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How bass reflex cabinets work - a short explanation by David Haigner: You know the effect of producing a tone by blowing across the opening of a bottle. For larger bottles and longer necks, the tone lowers in frequency. That's the Helmholtz resonator in action (abbreviated: HR). Here's an easy physical comparison to our bass reflex speaker box. The volume inside the port pipe (bottle neck) is a hydraulic mass. The main volume of the bottle presents the compliance (spring). Now set the hydraulic mass into vibration and it will resonate like any spring-suspended mass.

From this it is obvious that larger masses (longer air pipes) and larger enclosures (higher compliances) will resonate at lower frequencies. But there is another nasty and less intuitive fact. If you widen the neck (which also increases the air mass in the duct), the HR frequency goes up! Why? Well, it is a hydraulic mass. This means cross section is important, e.g. the wider cross section of a duct displaces more air volume at some excursion than a smaller-size duct, port or bottle neck. More moving air volume means more compression of the main volume, which translates into higher internal pressure and results in a stiffer compliance. This again gives a higher HR frequency. And the higher mass of the wider duct is compensated because the internal pressure produces a higher force on a larger duct area (F=p*Area).

Now to the bass reflex cabinet. The front wave of our transducer is 180° out of phase with its back wave. The cabinet prevents the cancellation of in/out-of-phase emissions at low frequencies. If we make a hole into the cabinet with our reflex port, doesn't that produce phase interference with the front wave again? Yes, but only partially. To get a picture of it, imagine your hand holding a rubber string (spring). Now attach a mass on the other end of the compliant string and start to move your hand slowly up and down. The mass will follow your movement with the same amplitude. If you now accelerate the up-and-down frequency slowly, the mass will follow with increasing phase lag while the frequency of your movement increases.

At a certain frequency, the amplitude gets larger and larger and the phase lag becomes 180 degrees. The mass now moves in the opposite direction of your hand and the excursion is large even if you hardly move your hand. That's resonance. With further increased frequency, the phase lag progresses towards 360 degrees and the mass will move less and less. In this example, the moving mass becomes the duct (our hydraulic air mass again), your hand transforms into the transducer and the compliant rubber string is the cabinet volume.

Now we have arrived at the reflex enclosure. The 180° phase shift of the box/port tuning radiates the driver's rear wave just in phase with the front wave to add overall output at this frequency and somewhat around it. At much lower frequencies, there is no phase lag however. Here the port output cancels the front wave again (reflex cabinets fade out at 24dB/octave in their lowest frequencies, sealed boxes at 12dB/oct). At frequencies much above the Helmholtz resonance, there again is phase cancellation but now it is hardly noticable because of the much decreased port output.

Design issues: A typical reflex design sets the port resonance somewhat lower than the closed-box resonant frequency to compensate for its falling LF response. A small enclosure needs a long, narrow pipe to create a low Helmholtz frequency. This means a high hydraulic mass, which results in a slow resonator 'slew rate'. This is why a low-tuned small reflex cabinet follows the signal very slowly in the HR's range, producing long group delay times (typically a 25 liter cabinet with an 8-inch driver and an HR tuning of 35Hz delays port output by up to 35ms. To put that into perspective, imagine the instrument playing the bass fundamentals about 10 meters farther away than the harmonics. That's really slow bass response). At higher volumes, the port starts chuffing because of too much air volume displacement. But to increase the port area would require a very much longer port to slow down the response even more. That's senseless.

Do you want faster-sounding bass reflex designs with more linear max output? Easy but huge by comparison. We need a short wide duct (low hydraulic mass = fast response) but for a low cut-off frequency, this mandates a large cabinet volume for high compliance. Large cabinets go well with high-compliance low-mass drivers where high efficiency equals low driver mass and large cone area. That depends on a large cabinet volume for low resonance just like the HR. This is the ticket to a 'fast' sounding design that also goes low. Unfortunately those high-sensitivity, low-mass, high-compliance woofers are rare today because the PA industry favors small cabinets and high power capacity, hence large heavy voice coils. For context, the Rho widebander's moving mass is 10g. Typical 8-inch units today weigh 22 - 30g!