PA Systems and Loudspeakers

A PA loudspeaker is not one device making sound. It is two or three specialised drivers, each handed a slice of the spectrum, in a box whose shape is an argument about physics — and aimed at one patch of floor. Every one of those choices costs something, and the cabinet you just unloaded made all of them for you.

Musicians shop for speakers the way they shop for amplifiers, by finding the largest number on the panel. But the two figures that decide whether a box works in your room — how much sound it makes, and where that sound goes — are measured under conditions almost nobody publishes, so they cannot honestly be compared across brands.

Without a Box, a Woofer Cancels Itself

The back of a cone radiates as hard as the front and in the opposite polarity, so what matters is how far the rear output has to get to reach the front, measured against the wavelength. A few centimetres around the frame is a rounding error to a cymbal and a large fraction of a bass note. The top escapes intact; the bottom meets its own inverse at the rim and vanishes, leaving a driver working hard and producing almost nothing. An enclosure exists to seal that path off, and the choice of enclosure settles nearly everything else about the box.

A sealed box traps a fixed volume of air and works it as a spring. Output falls at 12 dB per octave below cutoff, and that spring goes on controlling the cone all the way down, which makes the design mechanically hard to hurt. The cost is level: the theoretical best a sealed box can manage is about 2.9 dB behind a ported one, and matching a ported box's efficiency and cutoff takes roughly twice the volume. A ported box cuts an opening whose slug of air resonates against the air inside the cabinet, tuned so the rear wave arrives in step with the front one and adds to it. Two things invert below that tuning. The rolloff steepens to 24 dB per octave, and the port stops loading the cone, which then travels a very long way on very little power. Resonance also holds the bottom octave back in time, so a ported cabinet can measure flat and still sound late and thick underneath.

Horn-loading is the efficient option and the physically expensive one. A slowly widening tube makes the air at the driver's end behave as though it were much heavier. A diaphragm pressing on that stiffer load reaches the same pressure over a far shorter distance, which is why a horn-loaded driver puts roughly ten times — 10 dB — more sound into a room for the same amplifier input. But it only loads down to the frequency its mouth can match, and the two rules in circulation put that mouth between a quarter and a third of a wavelength across. A 40Hz wave is 8.6 m long, as the rooms lesson established, so a horn that genuinely loads 40Hz wants a mouth two to three metres wide. One trade sits under all three designs: efficiency, box size, and how low it goes. Choose two.

High Frequencies Cannot Get Out Without a Horn

Above a couple of kilohertz the problem inverts. Excursion barely matters at wavelengths of centimetres, but a small stiff diaphragm couples to thin air appallingly badly, and most of what you put in never becomes sound. A compression driver squeezes a domed diaphragm into a cavity much smaller than the dome and lets the result out through a narrow throat. In between sits the phase plug, a set of channels cut so that sound leaving the centre of the dome and sound leaving its edge travel the same distance to the throat. Without it the two arrive out of step and cancel on the way out. The horn on the front of that throat is the matching device — high impedance where the driver meets it, open air at the mouth, a controlled expansion between.

Efficiency is only half the reason it is there. Left bare, a diaphragm's pattern is decided by its own diameter against the wavelength, so it starts wide and collapses into a beam across the top octaves, and no amount of EQ redirects a beam. Fit a horn and the pattern belongs to the horn's geometry instead — which is the only reason a cabinet can quote a coverage angle at all. Constant-directivity profiles hold roughly one angle across their range; older radial and exponential horns narrow as they climb.

Below the horn's cutoff frequency the whole arrangement stops working. The throat no longer holds the diaphragm in check, and a diaphragm with almost no room to move is suddenly being asked to make long waves. Which is why no horn driver is ever handed the whole signal.

A Crossover Point Is a Seam, and Seams Show

A crossover divides the band so each driver gets only what it can reproduce and, more urgently, only what it can survive. Send a full-range signal to a compression driver and the failure is not muddy bass. It is a diaphragm.

Passive crossovers live inside the cabinet, between amplifier and drivers, built from capacitors and inductors carrying the whole output voltage. They take a share of the power with them as insertion loss, and they put reactance in the one place the amplifier was relying on a direct connection. Active crossovers split at line level ahead of separate amplifier channels — bi-amping — so nothing is lost in the filters, corner frequencies move without a soldering iron, and a loud low note can no longer eat the headroom the cymbals needed.

