Wave Properties
Frequency, wavelength, amplitude, phase, wave speed, transverse vs longitudinal waves, and the Doppler effect.
Waves and Optics
Wave mechanics, interference, diffraction, polarisation, and geometrical optics — from sound to light to quantum probability waves.
Overview
Waves are periodic disturbances that transport energy without transporting matter. They appear throughout physics: mechanical waves in strings and air, electromagnetic waves (light, radio, X-rays), seismic waves, and quantum probability waves. Optics applies wave principles specifically to light, covering both the wave (physical optics) and ray (geometrical optics) descriptions.
Core Wave Concepts
The Wave Equation
The one-dimensional wave equation ∂²y/∂t² = v²∂²y/∂x² has sinusoidal solutions y(x,t) = A sin(kx − ωt + φ), where k = 2π/λ is the wave number, ω = 2π/T is the angular frequency, and v = ω/k is the phase velocity. The same equation governs sound, light, and — in a modified form — quantum wavefunctions.
Superposition and Interference
Waves obey the superposition principle: the total displacement is the sum of individual displacements. When two coherent waves overlap, they interfere: constructively when in phase (path difference = nλ) and destructively when out of phase (path difference = (n+½)λ). Young's double-slit experiment is the paradigmatic demonstration of wave interference.
Diffraction
Waves bend around obstacles and spread through apertures — diffraction. The single-slit pattern has a central maximum of width 2λL/a. Diffraction gratings with many slits produce sharp bright fringes and are used in spectroscopy. Fraunhofer diffraction describes the far-field pattern; Fresnel diffraction handles the near-field.
Standing Waves and Resonance
When two identical waves travel in opposite directions, they superpose to form a standing wave with fixed nodes and antinodes. A string fixed at both ends supports standing waves at f_n = nv/2L. Resonance occurs when a driving frequency matches a natural frequency — the basis of musical instruments, microwave cavities, and laser resonators.
Geometrical Optics
When wavelengths are much shorter than obstacles, light travels in straight rays. Snell's law n₁ sin θ₁ = n₂ sin θ₂ governs refraction. Total internal reflection occurs when θ > θ_c = arcsin(n₂/n₁) — exploited in optical fibres. Lenses and mirrors focus light via thin-lens equations: 1/f = 1/d_o + 1/d_i.
Learning Pathways
Wave Phenomena
Interference, diffraction, standing waves, resonance, polarisation, and geometrical optics.
Fourier and Coherence
Fourier analysis of waves, coherence and lasers, nonlinear optics, and wave-particle duality.
Key Articles
The Doppler Effect
Sound and light frequency shifts due to relative motion — from sirens to redshift.
Read →Standing Waves
Nodes, antinodes, harmonics, and why guitar strings sing.
Read →Fraunhofer vs Fresnel Diffraction
Far-field and near-field diffraction patterns and their practical applications.
Read →Brewster's Angle
Perfect polarisation by reflection and its use in photography and optics.
Read →Fourier Series in Physics
Decomposing any periodic signal into sinusoids — the most useful tool in wave physics.
Read →Sonic Booms
Mach cones, shock waves, and the physics of supersonic flight.
Read →Frequently Asked Questions
What is the wave equation?
∂²y/∂t² = v² ∂²y/∂x². Solutions are sinusoids propagating at speed v. The same form describes sound, light, and quantum wavefunctions.
What is the difference between constructive and destructive interference?
Constructive: waves in phase add amplitudes (path difference = nλ). Destructive: waves out of phase cancel (path difference = (n+½)λ).
What causes soap-bubble colours?
Thin-film interference: light from the front and back film surfaces travels slightly different paths, causing certain wavelengths to interfere constructively.
What is polarisation?
The orientation of a transverse wave's oscillation. Polarising filters transmit one orientation; used in LCDs, sunglasses, and optical communications.