A level Physics waves

By The STEM-Tutor team · Updated October 2026

Waves connect sound, light and the rest of physics. Here are the A level ideas you need, with a focus on stationary waves and interference.

Wave basics

• v = fλ and f = 1/T.
• Transverse waves oscillate perpendicular to the direction of travel; longitudinal waves oscillate parallel to it.
• Only transverse waves can be polarised.
• Phase difference describes how far one point on a wave is ahead of another.

Superposition

When waves meet, their displacements add. Constructive interference happens when they arrive in phase, and destructive interference when they arrive in antiphase.

Stationary waves

• Formed when two waves of the same frequency travel in opposite directions and superpose, often by reflection.
• Nodes have zero amplitude; antinodes have maximum amplitude.
• On a string fixed at both ends, the first harmonic has a wavelength of twice the string length.
• Stationary waves do not transfer energy along the medium.

Interference and diffraction

• Young's double slit: fringe spacing w = λD/s.
• Diffraction grating: d sinθ = nλ.
• Coherent sources have a constant phase difference and the same frequency.

Refraction

n = c/v and n₁sinθ₁ = n₂sinθ₂. Total internal reflection happens when light goes into a less dense medium at more than the critical angle, as in optical fibres.

Exam tips

1. Sketch the stationary wave pattern before calculating wavelengths.
2. Learn the conditions for observable interference in words.
3. Check units: wavelengths of light are often in nanometres.

What a wave really is

A wave transfers energy from one place to another without transferring matter. In a transverse wave, such as light or a wave on a string, the oscillations are at right angles to the direction of energy transfer. In a longitudinal wave, such as sound, the oscillations are parallel to it, forming compressions and rarefactions. Only transverse waves can be polarised, which is strong evidence that light is transverse.

Two points on a wave are in phase if they move in the same way at the same time. The phase difference between points one wavelength apart is 360° or 2π radians; points half a wavelength apart are in antiphase, 180° or π radians.

Worked examples

Example 1: the wave equation

A sound wave has frequency 512 Hz and travels at 340 m/s. Find its wavelength.

• λ = v/f = 340/512 ≈ 0.66 m.

Example 2: a stationary wave on a string

A string 0.80 m long vibrates in its third harmonic. The wave speed is 120 m/s. Find the wavelength and frequency.

• The third harmonic has three loops, so L = 3λ/2 and λ = 2 × 0.80/3 ≈ 0.53 m.
• f = v/λ = 120/0.533 = 225 Hz, which is three times the fundamental of 75 Hz.

Example 3: Young's double slits

Light of wavelength 600 nm passes through slits 0.50 mm apart onto a screen 2.0 m away. Find the fringe spacing.

• w = λD/s = (600 × 10⁻⁹ × 2.0)/(0.50 × 10⁻³) = 2.4 mm.

Example 4: a diffraction grating

A grating has 300 lines per mm. Light of wavelength 550 nm falls on it. Find the angle of the second-order maximum.

• d = 1/300 mm = 3.33 × 10⁻⁶ m.
• sinθ = nλ/d = 2 × 550 × 10⁻⁹ / 3.33 × 10⁻⁶ = 0.33, so θ ≈ 19.3°.

Example 5: refraction and critical angle

Light passes from air into glass of refractive index 1.5 at 40° to the normal. Find the angle of refraction and the critical angle for glass to air.

• sin r = sin 40°/1.5 = 0.429, so r ≈ 25.4°.
• sin C = 1/1.5, so C ≈ 41.8°. Beyond this angle, light inside the glass is totally internally reflected.

Example 6: path difference

Two speakers in phase emit sound of wavelength 0.50 m. A listener is 4.0 m from one and 5.25 m from the other. Is the sound loud or quiet?

• Path difference = 1.25 m = 2.5λ, a half-integer number of wavelengths.
• The waves arrive in antiphase, so there is destructive interference: the sound is quiet.

Optical fibres

An optical fibre carries light by total internal reflection. A core of higher refractive index is surrounded by cladding of lower refractive index. The cladding protects the core and stops signals crossing between fibres. Two effects spread a pulse out and limit how fast data can be sent: material dispersion, where different wavelengths travel at different speeds, and modal dispersion, where rays take different paths. Using monochromatic light reduces material dispersion, and a very narrow core reduces modal dispersion.

Common mistakes

• Forgetting that stationary waves have nodes, where there is no motion, and that the distance between adjacent nodes is half a wavelength.
• Using the slit width instead of the slit separation in the double-slit formula.
• Rounding the grating spacing too early, which throws off the angle.
• Not mentioning coherence: a stable interference pattern needs a constant phase difference.

Practice questions

Try each one before opening the answer.

Frequently asked questions

What is the difference between a progressive and a stationary wave?

A progressive wave transfers energy, and every point has the same amplitude. A stationary wave stores energy, with nodes and antinodes, and points between two nodes move in phase.

Why does diffraction depend on the size of the gap?

Diffraction is most noticeable when the gap is about the same size as the wavelength. Much wider gaps let the wave pass with little spreading.

Key takeaways

• Waves transfer energy, not matter.
• v = fλ applies to every wave.
• Stationary waves form when two waves of the same frequency travel in opposite directions.
• Use w = λD/s for double slits and d sinθ = nλ for gratings.
• Total internal reflection needs an angle above the critical angle and a move into a less dense medium.

Where to go next

Waves link to the required practicals and to quantum physics.

• A level Physics required practicals
• A level Physics formula sheet
• A level Physics topics

Waves is a highly visual topic, so sketch the situation for every question: a quick diagram of slits, fringes or a stationary wave often shows you the answer before any calculation.