Waves

Waves transfer energy without transferring matter. Understanding wave behaviour — including reflection, refraction, diffraction, interference, and the wave-particle duality — is essential for explaining phenomena from sound to light to quantum mechanics.

• Progressive waves — transverse (displacement perpendicular to propagation: light, electromagnetic) vs. longitudinal (displacement parallel to propagation: sound)
• Wave terms — amplitude, wavelength $\lambda$, frequency $f$, period $T = \frac{1}{f}$, wave speed $v = f\lambda$
• Phase and phase difference — in phase ($\Delta\phi = 0$ or $2\pi$), antiphase ($\Delta\phi = \pi$); path difference $\Delta x = \frac{\lambda \Delta\phi}{2\pi}$
• Electromagnetic spectrum — radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; all travel at $c = 3.0 \times 10^8\,\text{m/s}$ in a vacuum

• Principle of superposition — resultant displacement is the sum of individual displacements
• Constructive interference — path difference $= n\lambda$; amplitudes add
• Destructive interference — path difference $= (n + \frac{1}{2})\lambda$; amplitudes cancel
• Two-source interference — Young”s double slit: fringe spacing $\Delta y = \frac{\lambda D}{s}$; coherent sources required
• Diffraction gratings — $d\sin\theta = n\lambda$; calculating wavelength or grating spacing; resolving power
• Stationary (standing) waves — formed by superposition of two progressive waves travelling in opposite directions; nodes (zero amplitude) and antinodes (maximum amplitude); fundamental frequency and harmonics

• Snell’s law — $n_1 \sin\theta_1 = n_2 \sin\theta_2$; refractive index $n = \frac{c}{v}$
• Total internal reflection (TIR) — occurs when $\theta > \theta_c$ and light travels from a more dense to less dense medium; critical angle $\sin\theta_c = \frac{n_2}{n_1}$ ($n_1 > n_2$)
• Optical fibres — TIR in the core; cladding with lower refractive index; applications in communications and medicine; modal and material dispersion
• Lenses — converging and diverging; focal length, principal focus, magnification $m = \frac{v}{u}$; the lens equation $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Polarisation is evidence for the transverse nature of electromagnetic waves. Only transverse waves can be polarised — longitudinal waves (sound) cannot.

• Polarisation by reflection — light reflected from a non-metallic surface is partially polarised; the reflected light vibrates in one plane
• Polarising filters — transmit only one plane of vibration; rotating the filter varies the transmitted intensity from maximum to zero (when crossed at 90°)
• Malus’s law — $I = I_0 \cos^2\theta$, where $\theta$ is the angle between the polariser and the analyser
• Applications — sunglasses (reduce glare from reflective surfaces), LCD screens, stress analysis in engineering

1. Draw wave diagrams. Sketch displacement-distance and displacement-time graphs for transverse and longitudinal waves. Label amplitude, wavelength, and period.
2. Understand coherence. Interference requires coherent sources (constant phase relationship). In exams, always mention this when describing interference experiments.
3. Practise fringe spacing calculations. Young’s double slit and diffraction grating problems are standard exam fare. Know the derivations, not just the formulas.
4. Stationary vs. progressive waves. Be able to compare them: stationary waves store energy, progressive waves transfer energy; stationary waves have nodes, progressive waves do not.
5. For TIR problems. Always check two conditions: (1) light travels from more dense to less dense medium, AND (2) angle of incidence exceeds the critical angle.

Follow the sidebar order. Each page provides physical principles, derivations, worked examples with diagrams, and exam-style problems. Start with wave properties, then superposition and interference, then refraction and TIR.

This section provides comprehensive A-Level Physics content for Waves, covering all specification points with detailed explanations, worked examples, and practice questions.

Each page in this section includes:

• Definitions: Clear, precise explanations of key concepts
• Worked Examples: Step-by-step solutions with annotations
• Practice Questions: Multiple-choice and structured questions with mark schemes
• Common Pitfalls: Errors to avoid and how to fix them
• Exam Tips: Strategies for maximising marks in this topic

1. Read the introductory page to understand the topic overview
2. Work through each sub-topic in order
3. Attempt the practice questions before checking solutions
4. Use the flashcards to revise key terminology
5. Complete the diagnostic test to identify remaining gaps

• Core definitions and principles
• Application to examination-style questions
• Links to related topics across the specification
• Assessment objective alignment (AO1, AO2, AO3)

• Active Recall: Test yourself regularly rather than re-reading notes
• Spaced Practice: Revisit this topic at increasing intervals
• Interleaving: Mix with other topics during revision sessions
• Elaboration: Explain concepts in your own words

Focus on command word interpretation and mark scheme analysis. Practice timing yourself on questions to build speed and accuracy. Review examiner reports for this topic to understand common student errors.

The universe operates through fundamental forces and energy transfers. Forces are pushes and pulls that change motion, energy is the currency that drives all processes, and waves transfer energy without transferring matter. These principles connect seemingly different phenomena - from the orbit of planets to the vibration of atoms - under unified explanations that reveal the elegant simplicity underlying nature’s complexity.

• Mechanics
• Waves
• Electricity
• Fields