Why Low-Frequency Noise Is the Hard Problem

Why this matters

Absorption, screening and sealing are each sized against wavelength, and at low frequency the wavelength is longer than the building element you were going to install them in. That is why the three controls that solve a hiss complaint in an afternoon all fail together on a rumble, and why the second attempt fails the same way as the first. Nothing was defective and nobody was lazy. The products were bought in a frequency range where their mechanism does not exist. Knowing that before the first purchase is the difference between one honest conversation and three disappointing site visits.

Wavelength is the ruler

Wavelength in air is the speed of sound divided by frequency. Take the speed as about 1125 ft/s, which is dry air near 70 F; it rises with temperature, by roughly 1 ft/s per degree F, so a hot plant room shifts these numbers by a few percent and nothing here depends on that.

The quarter-wavelength column is not decoration. A porous absorber works on air particle velocity, and against a rigid backing the particle velocity is at its maximum a quarter wavelength out from that backing. So a porous absorber's useful range starts around the frequency whose quarter wavelength equals the absorber's thickness plus its airspace, measured to the backing. That is the single relationship that decides most of what follows.

Worked example: a conference room beside a mechanical room

A conference room shares a wall with a mechanical room and is unusable during plant operation. Readings are LAeq,15min, dB re 20 uPa, at the head of the table, class 1 meter calibrated before and after, with the residual measured at 33 dB(A) with the plant off, more than 10 dB below every figure here, so no background correction applies to any of them.

Summed: 51.5 dB(A). The same bands summed with C-weighting give 73.7 dB(C), so C minus A is 22.2 dB, well over the 15 dB screen that the band-data card sets for a low-frequency-dominated problem. Applying that card's gate, the highest A-weighted band is 125 Hz at 47.9, and the only band within 5 dB of it is 63 Hz at 47.8. Any control has to work at 63 and 125 Hz or it will not move the number.

Note what A-weighting did on the way through. The 63 Hz band is the loudest thing in the room by 10 dB unweighted and arrives in the A-weighted column tied for second. Report only 51.5 dB(A) to a landlord and you have described a room that sounds mildly busy. The people in it describe a room they cannot hold a meeting in.

What each receiver-side control would have to be

The building offers a 14 in plenum above the conference-room ceiling, a corridor that could take a screen giving about 0.5 ft of path-length difference, and the existing partition.

The absorber. At 14 in, or 1.17 ft, to the backing, the quarter-wavelength frequency is 1125 divided by four times 1.17, which is about 240 Hz. Line that whole plenum and you have bought absorption that begins to earn its keep at 240 Hz, in a room whose problem sits two octaves below that. Nothing is wrong with the product. The depth needed at 63 Hz is 4.5 ft and the building has 14 in. A tuned membrane or resonant absorber can work at 63 Hz in far less depth, but only over a narrow band around its tuning, and it has to be designed to the measured frequency and verified after installation rather than bought off a shelf.

The barrier. Barrier performance is governed by the Fresnel number, which is twice the path-length difference divided by the wavelength, holding the source and receiver positions fixed. At fixed geometry the Fresnel number is directly proportional to frequency, so it collapses as frequency falls. With 0.5 ft of path difference: at 1000 Hz the Fresnel number is 2 times 0.5 divided by 1.13, which is 0.89, and a screen in that range is worth installing. At 63 Hz the same geometry gives 2 times 0.5 divided by 17.9, which is 0.056. To get back to 0.89 at 63 Hz the path difference would have to be about 7.9 ft, meaning a screen roughly an order of magnitude taller than the one that works at 1 kHz. Take the actual decibels from the barrier's own tested data or a design calculation, not from a rule of thumb; the point here is the ratio, and the ratio is decisive.

The mass. Transmission loss through a single limp panel rises about 6 dB per doubling of frequency at constant surface mass, so the same wall gives roughly 12 dB more at 250 Hz than at 63 Hz. Recovering that 12 dB at 63 Hz through mass alone means two doublings of surface mass, which is four times the weight of wall, with the structural consequences that implies. Whether mass law even applies to your particular wall at 63 Hz is a separate question with its own conditions, and a sibling card owns it.

