What a Small Hole Does to a Large Wall

Why this matters

Everyone in the trades knows a gap leaks sound. Almost nobody has an accurate sense of how much, and the reason is that the quantity which adds across a wall is the open area fraction, not the decibels. A quarter-inch undercut under one door will take a good demising wall down by more than 10 dB, and it will do most of that damage in exactly the frequency range that carries speech. This card gives you the one relationship that puts a hard ceiling on an assembly from its open area alone, so you can tell a customer what a wall can possibly deliver before anyone builds it, and so you stop spending on mass when you should be spending on a seal.

The quantity that adds is not the decibel

Transmission loss is a logarithm of a ratio, and logarithms do not add across parallel elements. What adds is the transmission coefficient, the fraction of incident sound power that gets through, weighted by the area over which it acts.

composite coefficient = sum of (area x coefficient) / total area
composite TL = 10 log10 (1 / composite coefficient)

Convert each element to its coefficient with coefficient = 10 raised to minus TL over 10, add the area-weighted terms, convert back. That is the whole method, and everything below is a consequence of it.

An untreated opening is the extreme case. Treat its coefficient as 1, meaning it passes everything. That value holds for a thin barrier and an opening large compared with the wavelength at the frequency you care about. A deep, narrow slot through a thick wall does attenuate somewhat at high frequency, and a short duct-like opening can resonate and pass more than its geometric area at particular frequencies, so 1 is a working value rather than a guaranteed upper bound. Say which you are using.

The ceiling an opening sets on its own

Set the rest of the wall to perfect, coefficient zero, and the composite reduces to one term. The result is worth memorizing, because it is the sentence you can say at a walkthrough:

best possible TL = 10 log10 (1 / open area fraction)

One part in ten thousand of a 200 ft2 wall is 0.02 ft2, about 3 square inches, and it caps the wall at 40 dB. Every decade of tightening buys 10 dB and nothing else does. The unit of analysis is one partition between one pair of rooms, on one octave band or on a stated single-number basis, and the rule assumes the opening is untreated.

What counts as an opening

More than people think, and the list is where the money goes.

• Door undercuts and unsealed door perimeters. Usually the largest single opening in any partition.
• Back-to-back electrical boxes in one stud cavity, and any box whose plaster ring is not sealed to the board.
• Unsealed top and bottom tracks, particularly at a fluted deck where the flutes leave open triangles.
• Pipe and conduit sleeves with an annular gap, and cable trays crossing a wall.
• Transfer grilles and undercut returns, which are deliberate openings and are covered by a sibling card on elements that must open or pass something through.
• Ceiling-mounted devices on either side of a wall that stops at the ceiling line, which is a plenum path rather than a hole in the wall and is covered by the flanking card.

Sealant on the wrong side of the board does nothing. The seal has to be continuous across the plane you are trying to close, on both faces of a double-layer assembly, or you have closed one leaf and left the other open.

Worked example: a quarter inch under one door

An office demising wall, 200 ft2. The wall's own field performance is 45 dB apparent transmission loss, measured to ASTM E336 and classified per ASTM E413 in the editions the specification cites; that is a field value, not a laboratory class, and mixing a laboratory number into a field composite is the mistake this example exists to avoid. The door has a 1/4 in undercut across a 36 in leaf.

Correction, printed: aperture area comes out of the wall area. Gap = (0.25 / 12) ft x 3 ft = 0.0625 ft2, which is 9 square inches. Remaining wall area = 200 - 0.0625 = 199.9375 ft2. Charging the full 200 ft2 to the wall double-counts the opening.

Correction, printed: the aperture coefficient. Taken as 1.0, valid because a 1/4 in slot 36 in long is large compared with the wavelength through most of the speech range and the leaf is thin. Below roughly the 250 Hz band this overstates the leak slightly, which is stated rather than folded in.

• Wall coefficient: 10^-4.5 = 3.16e-5. Area-weighted: 199.9375 x 3.16e-5 = 0.00632 ft2.
• Gap: 0.0625 x 1.0 = 0.0625 ft2.
• Total 0.0688 ft2 over 200 ft2 gives a composite coefficient of 3.44e-4.
• Composite TL = 10 log10 (1 / 3.44e-4) = 34.6 dB.

A 45 dB wall now performs at 34.6 dB. The loss is 10.4 dB from an opening that is 9 square inches in a wall of 28,800 square inches.

