Bass Reflex Port

A Helmholtz resonator

Blow across a bottle and it sings at one pitch. The plug of air in the neck is a mass; the air inside is a spring. A reflex enclosure is the same device, tuned so the port takes over from the cone at the bottom of its range:

Solving for the length, with $A_p$ the total port area:

The moving air extends a little beyond each end of the tube. The end correction $k\,d$ removes that from the physical length: 0.425 $d$ for an end flush with a panel and 0.307 $d$ for an end hanging free inside the box.

Air speed

At tuning the port moves roughly the volume the cone would. The peak velocity estimate is

Keeping it below about 5% of the speed of sound (17 m/s) avoids turbulence noise. Richard Small's rule of thumb for the smallest clean diameter, in metres with $V_d = S_d X_{max}$ in cubic metres, is

The trade-off

A wider port is quieter but must be longer, and a long tube has its own organ-pipe resonance at $c/2L$ that can colour the midrange. Flaring both ends lets a narrower port run cleanly. If no port fits, a passive radiator does the same job without the tube.

References

1. A. N. Thiele, “Loudspeakers in Vented Boxes,” Proc. IRE Australia, vol. 22, no. 8, pp. 487–508, 1961. Reprinted J. Audio Eng. Soc., vol. 19, nos. 5–6, 1971. AES, part 1· AES, part 2
2. R. H. Small, “Direct-Radiator Loudspeaker System Analysis,” J. Audio Eng. Soc., vol. 20, no. 5, pp. 383–395, 1972. AES