16 Superposition and Standing Waves Superposition of Waves

16 Superposition and Standing Waves • Superposition of Waves • Standing Waves • Additional: Superposition of Standing Waves, Harmonic Analysis & Synthesis • Hk: 1, 29, 33, 47, 51.

Superposition Principle

Terminology • Phase Difference: The fractional part of a period which represents the offset in peak positions of waves. • Coherence: The existence of a correlation between the phases of two or more waves such that interference effects can be observed. • Interference: The variation with distance or time of the amplitude of a wave which results from the superposition of two or more waves.

Interference • Constructive Interference: Resultant amplitude is larger than either individual wave. • Destructive Interference: Resultant amplitude is less than either individual wave.

Examples Constructive Interference: Destructive Interference:

Phase Difference

Constructive Interference

Standing Waves …a wave in which the amplitude at a given location does not vary with time. Standing Wave Features: • Amplitude is zero at fixed ends • Nodes (other places with zero amplitude) • Anti-nodes (places with maximum amplitude)

Standing Wave: Both Ends Fixed

Standing Wave: One End Fixed, One End Free

fourier analysis

Summary • Superposition results in interference • Interference can occur due to Path Difference • Standing Waves, and conditions for • Harmonics and Fourier Analysis • /