440 Hz precision whistle

A 3D-printed whistle tuned to musical A — designed from acoustic first principles.

A Helmholtz-resonator whistle whose cavity dimensions were calculated, not guessed. Target frequency 440 Hz (concert A), printed in PETG, verified with a tuner. The case study walks through the resonator equation, the volume math, and the tweak that brought it back into tune after a first failed print.

Engineering details

Helmholtz frequency f = (c / 2π) · √(A / (V · L)), with c = 343 m/s. Solving for V at f = 440 Hz with neck area A = 12 mm² and effective neck length L = 8 mm gives V ≈ 11.5 cm³. The resonant cavity was modeled as a cylinder of Ø 28 mm × 19 mm height to match. The first print landed at 426 Hz; trimming the neck length by 0.6 mm corrected the pitch.