Waves and superposition: models, interference and diffraction
Key idea: Use signed displacement and phase consistently across time and space, then apply superposition to standing waves, interference and diffraction without confusing their distinct conditions.
Before you start: Oscillations objective chainQuantities & Measurement objective chain
By the end, you can
- Model mechanical and electromagnetic progressive waves, interpret time and position graphs, and use wave quantities, phase and energy transfer.
- Apply intensity–amplitude and inverse-square relationships, and use polarisation and Malus' law for electromagnetic waves.
- Apply superposition and explain standing-wave experiments, boundary conditions, nodes, antinodes and sound-wavelength measurement.
- Analyse coherent two-source interference and Young double-slit fringes using phase and path difference.
- Use diffraction gratings, single-slit first minima and the Rayleigh criterion with their distinct aperture spacings and assumptions.
Starting-point self-check
1. Check your starting point
Attempt all seven groups without notes and mark the first graph axis, phase conversion, boundary condition or aperture spacing you could not justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Wave models, quantities, graphs and transfer 10(a)–(f)
Question 1
A spatial profile has wavelength 0.80 m and a time trace at one point has period 0.25 s. Find frequency and speed, state what a horizontal separation means on each graph, and compare what oscillates in a water wave and an electromagnetic wave.
Check the model response
f = 1/T = 4.0 Hz and v = fλ = 3.2 m s⁻¹. A horizontal separation on the spatial graph represents distance and can give wavelength; on the time trace it represents time and can give period. Water particles oscillate in a material medium, whereas electromagnetic fields oscillate in space and time. Energy is transferred without net transfer of the medium.
repair
2. Repair the eleven common breaks
Use only the repair matching an error, then redraw the axes, signed displacement, boundary conditions, rays or aperture before retrying.
Wave models, quantities, graphs and transfer 10(a)–(f)
Check this idea
Misconception: A progressive wave carries particles from source to receiver.
Repair: Particles of a mechanical medium oscillate about equilibrium; the disturbance and energy progress without net matter transfer.
Check this idea
Misconception: Horizontal crest spacing always represents wavelength.
Repair: It is wavelength only on a displacement–position graph at one instant. On a displacement–time graph at one position, crest spacing is period.
worked example
3. Follow seven worked models
Follow how each solution fixes the graph type, energy-spreading model, transmission axis, boundary condition, path difference or aperture before calculating.
Wave models, quantities, graphs and transfer 10(a)–(f)
Model 1
Two points 0.15 m apart on a 0.60 m wavelength are compared at one instant. Find their phase difference. If frequency is 12 Hz, derive and find wave speed.
Check the model response
Δφ = 2πΔx/λ = 2π(0.15/0.60) = π/2 rad. In one period T, a crest advances one wavelength λ, so v = λ/T = fλ = 12(0.60) = 7.2 m s⁻¹.
guided practice
4. Guided practice
Use each hint only to select the graph interval, spreading surface, polarisation reference, mode shape, interference condition or aperture equation.
Wave models, quantities, graphs and transfer 10(a)–(f)
Question 1
A longitudinal wave has compression spacing 0.45 m and frequency 800 Hz. Find speed and the phase difference between points 0.15 m apart, then state how to sketch its spatial graph.
Hint: Successive compressions are one wavelength apart; phase uses 2πΔx/λ.
Check the model response
v = fλ = 800(0.45) = 360 m s⁻¹. Δφ = 2π(0.15/0.45) = 2π/3 rad. A displacement graph still plots signed particle displacement against position; compressions are represented through particle crowding or pressure, not by calling the wave transverse.
independent practice
5. Independent practice
Solve without repair notes and state the graph, source, boundary, coherence and aperture assumptions used.
Wave models, quantities, graphs and transfer 10(a)–(f)
Question 1
A wave travels 18 m in 0.060 s and has wavelength 0.75 m. Find speed, frequency and period. Explain why the medium has no net displacement after many cycles.
Check the model response
v = 18/0.060 = 300 m s⁻¹, f = v/λ = 400 Hz and T = 1/f = 2.50 ms. Medium particles oscillate about fixed equilibrium positions, so their cycle-average displacement is zero even though the wave transfers energy.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Wave models, quantities, graphs and transfer 10(a)–(f)
Question 1
Define amplitude, phase difference and wavelength. A 25 Hz progressive wave has wavelength 1.60 m; derive v = fλ, find speed, distinguish its time and space graphs, and explain energy transfer without matter transfer.
Check the model response
Amplitude is maximum displacement from equilibrium; phase difference is relative position within a cycle; wavelength is shortest distance between points in phase. A crest travels λ in T, so v = λ/T = fλ = 40.0 m s⁻¹. A time graph at one position gives period; a spatial graph at one instant gives wavelength. Medium particles oscillate locally while energy propagates.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Wave models, quantities, graphs and transfer 10(a)–(f)
Question 1
A time trace repeats every 4.0 ms and the corresponding spatial profile repeats every 1.20 m. Find frequency, speed and phase difference for a 0.30 m separation.
Check the model response
T = 4.0 ms gives f = 250 Hz. v = fλ = 300 m s⁻¹. Δφ = 2π(0.30/1.20) = π/2 rad.