What a wave is

A wave transfers energy from one place to another without transferring matter. As a wave passes, the particles only oscillate about a fixed point — they don't travel along with the wave.

• Amplitude — the distance from the rest (equilibrium) position to the maximum displacement.
• Wavelength (λ) — the distance from one point on a wave to the same point on the next wave.
• Frequency (f) — the number of waves passing a point each second, measured in hertz (Hz).
• Period (T) — the time for one complete wave to pass.
• Wavefront — a line joining points that are all in the same part of their oscillation (e.g. all crests).

Watch out: a floating cork bobs up and down as ripples pass — it doesn't get carried to the shore. That's the key idea: waves carry energy, not matter.

Transverse vs longitudinal

Waves come in two kinds, sorted by the direction the particles vibrate compared to the direction the wave travels.

In a transverse wave the vibration is at right angles to the direction of travel (peaks and troughs). In a longitudinal wave the vibration is along the direction of travel (compressions and rarefactions).

Which type of wave?

The wave equation

Speed, frequency and wavelength are tied together for every wave:

And frequency and period are reciprocals of each other:

Rearranging: f = v ÷ λ and λ = v ÷ f. Cover the symbol you want in the triangle to find which way to divide.

Your turn — wave speed

Your turn — rearranging

Your turn — period

Reflection, refraction & diffraction

In a ripple tank you can watch wavefronts behave in three ways:

• Reflection — waves bounce off a barrier. The angle of incidence = angle of reflection; speed, frequency and wavelength are unchanged.
• Refraction — waves change speed when they pass into shallower water. Frequency stays the same, so the wavelength changes and the wavefronts bend.
• Diffraction — waves spread out after passing through a gap or around an edge.

Supplement Supplement — diffraction is greatest when the gap is about the same size as the wavelength. A wide gap diffracts only a little at the edges; a narrow gap spreads the waves into strong semicircles.

Reflection & the plane mirror

The law of reflection says the angle of incidence equals the angle of reflection, both measured from the normal (the line at 90° to the surface).

The image you see in a plane mirror is:

• Upright and the same size as the object.
• The same distance behind the mirror as the object is in front.
• Virtual (the light only appears to come from behind the mirror) and laterally inverted.

Watch out: always measure angles from the normal, never from the mirror surface itself.

Refraction through glass

When light enters a denser medium (air → glass) it slows down and bends towards the normal. Leaving the glass it speeds up and bends away from the normal.

Misconception: refraction happens because the wave's speed changes, not because the glass "pulls" the light. The frequency stays the same; the wavelength changes.

Which way does it bend?

Refractive index Supplement

The refractive index n measures how much a material bends light. From Snell's law:

It is also the ratio of the speed of light in a vacuum to the speed in the medium — a bigger n means a slower, more strongly bending medium.

Your turn — refractive index Supplement

Total internal reflection Supplement

When light travels from a denser medium towards a less dense one, increasing the angle of incidence eventually reaches the critical angle (c) — where the refracted ray skims along the boundary at 90°. Beyond it, all the light reflects back: total internal reflection (TIR).

This is how optical fibres carry light (and data) around bends — used in high-speed communications and in medical endoscopes.

Your turn — critical angle Supplement

The converging lens

A converging (convex) lens refracts parallel rays so they meet at the principal focus (F). The distance from the lens to F is the focal length.

When the object is further than F, the image is real and inverted (it can be caught on a screen). When the object is closer than F, the image is virtual, upright and magnified — the magnifying-glass effect.

Magnification Supplement

Magnification compares the image size to the object size:

A magnification greater than 1 means the image is enlarged; less than 1 means diminished.

Your turn — magnification Supplement

Dispersion of white light

White light is a mixture of colours. A glass prism refracts each colour by a slightly different amount (violet most, red least), spreading them into a spectrum — this is dispersion.

Supplement Supplement — light of a single frequency (a single colour) is described as monochromatic.

The electromagnetic spectrum

All electromagnetic (EM) waves are transverse, need no medium, and travel through a vacuum at the same speed:

Misconception: gamma rays are not faster than radio waves. In a vacuum all EM waves travel at c — gamma simply has a much higher frequency and shorter wavelength.

Uses & dangers

• Radio — TV and radio broadcasting, astronomy, RFID.
• Microwaves — satellite TV, mobile phones, microwave cooking. Supplement phones & Wi-Fi use microwaves because they pass through some walls and need only a short aerial.
• Infrared — remote controls, thermal imaging, optical fibres; danger: skin burns.
• Visible light — vision, photography, illumination.
• Ultraviolet — security marks, sun-tanning, sterilising; danger: skin cancer and eye damage.
• X-rays — medical imaging, airport security; danger: ionising, can cause cell mutation.
• Gamma rays — sterilising equipment, killing cancer cells; danger: highly ionising.

Pattern: the higher the frequency, the greater the energy. UV, X-rays and gamma are ionising, which is why over-exposure is so harmful.

EM spectrum check

Sound waves

Sound is a longitudinal wave made by a vibrating source. It travels as compressions (particles squeezed together) and rarefactions (particles spread apart), and it needs a medium — it cannot travel through a vacuum.

• The louder the sound, the larger the amplitude.
• The higher the pitch, the greater the frequency.
• A healthy human ear hears from 20 Hz to 20 000 Hz.
• The speed of sound in air is about 330–350 m/s (much slower than light) and faster in liquids and solids.

Misconception: sound cannot travel through empty space. In a vacuum there are no particles to compress, so a ringing bell inside a vacuum jar falls silent.

Echoes & measuring the speed of sound

An echo is sound reflected off a hard surface. You can measure the speed of sound by clapping a known distance from a wall and timing the echo — remembering the sound travels there and back.

Supplement Supplement — ultrasound is sound above 20 000 Hz. It is partly reflected at boundaries, so a transceiver can use the echoes for SONAR depth-finding and for medical scans without ionising radiation.

Your turn — speed of sound

Name the wave behaviour

Tap the word that describes what is happening to the wave in each case.

Longer or shorter wavelength than visible light?

Tap an EM region, then tap the box for whether its wavelength is longer or shorter than visible light.

The equations to know

You've covered all four parts of Cambridge IGCSE Topic 3 — general wave properties, light, the electromagnetic spectrum and sound. Press Finish to see your score.