Wave Behaviour — Reflection, Refraction, Diffraction
What Is a Wave?
A wave is a regular disturbance that transfers energy in the direction of travel without transferring matter. When ripples spread across a pond, water molecules bob up and down — they do not travel across the pond. It is the disturbance, carrying energy, that moves outwards.
Waves are described by four key quantities. The amplitude is the maximum displacement from the rest position — a larger amplitude means a more energetic wave. The wavelength (symbol λ) is the distance between two successive identical points — for example, from crest to crest. The frequency (symbol f) is the number of complete waves passing a fixed point per second, measured in hertz (Hz). The period is the time for one complete wave to pass, measured in seconds.
Wave speed, frequency and wavelength are related by the wave equation:
$$v = f \times \lambda$$
where \(v\) is wave speed in m/s, \(f\) is frequency in Hz and \(\lambda\) is wavelength in m. This applies to all waves — water ripples, sound and all electromagnetic waves.
Transverse and Longitudinal Waves
Waves fall into two types depending on the direction of the disturbance relative to the direction of energy transfer. In a transverse wave, the oscillations are perpendicular to the direction of travel. Waves on a rope are a clear example: flick one end and the displacement is up-and-down while the energy travels along the rope. All electromagnetic waves are transverse.
In a longitudinal wave, the oscillations are parallel to the direction of travel. Sound waves in air are longitudinal: the air pressure alternately increases (compressions) and decreases (rarefactions) along the direction the sound moves. A slinky spring being pushed and pulled along its length is a useful physical model.
Question: A sound wave in air has a frequency of 440 Hz and a wavelength of 0.77 m. Calculate its wave speed.
Step 1 — identify the equation: \(v = f \times \lambda\)
Step 2 — substitute values: \(v = 440 \text{ Hz} \times 0.77 \text{ m}\)
Step 3 — calculate: \(v = 338.8 \text{ m/s}\)
This is close to the accepted speed of sound in air at room temperature (approximately 340 m/s), confirming the calculation is reasonable. Always check your answer makes physical sense.
Reflection
When a wave meets a boundary between two materials, it may be reflected, refracted or transmitted (or some combination). Reflection occurs when a wave bounces off a surface. The angle of incidence (measured from the normal — a line perpendicular to the surface) equals the angle of reflection. A smooth surface reflects waves in one direction (specular reflection), while a rough surface scatters them in many directions.
Refraction
Refraction happens when a wave passes from one medium into another and changes speed. Waves travel at different speeds in different substances, and these speeds may also vary with wavelength — which is why a prism splits white light into colours. Because the frequency of a wave cannot change (it is set by the source), a change in speed produces a change in wavelength. If the wave also hits the boundary at an angle, it changes direction. Light entering glass slows down, causing it to bend towards the normal. Light leaving glass speeds up and bends away from the normal.
Refraction is caused by a change in wave speed at a boundary. Frequency stays constant, so wavelength changes. If the wave hits the boundary at an angle, the direction of travel changes too. Waves slow down when entering a denser medium and speed up when leaving it. Wave speed can vary with wavelength, which is why different colours refract by different amounts.
A ripple tank can be used to measure the speed, frequency and wavelength of water waves. A vibrating dipper creates waves of known frequency. The wavelength is measured from photographs or stroboscopic images of the wave pattern, and wave speed is calculated using \(v = f \times \lambda\). The tank also allows students to observe reflection (using barriers) and refraction (using a shallow section, which slows the wave).
The speed of sound in air can be measured by timing an echo over a known distance. A clap near a wall, with an observer recording the time for the echo to return, gives a simple measure. More precisely, two microphones separated by a measured distance can be used with a data logger to time how long the sound takes to travel between them.
The Wave Model and Its Limits
The wave model is a powerful tool: it successfully predicts the behaviour of light and sound at boundaries, explains colour and musical pitch, and underpins technologies from radio to medical imaging. However, like all scientific models, it has limitations. At very small scales (atomic and subatomic), light also behaves as a stream of particles called photons — a description captured in quantum physics. The fact that wave and particle descriptions are both needed to fully explain light’s behaviour is an example of how scientific models develop as new evidence emerges. For your GCSE, the wave model is sufficient for all the topics assessed.
Understanding waves also connects to the electromagnetic spectrum — all electromagnetic waves are transverse and travel at the same speed through a vacuum. Their different properties (radio, microwave, infrared, visible, ultraviolet, X-ray, gamma) depend on their frequency and wavelength. The wave equation \(v = f \times \lambda\) applies to every one of them.