Helmholtz's Bottle

Plate 87 speaks for itself: “A bottle hums one note.”

The Physics

Blow across a bottle and the air in its neck bounces like a mass on the spring of the air inside. This one resonance sets the note.

f = (c / 2π) √(A / (V L_eff))

• f: resonant frequency, Hz
• c: speed of sound, m s⁻¹
• A: neck cross-section, m²
• V: cavity volume, m³
• L_eff: effective neck length, m

The air in the neck moves like a mass on a spring. c = 343 m/s.

Sources

• H. von Helmholtz, On the Sensations of Tone (1863).

On the poster

Plate 087, “Helmholtz's Bottle”: the pixel-art plate with its slogan “A bottle hums one note.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.