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Waves & Optics · Physics

Standing waves come from interference of equal-frequency waves.

Learn how boundary conditions create nodes and antinodes, and how harmonics label the allowed patterns (normal modes).

This topic

Standing Waves

Build the pattern logic first, then connect it to harmonics and mode counting.

Formation
Formation of standing waves
A standing wave is a stable spatial pattern created by superposition, typically from an incident and reflected wave of the same frequency.
  • Opposite-traveling waves idea
  • Why the pattern appears “fixed”
  • Where energy flows (and where it doesn’t)
  • Common misconceptions (it is still dynamic)
Start nano-lesson Superposition creates the pattern.
Constraints
Boundary conditions
Boundaries restrict how a wave can move. These restrictions determine which wavelengths “fit” and therefore which standing waves are possible.
  • Fixed vs free ends (conceptual)
  • What “fits” means physically
  • Allowed wavelengths on a segment
  • How reflections enforce conditions
Start nano-lesson Boundaries choose the wavelengths.
Features
Nodes and antinodes
Nodes are points of zero displacement amplitude; antinodes are points of maximum displacement amplitude. They define the geometry of the mode.
  • Node meaning and identification
  • Antinode meaning and identification
  • Spacing relationships (conceptual)
  • How amplitude varies in space
Start nano-lesson Mark nodes first; the rest follows.
Modes
Harmonics and normal modes
Normal modes are the allowed standing wave patterns. Harmonics label them in order: fundamental, second harmonic, and so on.
  • Fundamental vs higher modes
  • Mode number and pattern complexity
  • Frequency relationships (qualitative)
  • Connecting modes to resonance
Start nano-lesson Modes are “allowed patterns.”
Practice
Practice & Exercises
Practice sketching modes, counting nodes/antinodes, and connecting boundaries to allowed patterns.
  • Mode sketching from boundary descriptions
  • Node/antinode identification drills
  • “Which wavelengths fit?” reasoning
  • Harmonic labeling and interpretation
  • Exam-style standing wave sets
Open practice Draw the boundary condition first.