mfe-waveslisted

# Waves ## Summary **Waves** (Part II: Hearing) Chapters: 4, 5, 6, 7 Plane Position: (-0.4, 0) radius 0.4 Primitives: 50 Periodic phenomena and frequency analysis. How repetition creates structure — from simple oscillation to Fourier decomposition. **Key Concepts:** Simple Harmonic Motion, Frequency, Wave Function, Superposition Principle, Wave Equation ## Key Primitives **Simple Harmonic Motion** (definition): Simple harmonic motion (SHM) is periodic motion where the restoring force is proportional to displacement: F = -kx. The solution is x(t) = A*cos(omega*t + phi) where omega = sqrt(k/m). - modeling back-and-forth motion of a pendulum or spring - any system with a linear restoring force proportional to displacement **Frequency** (definition): The frequency f of a periodic phenomenon is the number of complete cycles per unit time. f = 1/T where T is the period. Measured in hertz (Hz = cycles/second). - determining how many oscillations occur per second - relating pitch of a sound to its physical frequency **Wave Function** (definition): The general sinusoidal wave function is y(x,t) = A*sin(kx - omega*t + phi), describing a traveling wave with amplitude A, wave number k, angular frequency omega, and phase offset phi. - describing a sinusoidal disturbance propagating through a medium - modeling light, sound, or any traveling periodic signal **Superposition Principle** (theorem): For linear systems, the net response at a given point caused by two or mo