Cambridge O Level Physics: Waves (5054) – Revision Notes

Short notes on topic 3, Waves, from the Cambridge O Level Physics 5054 syllabus (examined 2026 to 2028), covering sections 3.1 to 3.4. The study guide has the longer explanations and worked examples. Once the self-test below goes well, try the practice questions. Also useful: the Physics course hub, a printable checklist and our free diagnostics.

Equations

Quantity	Equation	Notes
Wave speed	v = fλ	Use m/s, Hz and m
Period	T = 1/f	T in s
Refractive index	n = sin i / sin r	i in the air, r in the material, both from the normal
Critical angle	n = 1 / sin c	Rearrange: sin c = 1/n
Linear magnification	image length / object length	No unit
Echo or sonar	distance = v × t / 2	Halve: the pulse goes there and back
Speed of sound by echo	v = 2d / t	d is the distance to the reflector

3.1 General properties of waves

Definitions to recite.

• Waves transfer energy without transferring matter.
• Frequency: the number of wavelengths that pass a point per unit time (Hz).
• Wavelength: the distance between two consecutive, identical points, such as two consecutive crests.
• Amplitude: the maximum distance from the mean position.
• Wavefront: a line joining points at the same stage of vibration.
• Crest (peak) and trough: highest and lowest points of a transverse wave.

Transverse	Longitudinal
Vibration at right angles to the direction of energy transfer	Vibration parallel to the direction of energy transfer
Electromagnetic radiation, surface water waves, seismic S-waves (secondary)	Sound waves, seismic P-waves (primary)
Crests and troughs	Compressions and rarefactions

Wave motion: shaking a rope or spring sends a pulse along it, and each part only vibrates about its rest position. Ripples in water show the same: a floating object bobs and stays put.

Three wave behaviours.

• Reflection at a plane surface: the wave bounces back.
• Refraction: a change of direction caused by a change of speed. The frequency stays fixed, so the wavelength changes too.
• Diffraction through a gap: spreading out. Most when the gap is about one wavelength. Less when the gap is much wider than the wavelength. A longer wavelength spreads more. At an edge a longer wavelength also bends round more.

Ripple tank, one line each.

• Reflection: a straight barrier turns the wavefronts back.
• Refraction: shallow water slows the waves, shortens the wavelength and changes direction.
• Gap: a narrow gap spreads the wavefronts into circles.
• Edge: the wavefronts curve round the end of a barrier.

Method: v = fλ.

1. Write down the two known quantities with units.
2. Convert units first (cm to m, kHz to Hz).
3. Rearrange: v = fλ, f = v/λ, λ = v/f.
4. Give the unit.

3.2 Light

Reflection

• The normal is at right angles to the surface. Angles of incidence and reflection are measured from it.
• Law of reflection: the two angles are equal.
• Plane mirror image: matches the object in size, sits behind the mirror at the object’s distance in front, and is virtual.
• Experiment: ray box, mirror, paper. Mark the ray, join the points, measure from the normal, repeat.
• Image position: pins in line with the image from two directions. The lines cross at the image.

Refraction

• Slower medium: ray bends towards the normal. Faster medium: away from the normal.
• Light through a rectangular block emerges parallel to its original path, shifted sideways. A triangular prism bends the ray towards its base.
• Experiments: trace the ray through a block on paper at several angles. For internal reflection, aim a ray at the flat face of a semicircular block through the curved face and raise the angle until the refracted ray runs along the face (angle c), then beyond it.
• Total internal reflection needs both: light travelling in the more dense medium towards the less dense, and i greater than c.
• At i equal to c, the refracted ray travels along the boundary.
• Optical fibres use total internal reflection. Used in telecommunications. Advantages: carry a large amount of information and avoid electrical interference. Use these as points, then add the context asked in the question.

Method: refractive index.

1. Is the ray going into the material (use n = sin i / sin r) or out (use n = sin r / sin i with r now in air)?
2. Put both angles measured from the normal.
3. Take sin, divide, then take the inverse sin.
4. Check: entering a denser medium, r is smaller than i.

Thin lenses

• Converging lens: parallel beam brought to the principal focus. Diverging lens: parallel beam spreads out.
• Focal length: lens centre to principal focus. Principal axis: line through the lens centre at right angles to it.
• Ray diagram: one ray parallel to the axis, through the focus after the lens; one ray through the centre, straight on.

Converging lens, object at	Image
More than 2F away	Inverted, real, diminished
Between F and 2F	Inverted, real, magnified
Less than F away (magnifying glass)	Upright, virtual, magnified

A diverging lens always gives a virtual, upright, smaller image.

• Real image: formed by converging rays. Virtual image: formed by diverging rays.
• Eye diagrams: a normal eye brings parallel rays to a focus on the retina. In short sight they focus in front of the retina, so a diverging lens spreads them first. In long sight the focus lies behind the retina, so a converging lens is used.

Dispersion

A prism refracts violet most and red least. Frequency increases: red, orange, yellow, green, blue, indigo, violet. Wavelength increases the other way.

