Normal Modes and Standing Waves
First published: 2016
Brief summary
OpenStax section on standing waves and resonance.
Article
Standing waves form when waves of the same frequency and amplitude travel in opposite directions and interfere. The resulting pattern has fixed nodes, where displacement remains zero, and antinodes, where the oscillation amplitude is greatest.
Boundary conditions restrict the wavelengths that can persist in a finite system. A string fixed at both ends must have nodes at both boundaries, so only wavelengths that fit an integer number of half-wavelengths along the string are allowed.
Each allowed pattern is a normal mode with a corresponding normal frequency. The lowest is the fundamental mode, and higher modes form a sequence of harmonics or overtones determined by the wave speed and system length.
Resonance occurs when a periodic driver matches a normal frequency and produces a large-amplitude standing wave. Similar behaviour occurs in strings, air columns, rods, buildings and many other systems with reflecting boundaries.
Source details and credits
- Source / publisher: OpenStax
- Source type: Textbook chapter
- URL type: WWW
- Credits: OpenStax
- URL: https://openstax.org/books/university-physics-volume-1/pages/16-6-standing-waves-and-resonance