The gaps. Sealing is the one control on the list that is genuinely more effective as frequency rises. A leak that ruins a partition in the speech range is a minor contributor at 63 Hz, so a low-frequency complaint is essentially never a sealing problem. Seal it anyway for the sake of the rest of the spectrum, but do not book it as the fix and do not let it be measured as one.

The room stops behaving like a room

The conference room is 24 ft long, so its first axial mode along that dimension sits at 1125 divided by twice 24, which is about 23 Hz, with the next two at about 47 and 70 Hz. That puts modal behaviour right across the complaint band. In that regime the level at 63 Hz is a strong function of where you stand: pressure maxima sit at the boundaries and are highest in the corners, and there are positions a few feet apart differing by more than 10 dB.

Two practical consequences. Measure low-frequency complaints at more than one position and report the spread, or your single reading is a statement about a chair rather than a room. And when a complainant says the hum is worse in one seat, believe them, because the room says so too.

What still has a mechanism down there

Three things, and they are all on the source side of the receiver.

Reduce the forcing. Blade-pass and shaft-order content moves in proportion to shaft speed at constant blade count, so a speed change moves the energy as well as reducing it. Identify the forcing frequency first with the spectrum worksheet, and observe the constraint that card states about what a speed change does to the process before touching a drive.

Isolate the structure-borne path. This is the exception on the list, and it is worth being precise about why. An isolator is not sized against wavelength, it is sized against the ratio of forcing frequency to the mount's own natural frequency, so a 63 Hz forcing frequency against a mount whose natural frequency sits in the single digits of hertz is a well-isolated case in principle. Its failure modes are different in kind: a rigid short circuit through a conduit, a pipe, a drain line or a wedged shim defeats the mount entirely, and a slow-speed machine whose forcing frequency approaches the mount's natural frequency is amplified rather than isolated. The library's isolating-connection card covers what those mounts can and cannot do.

Put the mass at the boundary as two leaves rather than one. A double-leaf partition can beat a single wall of the same total mass, but only above its own mass-air-mass resonance, and it is worse below it. A double leaf whose resonance lands above 63 Hz makes this complaint worse, not better, which is exactly the kind of detail a sibling card exists to keep you out of.

Sibling-rule check. Every level carries quantity, weighting, reference, bandwidth and time basis. The quarter-wavelength rule is stated for a porous absorber against a rigid backing with thickness measured to the backing, and it is applied only to that geometry. The Fresnel relationship is stated with source and receiver positions held fixed, and applied at fixed geometry. The 6 dB per doubling figure is stated at constant surface mass for a single limp panel and routed to the card that owns its conditions rather than being extended here. The double-leaf direction matches the card that owns it: better above the mass-air-mass resonance, worse below.

How to verify you got this right

Before buying anything, check your proposed control's published data for a figure in your own peak band, and check what mounting or backing that figure was measured with. An absorption coefficient measured with an airspace behind the sample does not apply to the same material glued flat to a wall, and the low-frequency end is where that difference is largest.

Afterwards, re-measure at the same positions and in bands, not overall. The failure signature is unmistakable: bands above 250 Hz down by several decibels, the 63 and 125 Hz bands unchanged to within a decibel, and an overall A-weighted level that moved just enough to look like progress in an email. If your post-install report shows exactly that, the control worked correctly and was aimed at the wrong octave.

References

• ASTM C423, absorption measured in a reverberation room, with the mounting designation that is part of every published coefficient; take absorption data with its mounting or do not take it
• Manufacturer barrier and absorber data giving performance per octave band, with the test method and edition stated on the report
• The building code as adopted and amended by your authority having jurisdiction, a named role with authority to interpret and enforce it, for any penetration of a rated assembly, which must be closed with a firestop system tested for that assembly
• See related: What Octave Bands Tell You That an Overall Level Cannot; What a Vibration Isolating Connection Can and Cannot Do; Why a Double Wall Beats a Heavy Wall and When It Does Not