3.3 Electromagnetic spectrum

Increasing frequency, decreasing wavelength: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Speed: 3.0 × 10⁸ m/s in a vacuum and about the same in air.

Region	Uses to learn
Radio	Radio and television, astronomy
Microwave	Satellite television, mobile phones, Bluetooth, ovens
Infrared	Appliances, remote controllers, intruder alarms, thermal imaging, optical fibres
Visible	Photography, vision
Ultraviolet	Security marking, counterfeit notes, sterilising water
X-rays	Medical imaging, security scanners, killing cancer cells, cracks in metal
Gamma	Treating cancer, sterilising food and equipment, cracks in metal

Dangers. Excess exposure heats soft tissue and burns. Ionising radiation: ultraviolet (skin cancer, cataracts); X-rays and gamma rays (cell mutation, cancer).

3.4 Sound

• Made by vibrating sources. Longitudinal, with compressions and rarefactions.
• Audible range for humans: 20 Hz to 20 000 Hz.
• Cannot travel in a vacuum because there are no particles to pass on the vibration. Demonstration: bell in an evacuated jar.
• Amplitude gives loudness. Frequency gives pitch.
• Timbre: the oscilloscope trace shape differs between sources even at the same pitch and loudness.
• Echo: reflection of sound. Show by directing sound at a hard board and detecting reflection.
• Speed in air: approximately 330 to 350 m/s. Solids faster than liquids, liquids faster than gases.
• Ultrasound: frequency above 20 kHz. Uses: cleaning, prenatal and other medical scanning, sonar.

Method: speed of sound in air. Measure the distance to a wall with a long tape. Clap and time the echo with a stopwatch. v = 2d/t. Repeat and average.

Method: echo or sonar depth. Distance travelled = v × t. Divide by 2 for the one-way distance.

Must-know distinctions

• Loudness is amplitude; pitch is frequency.
• Refraction changes speed and wavelength; frequency stays the same.
• Real image: can be caught on a screen. Virtual image: cannot.
• Critical angle belongs to the dense-to-less-dense direction; it does not exist going the other way.
• Ionising: ultraviolet, X-rays, gamma rays. Heating effect: microwaves and infrared.

Quick self-test

1. Water waves have a frequency of 12 Hz and a wavelength of 0.25 m. Find the speed.
2. A note has a frequency of 250 Hz. Find the period.
3. A ray in air strikes glass (n = 1.5), making 30° with the normal. Find the angle of refraction.
4. A microwave has a wavelength of 0.12 m. Find its frequency, using 3.0 × 10⁸ m/s.
5. An image is 9.0 cm tall and the object is 2.0 cm tall. Find the magnification.
6. A sonar pulse returns after 0.40 s. The speed in water is 1500 m/s. Find the depth.
7. A ray goes from air into a plastic. The angle of incidence is 60° and the angle of refraction is 35°. Find n.
8. A ray makes 62° with a plane mirror. Find the angle of reflection.
9. Calculate the critical angle of a glass with n = 1.5.
10. Sound at 170 Hz travels at 340 m/s. Find the wavelength.
11. State why sound cannot pass through a vacuum.
12. Give the property of a sound wave that sets its pitch.

Answers

1. v = fλ = 12 × 0.25 = 3.0 m/s.
2. T = 1/250 = 0.004 s.
3. sin r = sin 30° / 1.5 = 0.333, so r = 19.5°.
4. f = v/λ = 3.0 × 10⁸ / 0.12 = 2.5 × 10⁹ Hz.
5. 9.0 / 2.0 = 4.5.
6. 1500 × 0.40 / 2 = 300 m.
7. n = sin 60° / sin 35° = 1.51.
8. Angle of incidence = 90 − 62 = 28°, so the angle of reflection is 28°.
9. sin c = 1/n = 0.667, giving c = 41.8°.
10. λ = 340 / 170 = 2.0 m.
11. There are no particles to vibrate and pass the energy on.
12. The frequency.

Where marks are usually lost

• Using the surface rather than the normal as the line to measure angles from.
• Leaving out the halving step in echo and sonar questions.
• Quoting frequency, wavelength or speed without converting kHz, MHz or cm first.
• Writing that sound “goes faster in air than in water”.
• Describing the longitudinal wave as “up and down”.
• Stating total internal reflection without both conditions.
• Mixing up the order of the electromagnetic spectrum with the order of colours in dispersion.
• Saying a virtual image is “not there” instead of saying the rays only appear to come from it.

Frequently asked questions

What is the difference between loudness and pitch? Loudness depends on the amplitude of a sound wave, and pitch depends on its frequency.

What is the difference between a real and a virtual image? A real image can be caught on a screen. A virtual image cannot, because the rays only appear to come from it.

Which parts of the electromagnetic spectrum are ionising? Ultraviolet, X-rays and gamma rays are ionising, while microwaves and infrared mainly have a heating effect.

Does sound travel faster in air or in water? Sound travels faster in water than in air. Writing that sound goes faster in air than in water is a common error.

Official syllabus

Source: topic 3, Waves, of the Cambridge International Education O Level Physics 5054 syllabus for 2026 to 2028.