Ceiling check, printed. Area fraction 0.0625 / 200 = 3.13e-4, so the ceiling is 10 log10 (1 / 3.13e-4) = 35.0 dB. The composite came in at 34.6, just below its own ceiling as it must be, and the difference is the 0.4 dB the wall itself still costs.

How much the wall's own accuracy matters now. Suppose the 45 dB field figure was optimistic by 3 dB and the wall is really 42. Recomputing, the composite moves from 34.6 to 34.3 dB. A 3 dB error in the dominant-sounding number moves the answer by 0.3 dB, because once an aperture is in charge the wall has stopped being the variable. That is worth knowing before anyone spends a day arguing about the wall's rating.

Sibling-rule check, printed. The composite summed on area-weighted coefficient rather than by subtracting decibels: yes. The wall figure named as a field apparent value with its test method and edition basis: yes. The aperture coefficient stated with the geometry it holds for: yes. Gain quoted against its own ceiling: yes. No rounding taken in the direction that flatters the wall: the aperture coefficient of 1.0 is the pessimistic choice and is labelled as such.

The same gap, band by band

Composite arithmetic on a single number is a first pass. The real relationship is per band, and it changes the story completely, because the aperture passes everything at every frequency while the wall gets better as frequency rises.

Say the same wall measures 30 dB in the 125 Hz octave band and 52 dB in the 2000 Hz octave band, both unweighted, re 20 micropascals, field values.

• 125 Hz. Wall term 199.9375 x 1.00e-3 = 0.1999 ft2. Gap 0.0625. Composite coefficient 1.31e-3, TL = 28.8 dB. The gap costs 1.2 dB.
• 2000 Hz. Wall term 199.9375 x 6.31e-6 = 0.00126 ft2. Gap 0.0625. Composite coefficient 3.19e-4, TL = 35.0 dB. The gap costs 17.0 dB.

One gap, 1.2 dB of damage at 125 Hz and 17.0 dB at 2000 Hz. That is why a gap destroys speech privacy specifically: the consonants that carry intelligibility live in the bands where the wall was doing its best work and the hole does not care. It is also why a customer complaining about a bass hum through a wall is usually not describing a sealing problem, and a customer who can make out words usually is.

Closing it without breaking something else

• Rated openings. Do not add a gasket, sweep or seal to a fire door assembly or any rated opening protective unless that component is part of its listing, and do not obstruct a door in a required exit route. NFPA 80 and NFPA 101 apply in the editions your authority having jurisdiction adopted, binding the building owner and reaching you through the permit; 29 CFR 1910.36 and 1910.37 cover exit routes as a federal duty to your employees.
• Rated assemblies. A penetration through a fire-resistance-rated wall gets restored with its listed firestop system, not with acoustical sealant. Acoustical sealant has no fire rating and closing an acoustic gap with it in a rated wall leaves the assembly out of compliance.
• Air the building needs. Never close an undercut, transfer grille or louver that supplies combustion air or make-up air to a fuel-fired appliance while that appliance can fire, because restricting it can spill combustion products into the space; shut the appliance off and lock it out first. The same applies to a return path a fan system depends on.
• Dust, which is the route people drop. If closing the gap means cutting, grinding or sanding gypsum, joint compound, block or concrete, that releases respirable dust including crystalline silica. Use a tool with on-tool dust collection or a wet method, and respiratory protection only under a written program meeting 29 CFR 1910.134; the construction silica standard is 29 CFR 1926.1153. Read the sealant's safety data sheet before you open it and ventilate for solvent vapor as it directs.

How to verify you got this right

Take the open area of everything you can find, add it, divide by the partition area, and read the ceiling off the table. If that ceiling is below what the job needs, the wall type is irrelevant until the openings are closed, and you can say so before a single sheet of board is ordered. After sealing, re-measure rather than assuming: if the retest returns far less than the arithmetic predicted, you did not find all the open area, or the limiting element is no longer an aperture and the flanking card owns the next step.

References

• ASTM E336 (field measurement between rooms) and ASTM E413 (single-number classification), in the editions the project specification or the adopted code cites; consensus standards bind through that reference rather than on their own
• NFPA 80 and NFPA 101, in the editions adopted by the authority having jurisdiction; 29 CFR 1910.36 and 1910.37 for exit routes
• 29 CFR 1910.134 for respiratory protection programs; 29 CFR 1926.1153 for respirable crystalline silica in construction work
• See related: What Flanking Is and Why It Decides the Outcome; Why a Door or a Duct Is Usually the Weakest Element; Why a Wall Never Performs Like Its Rating; How to Firestop a Penetration So the Rating Survives