Neither kind hides the seam. At the crossover frequency both drivers radiate the same note from two different places, and two sources separated in space interfere. Put a fifteen-inch cone and a horn 30 cm apart, cross them at 2kHz where a wavelength is 17 cm, and the path difference reaches half a wavelength about 17 degrees off axis vertically. That direction gets a null, and somebody is standing in it. Steeper filters shrink the band where the two overlap, which is most of why fourth-order Linkwitz–Riley — 24 dB per octave, each leg 6 dB down at the corner, summing flat and in phase — became the default once DSP made it free.

Sensitivity Is a Coverage Spec Wearing a Disguise

Sensitivity is the on-axis level a metre away for one watt in, and it reads like the one honest number on the page. It is not, because it never separates how much sound a box makes from how tightly it aims it. Two real cabinets: a three-way quoting 95 dB with a 60 by 40 degree pattern, and a two-way quoting 96 dB with 90 by 60. A decibel apart, near enough identical. Except the Molloy estimator from the rooms lesson puts 90 by 60 near Q = 8.7 and 60 by 40 near 18, which is roughly 3 dB more of whatever the narrow box makes landing on the measurement microphone instead of going elsewhere. Correct for that and the cabinet with the lower printed number is turning appreciably more electricity into sound. Neither maker is lying; they are answering different questions with one word.

The conditions are worse. Neither sheet states the band the figure was averaged across, and since no loudspeaker is flat, the answer moves with the window you pick. Neither says whether the box faced free space or a boundary, and the rooms lesson has already priced what a boundary is worth. The volts question — 2.83 V being one watt into 8 ohms but two watts into 4 — belongs to the power lesson, and shifts the number 3 dB on its own.

Coverage angles carry their own fine print. The quoted figure is the angle inside which level has not yet fallen 6 dB below the axis, averaged over the mids and highs, and a box stops being directional once the wavelength outgrows it. What you match that angle to is not the room's width but the angle the audience subtends from the box. Fly a top 5 m up over a flat floor, ears at 1.7 m: the nearest listeners at 4 m sit 40 degrees below horizontal, the back row at 20 m sits 9 degrees below, and sixteen metres of audience turns out to be a thirty-degree vertical problem. Sixty degrees of vertical pattern spends half of itself on bare floor and ceiling. Horizontally, a twelve-metre-wide floor swings from 113 degrees at the front row to 33 at the back, which is why patterns are wider across than up and down, and why front rows are the hardest thing in a room to cover.

A Line Array in a Small Room Is a Point Source in Costume

A point-source cabinet radiates into a growing sphere and sheds 6 dB per doubling of distance, which the outdoor lesson walked across a field. A tall column of boxes behaves differently while you are close to it — the wavefront is nearer a cylinder than a sphere, its area grows with radius rather than radius squared, and level falls closer to 3 dB per doubling. Trading 6 for 3 across four doublings keeps 12 dB you would otherwise buy with amplifiers.

The catch is that this is a near-field effect with a finite range, and the range depends on how long the array is and which frequency you are asking about. Longer arrays and higher frequencies push the transition out; short arrays and low frequencies drag it in. Past it the array sheds 6 dB per doubling like everything else, and there is only a certain distance out to which a finite line beats an equally loud point source at all.

That is the argument against hanging four small elements in a two-hundred-capacity room. An array shorter than about 3 m has already gone omnidirectional by 100Hz, whose wavelength is 3.4 m — so the pattern control you paid for is missing in the band a tight room needs it most. The cylindrical zone may not reach the back wall, and indoors most of the audience sits beyond critical distance anyway, listening mainly to the room.

What Actually Kills Drivers

• Clipping does not send DC anywhere — a working amplifier puts out alternating current however flat its peaks go. Heat belongs to the power lesson; travel belongs here, and travel is what you cause on the day.
• Learn your box's two excursion limits — Xmax is how far the cone moves while the motor stays linear, Xmech how far it moves before something tears. Between them, distortion. Past them, an invoice.
• High-pass at the cabinet's tuning frequency — below tuning a ported box stops loading its cone, so a subsonic thump moves the driver further than a full-level kick drum does.
• Count sub-audible energy as signal — handling noise, a dropped stand, a boot on a hollow riser and unfiltered plosives all spend excursion on material nobody can hear.
• Never let a full-range feed reach a horn driver — a bi-amp send on the wrong amplifier, or a passive network bypassed during a repair, finishes a compression driver in seconds.
• Bring amplifiers up last and take them down first — a switch-on transient from anything upstream reaches the drivers at full amplitude with nothing in its way.
• Read a rattle as a diagnosis — buzzing on a slow sweep, a rubbing coil, or a cone sitting off-centre while disconnected all say the suspension has already moved.
• Add boxes before you add watts — over-excursion means the system is short of radiating area, and a bigger amplifier only reaches the tearing point sooner.