Deep Physics: Waves and Oscillations for Talented High Schoolers, Princeton
Real waves and oscillations, taught from the simple harmonic oscillator up through standing waves, interference, and resonance. For talented high schoolers.
A World Through the Lens of Waves and Oscillations
Anything that can vibrate, will. Anything that can carry a wave, does. The everyday world is full of motion that swings, ripples, and rings.
Push a child on a swing once a second. If your timing matches the swing’s natural rhythm, it climbs higher every push. Mismatch the timing and the swing dies. The energy you supply is the same. Only the timing changed.
Pluck a guitar string. It does not produce one frequency. It produces an entire harmonic series, a fundamental and its overtones, all from one motion. The shape of the string decides which frequencies survive.
Drop two stones into still water. The two ripples pass straight through each other. They emerge unchanged on the other side, as if neither had ever met the other.
Stand by a doorway. You hear someone speaking in the next room before you can see them. Sound bends around the door’s edge. Light, with a much shorter wavelength, barely bends at all.
All four phenomena share a single mathematical structure. A restoring force gives every oscillator the same equation of motion. A wave equation governs every linear wave: mechanical, acoustic, electromagnetic, quantum. Superposition makes them add. With these tools, you have the language in which every wave in physics is written.
This course teaches you what physicists actually know about it. From first principles.
You will:
- Derive the period of a simple harmonic oscillator from a single physical principle: a restoring force proportional to displacement.
- Add two waves and predict, point by point, where they reinforce and where they cancel.
- Find the standing-wave modes of a stretched string and an open or closed pipe from boundary conditions alone.
- Predict the speed of a wave from the physical properties of the medium it travels through.
By the end, you will think about oscillation, wave, and resonance the way a physicist thinks about them.
What You Will Actually Understand
By the end of the course, you will understand six core ideas of waves and oscillations.
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 and the equation of motion they generate. Period, frequency, amplitude, and phase. Energy stored in the oscillation, traded between kinetic and potential, and conserved across the cycle.
2. Damped and Driven Oscillations
What friction does, and what a periodic push can undo. Damping that drains energy from each cycle. External periodic forcing that pumps it back in. Resonance: the special frequency at which a small steady drive produces a large response. The quality factor as a measure of how sharp that response is.
3. Mechanical Waves
How a disturbance travels without the medium going anywhere. Transverse and longitudinal waves. Wavelength, frequency, period, and wave speed, with the relation among them. The wave equation, derived for a stretched string, and the discovery that the same form fits sound, water, and light.
4. Superposition and Interference
Two waves passing through each other, point by point. Linearity and the superposition principle. Constructive and destructive interference. Beats from two slightly different frequencies. The two-slit pattern: a single calculation that gives a striking prediction.
5. Standing Waves and Normal Modes
Why a string of fixed length sings in only certain notes. Boundary conditions on strings, open pipes, and closed pipes. The discrete spectrum of allowed modes. Fundamental and overtones. Resonant frequencies set by geometry alone, the bridge from continuous waves to quantized spectra.
6. Reflection, Refraction, and Diffraction
Why waves bend at boundaries and around obstacles. Wavefronts and Huygens’ principle. Reflection at an interface. Refraction and Snell’s law from a change in wave speed. Diffraction at an opening, where the size of the opening relative to the wavelength decides what you see.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort. The destination, a working understanding of oscillations and waves from the simple harmonic oscillator through standing waves and diffraction, stays the same.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and transcripts apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Waves and Oscillations is one of eight semester-long physics courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ.
Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Optics and atomic structure. Special Relativity. Quantum mechanics.
The Lyceum is built on the Deep Physics methodology.