Waves and Oscillations

Everything Oscillates

Oscillation is one of the most universal phenomena in nature. Atoms vibrate. Strings resonate. Ocean waves travel. Sound propagates through air. Light is an oscillating electromagnetic field. Quantum particles are described by wavefunctions. Understanding oscillations and waves is not just useful — it is essential.

Simple Harmonic Motion Revisited

This course begins where Classical Mechanics left off: with simple harmonic motion. A mass on a spring, a simple pendulum at small angles, an electrical LC circuit — all obey the same equation. You will solve it analytically and understand the role of frequency, amplitude, and phase.

Damped and Driven Oscillations

Real oscillators lose energy to friction and air resistance. Damped oscillations eventually come to rest. Driven oscillators respond to an external periodic force. When the driving frequency matches the natural frequency, resonance occurs: energy builds up dramatically in the system. Resonance is beautiful and dangerous — it can shatter a wine glass or collapse a bridge.

Wave Motion

A wave is a pattern that moves through a medium without the medium itself translating. Sound is a pressure wave through air. Water waves involve surface motion. Waves on a string carry energy from one end to the other. You will learn to describe waves mathematically using the wave equation.

Superposition and Interference

Two waves can occupy the same space simultaneously, and their amplitudes add. This is the principle of superposition. When waves add constructively, the amplitude grows. When they add destructively, they cancel. Interference is responsible for the colorful patterns in thin films, the dark and bright bands in Young's double-slit experiment, and the noise-canceling in headphones.

Standing Waves and Resonance

When a wave reflects back and forth in a bounded region, standing waves form. These are the modes of a vibrating string, a pipe organ, a microwave cavity. Only specific frequencies are allowed — those whose wavelength fits the boundary conditions. These resonant frequencies are why musical instruments produce specific pitches.

Sound and the Doppler Effect

Sound is a longitudinal pressure wave. Intensity, frequency, pitch, and the decibel scale are all explored here. When a source or observer moves relative to the medium, the observed frequency changes: this is the Doppler effect. It explains ambulance sirens, radar guns, and the redshift of distant galaxies.