
Examples:
- All electromagnetic waves (light, radio, microwaves, X-rays, etc.)
- S-waves (seismic secondary waves)
- Waves on a string/rope
- Water surface waves
Diagram representation: sinusoidal curve; peaks (crests) and troughs visible.
Longitudinal waves
Longitudinal waves: oscillation is parallel (along the same direction) to wave travel.
Examples:
- Sound waves
- P-waves (seismic primary waves)
- Compression waves in a spring (Slinky)
Key features: compressions (regions of high pressure/density) and rarefactions (regions of low pressure/density). Wavelength = distance from one compression to the next.
Longitudinal waves need a medium to travel through (they cannot travel through a vacuum).
Comparing transverse and longitudinal
| Feature | Transverse | Longitudinal |
|---|---|---|
| Oscillation direction | Perpendicular to travel | Parallel to travel |
| Visible features | Crests and troughs | Compressions and rarefactions |
| Can travel in vacuum? | Yes (EM waves) | No (sound needs medium) |
| Examples | Light, radio, water waves | Sound, P-waves |
Measuring wave speed — ripple tank and string
Ripple tank (water waves): stroboscope freezes the wave pattern; measure wavelength directly with ruler; count frequency from stroboscope frequency.
String/signal generator: set frequency on signal generator; measure wavelength of standing wave pattern; use v = fλ.
Sound oscilloscope method: microphone connected to oscilloscope; read period T from time axis; f = 1/T; measure λ using two microphones and path difference.
⚠Common mistakes
- Confusing wavelength and amplitude on a wave diagram — wavelength is horizontal (crest to crest); amplitude is vertical (rest to crest).
- Longitudinal waves CAN be drawn as a transverse-style diagram to show the compression pattern — but the actual particle oscillation is horizontal.
- Period and frequency are reciprocals: if f = 50 Hz, T = 1/50 = 0.02 s.
- Wave speed depends on the medium, not the frequency (for a given medium, changing frequency just changes wavelength, keeping speed constant).
AI-generated · claude-opus-4-7 · v3-edexcel-combined-science