Pulses and progressive waves, transverse versus longitudinal waves, wave parameters (v = fλ, period, frequency, amplitude, wavelength), displacement-position and displacement-time graphs, and the four wave behaviours (reflection, refraction, diffraction, interference).
A wave is a transfer of energy from one place to another by means of a disturbance, without any net transfer of matter.
A single disturbance that travels through a medium is a pulse. When disturbances are repeated continuously, a progressive wave is produced.
In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave travel.
Examples: light (all electromagnetic waves), water waves, waves on a rope.
In a longitudinal wave, the particles of the medium oscillate parallel to the direction of wave travel, producing compressions (regions of high pressure and density) and rarefactions (regions of low pressure and density).
Examples: sound waves, seismic P-waves.
| Quantity | Symbol | Definition | Unit |
|---|---|---|---|
| Amplitude | Maximum displacement of a particle from its rest (equilibrium) position | m | |
| Wavelength | Distance between two successive points in phase (e.g. crest to crest) | m | |
| Period | Time for one complete oscillation | s | |
| Frequency | Number of complete oscillations per second; | Hz | |
| Wave speed | Speed at which the wave pattern moves through the medium | m s⁻¹ |
where is the wave speed (m s⁻¹), is frequency (Hz), and is wavelength (m).
A displacement-position (or displacement-distance) graph shows the displacement of every particle at one instant in time. It is a "snapshot" of the wave. The wavelength can be read directly from the graph.
A displacement-time graph shows how the displacement of one particle varies over time. The period can be read from this graph.
From a sinusoidal wave graph (displacement vs position):
Suppose amplitude m, wavelength m, and period s.
From the 2017 exam: a wave of frequency 10 Hz and wavelength 250 m has speed:
All waves (including light, sound, and water waves) can exhibit the following four behaviours.
When a wave meets a boundary, part of it bounces back. The angle of incidence equals the angle of reflection (measured from the normal).
When a wave passes from one medium into another where its speed is different, it changes direction (unless it arrives perpendicular to the boundary). The frequency is unchanged; wavelength and speed change. A wave that slows down bends toward the normal.
When a wave passes through a gap or around an obstacle, it spreads out. Diffraction is most pronounced when the gap size is similar to the wavelength. Sound diffracts easily around corners because its wavelength (0.1 m to 10 m) is comparable to everyday obstacles.
When two waves overlap, their displacements add algebraically (principle of superposition).
On a displacement-position graph, wavelength is crest to crest (or trough to trough, or any point to the next identical point). Do not confuse this with a displacement-time graph, on that graph, you read off the period, not the wavelength.
Frequency and period are always reciprocals: . Learn to state both the value and the unit when reading from a graph.