Physics of Waves Course

Lesson 1 • What Is a Wave?

Defines waves as disturbances propagating through space and time. Distinguishes mechanical from electromagnetic waves and introduces the concept of energy transport.

Lesson 2 • Energy and Power in Waves

Quantifies energy transport using intensity and power expressions. Connects amplitude and frequency to the rate of energy flow.

Lesson 3 • Mathematical Description of Waves

Develops the sinusoidal wave function y(x,t) and the general wave equation. Provides the algebraic tools used throughout the course.

Lesson 4 • Wave Speed in Different Media

Relates wave speed to medium properties such as tension, density, and elasticity. Builds intuition for how material properties control propagation.

Lesson 1 • Stationary Waves on Strings

Derives stationary waves from two counter-propagating waves of equal frequency. Identifies nodes, antinodes, and harmonic mode shapes.

Lesson 2 • Constructive and Destructive Interference

Analyses conditions producing maximum and zero amplitude from two coherent sources. Links path-length difference to interference outcome.

Lesson 3 • Beats and Amplitude Modulation

Explains the beat phenomenon from two slightly different frequencies. Derives beat frequency and connects it to amplitude modulation in signals.

Lesson 4 • Phasors and Complex Notation

Introduces phasor representation to simplify superposition calculations. Provides the complex exponential form used in advanced wave analysis.

Lesson 1 • Snell's Law and Refraction

Derives Snell's law from wave speed differences across a boundary. Applies the law to predict bending direction and angle for any wave type.

Lesson 2 • Total Internal Reflection

Identifies the critical angle condition and evanescent wave behaviour. Explains practical applications such as waveguides and fibre optics principles.

Lesson 3 • Reflection at Boundaries

Examines wave reflection from fixed and free boundaries, including phase inversion. Derives reflection coefficients for amplitude and intensity.

Lesson 4 • Huygens' Principle

Uses Huygens' construction to predict wavefront evolution after obstacles and apertures. Provides the geometric foundation for diffraction analysis.

Lesson 1 • Driven Oscillations and Damping

Models forced oscillations with damping using the driven harmonic oscillator equation. Analyses amplitude and phase response as functions of driving frequency.

Lesson 2 • Stationary Waves in Pipes

Derives harmonic frequencies for open and closed pipes using boundary conditions. Connects pipe geometry to the harmonic series produced.

Lesson 3 • Vibrating Membranes and Plates

Extends stationary wave analysis to two-dimensional surfaces. Identifies nodal lines and mode shapes for circular and rectangular membranes.

Lesson 4 • Coupled Oscillators and Normal Modes

Analyses systems of coupled oscillators to find normal mode frequencies. Introduces the concept of mode splitting and energy exchange between coupled resonators.

Lesson 1 • Nature of Sound Waves

Describes sound as longitudinal pressure and displacement oscillations in a medium. Derives the speed of sound from bulk modulus and density.

Lesson 2 • Sound Intensity and Decibels

Defines sound intensity and the logarithmic decibel scale. Applies intensity calculations to source power, distance, and hearing thresholds.

Lesson 3 • The Doppler Effect

Derives observed frequency shifts for moving sources and observers. Extends the analysis to shock waves and the Mach number.

Lesson 4 • Room Acoustics and Reverberation

Introduces reverberation time and its dependence on room volume and absorption. Connects acoustic design principles to intelligibility and sound quality.

Lesson 1 • Maxwell's Equations and Wave Derivation

Derives the electromagnetic wave equation from Maxwell's four equations. Shows that the speed of light emerges from electric and magnetic constants.

Lesson 2 • Energy Transport and the Poynting Vector

Defines the Poynting vector as the directional energy flux of an EM wave. Derives radiation pressure and connects intensity to field amplitudes.

Lesson 3 • Properties of Plane EM Waves

Characterises the mutual perpendicularity of E, B, and propagation direction. Establishes the relationship between E and B amplitudes.

Lesson 4 • Polarisation of EM Waves

Classifies linear, circular, and elliptical polarisation states. Applies Malus's law and analyses polarisation by reflection and scattering.

Lesson 1 • Single-Slit Diffraction

Derives the single-slit intensity pattern using Huygens' principle and phasor summation. Identifies minima positions and the central maximum width.

Lesson 2 • Thin-Film Interference

Analyses constructive and destructive interference in thin transparent films. Accounts for phase shifts on reflection and optical path length differences.

Lesson 3 • Circular Apertures and Resolution Limits

Derives the Airy disk pattern for circular apertures. Applies the Rayleigh criterion to set resolution limits for optical instruments.

Lesson 4 • Double-Slit Interference and Diffraction

Combines double-slit interference with single-slit diffraction envelopes. Predicts missing orders and the full intensity pattern.

Lesson 1 • Dispersion and Group Velocity

Distinguishes phase velocity from group velocity in dispersive media. Derives the group velocity from the dispersion relation and analyses pulse spreading.

Lesson 2 • Introduction to Quantum Wave Mechanics

Connects classical wave concepts to the Schrödinger equation and de Broglie wavelength. Highlights wave-particle duality as an extension of classical wave physics.

Lesson 3 • Waves in Periodic Structures

Analyses wave propagation in periodic media using Bloch's theorem and band theory. Identifies pass bands, stop bands, and their physical origins.

Lesson 4 • Nonlinear Waves and Solitons

Introduces nonlinear wave equations and the balance between dispersion and nonlinearity. Describes soliton solutions and their stability properties.