Ported Box - Helmholtz Resonance

This is the truth page behind the port calculators. Use it when the numbers look suspicious and you need to confirm how box volume, port area, tuning frequency, and effective length are interacting.

Tiny Version

This is the rule for how the box and helper tunnel sing together.

Builder Version

Calculators are faster. This page is the backstop when you need to confirm the math and make sure the result still agrees with the corrected installer example.

Unit Discipline

Keep one unit system through the actual calculation. The example below uses SI inside the equation, then translates back to inches for the final physical port length.

Core Relationship

F_b = (c / (2 x pi)) x sqrt(S_p / (V_b x L_eff))

L_eff = L_physical + end corrections

Effective length includes the extra air-end behavior at the port ends. Physical length is the actual tube you cut.

Worked Example

Box volume: 2.0 ft^3 = 56.6 L = 0.0566 m^3
Target tuning: 35 Hz
Port: 4-inch round port, area about 12.57 in^2 = 0.00811 m^2

35 = (343 / (2 x pi)) x sqrt(0.00811 / (0.0566 x L_eff))
L_eff = 0.348 m = 13.7 in
L_physical = 13.7 - 2.59 - 2.59 = 8.5 in

Result: about 8.5 inches physical length for a 4-inch round port in a 2.0 ft^3 box tuned to 35 Hz. This matches the corrected installer-level sanity check.

Why Physical Length Is Shorter

The air at the port ends behaves like part of the resonant system, so the effective length is longer than the actual tube you cut.

Port Velocity Sanity Check

V_port = (S_d x X_max x F_b) / S_p

Using a typical 12-inch subwoofer with S_d = 480 cm^2, X_max = 12 mm, F_b = 35 Hz, and S_p = 81 cm^2 gives about 2.49 m/s, which is comfortably below the rough 30 m/s port-noise guideline.