Waves

Key Definitions

• Wave – a disturbance that transfers energy from place to place without transferring matter overall.
• Amplitude – maximum displacement of a point on the wave from its rest position.
• Wavelength λ – distance between two identical points on neighbouring waves (e.g. crest to crest).
• Frequency f – number of waves passing a point per second (unit: hertz, Hz).
• Period T – time taken for one complete wave (seconds).
• Wavefront – line joining points that are in phase (e.g. all crests).

Wave Equations

Typical units: v in m/s, f in Hz, λ in m, T in s.

Common Mistake: “Half a Wave”

In diagrams it's very easy to mix up amplitude and wavelength:

• The distance from the middle line to the crest is the amplitude, not “half a wavelength”.
• One whole wavelength is from crest to next crest, trough to next trough, or any point to the next identical point on the wave.
• If you only measure from the middle line to a crest and label it λ, examiners will mark it wrong – that is just the amplitude.

Safe rule: always show wavelength between two crests or two troughs when you draw it.

Transverse Wave Shape

Transverse Waves

• Oscillations are at right angles to the direction of energy transfer.
• Examples: water waves, waves on a string, all electromagnetic waves (light, radio, etc.).

Longitudinal Waves

• Oscillations are parallel to the direction of energy transfer.
• They have compressions and rarefactions.
• Examples: sound waves in air, waves along a slinky pushed and pulled.

Visualising Both Types

Reflection

• Law of reflection – angle of incidence = angle of reflection.
• Both angles are measured between the ray and the normal (a line at 90° to the surface).
• Plane mirrors produce a virtual image the same size as the object, same distance behind the mirror.

Refraction

• Refraction is the bending of light as it passes from one medium to another.
• It happens because the wave’s speed changes.
• Going into a denser medium (higher refractive index): speed decreases and ray bends towards the normal.
• Going into a less dense medium: speed increases and ray bends away from the normal.

Total internal reflection happens when light tries to pass from higher to lower n, with angle of incidence > critical angle c.

Key Facts

• Sound is a longitudinal wave caused by vibrating objects.
• It needs a medium (solid, liquid or gas) – it cannot travel in a vacuum.
• Sound travels fastest in solids, slower in liquids, slowest in gases.
• Typical speed of sound in air ≈ 340 m/s (at room temperature).
• Human hearing range: about 20 Hz to 20 kHz (falls with age).

We can measure the speed of sound by timing echoes or using microphones and a data logger.

Echo Distance

If you time an echo (sound bouncing off a cliff), remember the sound travels to the wall and back again – twice the distance.

Order & Properties

All electromagnetic (EM) waves:

• are transverse,
• travel at the same speed in a vacuum (≈ 3.0 × 10⁸ m/s),
• transfer energy and can be reflected, refracted, absorbed.

The spectrum in order of increasing frequency (and energy):

• Radio waves
• Microwaves
• Infrared
• Visible light
• Ultraviolet
• X-rays
• Gamma rays

Uses & Dangers

Typical uses (examples you can quote in answers):

• Radio – broadcasting, communications.
• Microwaves – satellite links, cooking food.
• Infrared – heaters, night-vision cameras.
• Visible – cameras, optical fibres.
• Ultraviolet – tanning beds, security markings, sterilising equipment.
• X-rays – medical imaging, security scanners.
• Gamma – sterilising food/equipment, cancer treatment.

Higher-energy waves (UV, X-ray, gamma) can cause cell damage and cancer – you need to know the dangers as well as the uses.