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Waves are one of the most important concepts in physics. They transfer energy without transferring matter, and their behaviour underpins everything from sound and light to quantum mechanics. This topic covers progressive and stationary waves, the electromagnetic spectrum, refraction, diffraction, interference, and polarisation.
A progressive (or travelling) wave carries energy from one place to another. Key terminology:
Key Definition: Amplitude (A) — the maximum displacement of a particle from its equilibrium position.
Key Definition: Wavelength (λ) — the minimum distance between two points oscillating in phase (e.g. crest to crest).
Key Definition: Frequency (f) — the number of complete oscillations per second, measured in hertz (Hz).
Only transverse waves can be polarised.
All electromagnetic (EM) waves are transverse, travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum, and consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.
| Region | Approximate Wavelength | Approximate Frequency | Typical Source |
|---|---|---|---|
| Radio waves | > 0.1 m | < 3 GHz | Oscillating circuits |
| Microwaves | 1 mm – 0.1 m | 3 GHz – 300 GHz | Magnetron |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz | Hot objects |
| Visible light | 400 nm – 700 nm | 430 THz – 750 THz | Very hot objects, LEDs |
| Ultraviolet | 10 nm – 400 nm | 750 THz – 30 PHz | The Sun, UV lamps |
| X-rays | 0.01 nm – 10 nm | 30 PHz – 30 EHz | X-ray tubes |
| Gamma rays | < 0.01 nm | > 30 EHz | Nuclear decay |
All EM waves obey c = fλ. The visible spectrum runs from red (~700 nm) to violet (~400 nm).
Exam Tip: You may be asked to identify a type of EM radiation from its wavelength or frequency. Memorise the approximate boundaries. Also know typical applications: radio for broadcasting, microwaves for cooking and satellite communication, infrared for thermal imaging and remote controls, UV for sterilisation, X-rays for medical imaging, gamma rays for cancer treatment and sterilisation.
Two points on a wave (or two waves) may oscillate with a phase difference, measured in degrees or radians.
Key Definition: Phase difference is the fraction of a cycle by which one oscillation leads or lags another.
| Phase difference | Relationship |
|---|---|
| 0° (0 rad) | In phase — oscillate together |
| 90° (π/2 rad) | Quarter of a cycle apart |
| 180° (π rad) | In antiphase — exactly opposite |
| 360° (2π rad) | In phase again (one full cycle) |
Phase difference in radians can be calculated from path difference:
Δφ = (2π / λ) × Δx
where Δx is the path difference between the two waves.
Key Definition: The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.
This principle leads to interference and the formation of stationary waves.
Polarisation is the restriction of the oscillations of a transverse wave to a single plane. An unpolarised wave oscillates in all planes perpendicular to the direction of travel. A polarising filter (Polaroid) transmits only oscillations in one particular plane.
Evidence that light is transverse: If light were longitudinal, it could not be polarised. The fact that polarising filters reduce the intensity of light confirms its transverse nature.
When polarised light of intensity I₀ passes through a second polarising filter (the analyser) at angle θ to the transmission axis:
I = I₀ cos²θ
At θ = 0°, all light is transmitted (I = I₀). At θ = 90°, no light is transmitted (I = 0). For unpolarised light passing through a single polariser, the transmitted intensity is I₀/2.
A stationary wave is formed when two progressive waves of the same frequency, wavelength, and amplitude travel in opposite directions and superpose. Unlike progressive waves, stationary waves do not transfer energy.
Key features:
For a string fixed at both ends, the fundamental mode (first harmonic) has one antinode and two nodes (at the ends). The frequency of the first harmonic is:
f₁ = 1/(2L) × √(T/μ)
where L is the length of the string, T is the tension, and μ is the mass per unit length. Higher harmonics occur at integer multiples of f₁ (i.e. f₂ = 2f₁, f₃ = 3f₁, etc.).
Closed pipe (closed at one end, open at the other):
Open pipe (open at both ends):
Described diagram — Harmonics in a closed pipe: The first harmonic shows a quarter-wave pattern: a node at the closed end and an antinode at the open end. The third harmonic shows three-quarters of a wave fitting in the pipe (one and a half quarter-waves), with two nodes and two antinodes. The fifth harmonic fits five quarter-waves.
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