Port Tuning Frequency (Fb) Bass Reflex Box Tuning Frequency (Fb)

What port tuning frequency (Fb) is

Port tuning frequency, written Fb, is the frequency at which the air mass in a bass reflex port resonates against the air trapped in the cabinet. This is Helmholtz resonance, the same physics that makes a bottle hum when you blow across its neck. At Fb the port delivers nearly all of the system's output while the woofer cone barely moves, which is why a vented box can play deeper and louder than a sealed box of the same size. Albert Thuras of Bell Telephone Laboratories filed a vented-enclosure patent (US 1,869,178) on August 15, 1930, which was granted on July 26, 1932. It describes an enclosed diaphragm whose rear-wave sound is reinforced through a passage of tuned air mass.

Fb is not the driver's free-air resonance (Fs), and it is not the -3 dB point (f3). A designer picks Fb from the driver's Thiele-Small parameters through a tuning ratio H, where Fb = H x Fs. A sealed box has no port, so it has no Fb.

How Fb is calculated

Three dimensions set the tuning: internal box volume (Vb), port cross-section area (Sp) and port length (Lp). Raising Vb lowers Fb. Widening the port forces it to be longer to hold the same Fb. Audio Judgement's design formula for a round port, with dimensions in inches, is Lv = (14,630,000 x R²) / (Fb² x Vb) - 1.463 x R. The 14,630,000 constant implies a speed of sound near 344 m/s, and the 1.463 x R term is the end correction. Wikipedia's Helmholtz page uses a different end correction, Leq = Ln + 0.3 D, so published tables disagree by a hertz or two.

Worked example: an 8-inch woofer

Audio Judgement's example driver has Fs = 47 Hz, Qts = 0.52 and Vas = 7.86 L, in an SQB3 alignment. The table gives H = 0.8116, a box ratio of 0.1971 and f3/Fs = 0.6835. That makes Vb = 7.86 / 0.1971 = 39.88 L (2,433.63 in³), Fb = 0.8116 x 47 = 38.14 Hz and f3 = 0.6835 x 47 = 32.12 Hz. With a 4 in port (radius 2 in), Fb² = 1,454.66, so Lv = (14,630,000 x 4) / (1,454.66 x 2,433.63) - 1.463 x 2 = 16.53 - 2.93 = 13.6 in.

As a cross-check, a 4 in round port has an area of 0.00811 m². A Helmholtz calculation with c = 344 m/s and the 1.463 x R end correction returns 38.2 Hz. Swapping in the 0.3 D end correction moves the answer to 40.3 Hz, a 2 Hz shift on a 38 Hz tune. That gap is why builders measure the impedance curve of the finished box instead of trusting the formula alone.

What happens around Fb

Below Fb the port and the driver move out of phase and partly cancel. Each falls at 12 dB per octave by itself, so their sum falls at 24 dB per octave, the fourth-order response of a vented box (audioXpress). In audioXpress's fourth-order Butterworth example with f3 = 100 Hz, port air velocity peaks at 87 Hz (0.872 x f3) and cone displacement peaks at 143 Hz (1.432 x f3), where the port is 3.63 dB and the driver 5.86 dB below mid-band level. Cone displacement then rises sharply below f3, so high-powered vented systems are often protected by a high-pass filter at the tuning frequency (Wikipedia). See infrasonic filter.

Port velocity, the limit on a low Fb

A low Fb needs a long port, and a long port needs a wide opening or the air inside moves too fast. Fast air through the opening makes turbulence, heard as wheezing called chuffing. SpeakerDesign.dev puts the target below 17 m/s, roughly 5% of the speed of sound, at maximum amplifier power. A 4 in round port (0.00811 m²) at 17 m/s passes at most about 0.138 m³/s, or 138 L/s. A 2 in port has a quarter of the area and a quarter of that ceiling, about 34 L/s. The cone must displace the same volume either way, so the narrow port fits the cabinet but chuffs first.

Port tuning vs a sealed box

A sealed box with a Qtc of 0.707 gives a flat response with good transients. A vented box adds a second resonance, and the interaction leaves less damping and more group delay: the bass arrives as a resonant tail behind the main body of the sound (Wikipedia). Ported alignments also punish errors. Audio Judgement notes that a small misalignment, such as box leakage that differs from the assumed QL of 7, can cause notable bass boosts or cuts and transient ringing. Our sealed vs ported subwoofer entry compares output and extension, and subwoofer group delay covers the timing cost.

Choosing Fb for movies

ITU-R BS.775-4 says the LFE channel should be capable of handling signals in the range of 20 to 120 Hz, so tunings such as Hsu's 18 Hz and 22 Hz sit at or just around the bottom of that band. A tune far below the lowest program content spends port length and cabinet volume on frequencies the mix rarely contains. A tune above it leaves the bottom octave to the 24 dB per octave roll-off. Because Fb moves with port length, a higher Fb also means a shorter port for the same port area.

Where Fb shows up in real subwoofers

Hsu Research's VTF-3 MK5 HP uses a 15 in woofer and lists a hybrid tuning of 18 Hz ported, 22 Hz ported or sealed. Hsu rates low-end extension (+/- 2 dB) at 17 Hz with one port open and 22 Hz with two ports open, publishes separate response curves for each case, and quotes a Q control range of 0.3 to 0.7 with a 24 dB per octave crossover. Amplifier power is listed as 2,000 W short term and 600 W continuous. For how tuning interacts with room size and multiple subs, see how to choose a subwoofer and dual subwoofers. Treat a tuning number as the manufacturer's nominal value unless it comes with a measured impedance curve.