Waves and Oscillations
Real waves and oscillations for talented high schoolers.
Online from anywhere · or in-person in Princeton, NJ
A World Through the Lens of Waves and Oscillations
Waves and Oscillations is one of the six classical core courses of the Physics Lyceum: High School curriculum, taught on the Deep Physics model that runs through the whole SoTS Physics Lyceum.
The course runs on theory, problem-solving sessions, homework, and practical laboratory work. The Lyceum provides the equipment, and tuition covers it.
1. Simple Harmonic Motion
The cleanest oscillator in physics, and the model for everything else. The mass on a spring. The simple pendulum at small angles. Restoring forces, period, frequency, amplitude, and phase. Energy traded between kinetic and potential, conserved across the cycle. The universality of SHM: every system near a stable equilibrium behaves as one.
2. Damped, Driven, and Nonlinear Oscillations
What friction does, what a periodic push can undo, and what happens past the linear regime. Damped oscillations, resonance, and the quality factor. The step past linearity into anharmonic, parametric, and self-oscillations: where the clean sine wave breaks down and what replaces it. The bridge from textbook oscillators to the ones that turn up in the real world.
3. Mechanical Waves and the Wave Equation
How a disturbance travels without the medium going anywhere. Transverse and longitudinal waves. The wave equation as the shape that every traveling disturbance obeys. Wave speed predicted from the properties of the medium. Wave energy and impedance at boundaries: what passes through, what reflects.
4. Superposition, Interference, and Fourier Analysis
How waves combine, and how any periodic motion decomposes. Linearity and the superposition principle. Constructive and destructive interference, beats, the double-slit experiment. Fourier decomposition: any periodic motion as a sum of normal modes.
5. Standing Waves and Normal Modes
Why a string of fixed length sings in only certain notes. Standing waves built from counter-propagating traveling waves. Boundary conditions, the discrete spectrum of allowed modes, fundamental and overtones. The first appearance of an eigenvalue problem: a linear operator (the wave equation with boundary conditions) admits only a discrete set of solutions.
6. Refraction, Diffraction, Doppler, and Dispersion
What waves do at obstacles, when the source moves, and when the medium is choosy. Wavefronts and Huygens’ principle. Refraction and Snell’s law from a change in wave speed alone. Diffraction at apertures. The Doppler effect. Dispersion: when different frequencies travel at different speeds, and how a steady wave turns into a moving packet. Polarization of transverse waves.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.