Key Concepts: Standing Waves & Resonance

Standing Waves

• Formed when two identical waves travel in opposite directions and interfere.
• They have nodes (zero displacement) and antinodes (maximum displacement) at fixed positions.
• Energy oscillates between kinetic and potential forms but does not propagate — the wave pattern stands still.

Harmonics

• Fundamental (1st harmonic): Lowest frequency; L = λ/2 (string fixed at both ends).
• 2nd harmonic: L = λ. nth harmonic: L = nλ/2.
• f_n = nf₁ = nv/(2L) for a string fixed at both ends.

Resonance

• Resonance occurs when a system is driven at its natural frequency — amplitude increases dramatically.
• Examples: pushing a swing at the right frequency, a wine glass shattering from a matching sound wave.