Ported Box — Helmholtz Resonance

Tuning frequency:

F_b = (c / 2π) × √(S_p / (V_b × L_eff))

Effective port length:

L_eff = L_physical + k₁ × √(S_p) + k₂ × √(S_p)

Where: - k₁ = 0.732 (outer end, open) - k₂ = 0.732 (inner end, if chamfered) or 0.850 (if square)

Solving for port length:

L_physical = (c² × S_p) / (4π² × F_b² × V_b) − correction_terms

[VISUAL PLACEHOLDER: PortLengthNomograph.png] Description: Graphical calculator — three axes: box volume, port area, tuning frequency — with lines showing port length at intersection

Worked example:

Box volume: 2.0 ft³ = 56.6L = 0.0566 m³ Target tuning: 35 Hz Port: 4" diameter round (area = π × 2² = 12.57 in² = 0.00811 m²)

F_b = (343 / 2π) × √(0.00811 / (0.0566 × L_eff))

Solving for L_eff:

35 = 54.6 × √(0.1432 / L_eff)
35 / 54.6 = √(0.1432 / L_eff)
0.641 = √(0.1432 / L_eff)
0.411 = 0.1432 / L_eff
L_eff = 0.1432 / 0.411 = 0.348 m = 13.7 in

Subtract end corrections:

L_physical = 13.7 − (0.732 × √(12.57)) − (0.732 × √(12.57))
L_physical = 13.7 − 2.59 − 2.59 = 8.5 inches

Port length: 8.5 inches for a 4" round port in a 2 ft³ box tuned to 35 Hz.

Verify port velocity (at rated power):

V_port = (S_d × X_max × F_b) / S_p

If Sd = 90 cm², Xmax = 12mm, Fb = 35 Hz, Sp = 12.57 in² = 81 cm²:

V_port = (90 × 0.012 × 35) / 81 = 0.47 m/s

Well below 30 m/s limit — no port noise.