Key Concepts: Resonance in Air Columns

Resonance in Tubes

Sound waves in tubes create standing waves at specific resonant frequencies.

Open Tube (both ends open)

• Antinodes at both ends. Supports all harmonics.
• f_n = nv/(2L), where n = 1, 2, 3, ...
• Fundamental wavelength: λ₁ = 2L.

Closed Tube (one end closed)

• Node at closed end, antinode at open end. Supports only odd harmonics.
• f_n = nv/(4L), where n = 1, 3, 5, ...
• Fundamental wavelength: λ₁ = 4L.

Applications

• Musical instruments: flutes (open), clarinets (effectively closed).
• Organ pipes produce different pitches based on length and whether they're open or closed.