7.2 Transverse and longitudinal waves
- Syllabus
- 9702–2028–2029
- Topic
- 7.2
- Level
- AS
Learning objectives
Compare wave types by oscillation direction
| Feature | Transverse wave | Longitudinal wave |
|---|---|---|
| Local oscillation or displacement | perpendicular to energy propagation | parallel to energy propagation |
| Mechanical pattern | crests and troughs can represent opposite displacements | compressions and rarefactions arise from crowding and spreading |
| Example | wave on a stretched string; electromagnetic wave | sound wave in air; compression wave in a spring |
| Polarisation | possible | not possible |
Both types can be progressive waves that transfer energy, obey v = fλ, reflect, refract, diffract, interfere and form stationary waves. These shared behaviours do not determine whether a wave is transverse or longitudinal.
To classify a wave, identify the direction in which energy propagates and compare it with the direction of local oscillation. For example, a guitar string oscillates transversely while the sound it produces in air is longitudinal.
Transverse does not always mean vertical: the defining angle is 90° to propagation. Longitudinal does not mean slow, and its particles still oscillate about equilibrium rather than travelling with the wave.
Read wave graphs from their axes and physical meaning
| Representation | What it shows | What can be read |
|---|---|---|
| displacement–distance | all sampled particles at one instant | amplitude and wavelength; phase at different positions |
| displacement–time | one sampled particle at one position | amplitude and period; frequency from f = 1/T |
| particle-position diagram | actual particle locations at one instant | transverse displacement pattern, or longitudinal crowding (compression) and spreading (rarefaction) |
A sinusoidal displacement–distance graph can represent a longitudinal wave. Its vertical coordinate is signed particle displacement parallel to propagation; it is not a literal up-down shape. If positive displacement is defined along the propagation direction, displacement decreasing with distance (negative gradient) marks a compression, while increasing displacement (positive gradient) marks a rarefaction.
For a wave travelling to the right, the instantaneous particle velocity has the opposite sign to the local slope of a displacement–distance graph: positive slope means negative particle velocity, and negative slope means positive particle velocity. At maximum or minimum displacement, instantaneous particle velocity is zero.
Interpret in this order: read both axis labels and units; decide whether the graph is a time record or a spatial snapshot; identify the stated positive displacement and propagation directions; then use spacing, gradient and phase. Equivalent-phase spacing gives λ only on a distance axis and T only on a time axis.
Do not identify wave type from a graph's sinusoidal appearance. For a longitudinal displacement graph, maximum displacement is not the centre of a compression: compression and rarefaction depend on how displacement changes with distance.