Helmholtz Resonator Frequency Formula (With Flanged Neck End Correction)

Include the radiation mass end correction or your resonator will tune 20–30% too high!

A Helmholtz resonator behaves like a mechanical mass-spring oscillator: the air plug inside a cylindrical neck of radius r and physical length L acts as the oscillating mass, while the enclosed cavity volume V acts as an adiabatic air spring! Using raw physical neck length L in f = (c / (2*pi)) * SQRT(A / (V * L)) always overpredicts frequency because a hemispherical slug of air just outside BOTH ends of the neck co-oscillates with the plug!

For a neck with one flanged outer opening (+0.85*r) and one flanged/baffled inner opening (+0.85*r), acoustic effective length is L_eff = L + 1.7 * r (or L + 1.45*r for an unflanged pipe)! With speed of sound c = 343 m/s (20 °C air), neck radius r = 0.025 m (50 mm port, A = pi*r^2 = 0.0019635 m^2), physical neck L = 0.08 m (L_eff = 0.08 + 1.7*0.025 = 0.1225 m!), and cavity volume V = 0.004 m^3 (4 liters), the true Helmholtz frequency is 109.28 Hz—and quartering cavity volume to 1 liter doubles f_H to 218.56 Hz!

Helmholtz Resonant Frequency f_H with Double-Flanged End Correction (Hz)

Computes A_neck = PI() * r^2 and L_eff = L + 1.7 * r, then evaluates (c / (2*PI())) * SQRT(A_neck / (V * L_eff)).

=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 <= 0), "Invalid Resonator Geometry", ROUND((B2 / (2 * PI())) * SQRT((PI() * (B3 ^ 2)) / (B5 * (B4 + (1.7 * B3)))), 2))

Effective Acoustic Neck Length L_eff = L + 1.7 * r (Meters)

Adds Rayleigh's 2 * (8 / (3 * PI())) * r ≈ 1.7 * r double-flanged radiation end correction to physical neck length B4.

=IF(OR(B3 <= 0, B4 < 0), "Invalid Resonator Geometry", ROUND(B4 + (1.7 * B3), 4))

Further reading

• Microsoft Support — PI function