Energy adds, decibels do not
Sound transmission is reported in decibels, which are logarithmic, and this is the source of nearly every wrong intuition about it. Two identical leaks do not transmit twice the decibels; they transmit twice the ENERGY, which is three decibels more. A ten-decibel change is roughly what people describe as twice or half as loud, while the energy behind it has changed by a factor of ten.
So assemblies are combined on energy and then converted back. Each element's transmission coefficient is its fraction of incident energy that gets through; those are weighted by area, summed, and the total converted to a single transmission loss. Averaging the decibel ratings of the parts is not an approximation of this — it is a different calculation with a systematically optimistic answer.
The consequence is the fact worth carrying away from this page. An element with no transmission loss at all — an undersealed perimeter joint, an unbaffled transfer grille, a gap under a door — passes everything that reaches it. At one per cent of the wall area, such a path alone caps the composite at about twenty decibels, no matter what the other ninety-nine per cent is made of. A laboratory-rated wall built with an open perimeter is not a degraded wall; it is a different, much worse wall.
- S_i
- area of each element in the partition
- τ_i
- transmission coefficient of that element — the fraction of energy passed, with 1.0 for an open hole
- TL
- composite transmission loss in decibels
Mass law: six decibels per doubling, and why that is bad news
For a single limp panel, transmission loss rises by about six decibels for each doubling of surface mass, and by about the same for each doubling of frequency. That is the mass law, and it is the baseline every other technique is measured against.
Six decibels per doubling is a poor exchange rate. Going from one layer of board to two costs a full second layer of material and labour and buys around five decibels in practice. Going from two to four would buy five more. Mass alone reaches a useful rating only at weights that are structurally inconvenient — which is why heavy masonry walls sound good and lightweight ones need something other than mass.
The exception is low frequency, where mass is the only thing that works at all. Decoupling and absorption run out below a few hundred hertz, so a partition that must stop bass — a cinema, a plant room, a music space — is a mass problem however unattractive the exchange rate is.
Decoupling beats mass, and one screw undoes it
Breaking the structural path between the two faces of a partition is worth far more than adding mass to a connected one. Resilient channels, sound isolation clips, staggered studs and fully separate double-stud walls all do the same thing: they make the two leaves move independently so that vibration in one does not drive the other.
The gain is large — often ten to fifteen decibels over the same materials rigidly connected — and it is also FRAGILE in a way that mass is not. A screw long enough to pass through the board and the channel and reach the stud behind it creates a rigid bridge, and a wall with a line of such screws can lose most of the benefit the channel was installed for. This is the single most common reason a field wall under-performs its laboratory rating, and it is an installation fault rather than a design one.
It is also why the screw-length and channel-spacing pages exist at all and why they are unusually prescriptive. The quantities they return are trivial arithmetic; the reason for the numbers is not, and that is what this page is for. The same logic explains why a resilient layer must not be bridged by a rigid skirting, a door frame screwed through both leaves, or a continuous floor finish running under the wall.
The coincidence dip: every panel is transparent at one frequency
A panel does not follow the mass law everywhere. At its CRITICAL FREQUENCY, the wavelength of bending waves in the panel matches the wavelength of sound in the air striking it at an angle, the panel couples efficiently with the air on both sides, and its transmission loss collapses into a dip that can be ten decibels or more deep.
That frequency depends on the panel's thickness and stiffness: thin limp materials put it high and out of the way, thick stiff ones put it low. Glass is the classic case, because a single pane of common thickness lands its dip squarely in the speech range — which is why a thick single glazed window can sound worse than the thinner one it replaced at exactly the frequencies people care about.
The standard remedy is to use two DIFFERENT thicknesses rather than two of the same, so that each panel's dip falls where the other is still performing. The same principle applies to a double-layer board finish and to laminated glass, where the interlayer also damps the resonance rather than merely shifting it.
Flanking: the path that goes around what you built
A laboratory rating measures one assembly with every other path deliberately suppressed. A building has no such isolation, and sound arriving in the next room has usually travelled around the partition rather than through it: along a continuous floor slab or screed, over the top through a shared ceiling plenum, through ductwork connecting both rooms, or through the structure itself.
Small discrete paths matter far more than their size suggests, for the reason in the first section. Back-to-back electrical boxes in the same stud cavity, an unsealed pipe penetration, a recessed light, a poorly detailed door undercut — each is a fractional area with a transmission coefficient near one.
This is why field-measured performance is routinely several points below the laboratory rating of the same construction, and why the field metrics carry different names — an apparent or field rating rather than a laboratory one — so that the two are not compared as though they were the same measurement. The design consequence is that acoustic sealant at the perimeter, at penetrations and at the head and base track is a structural part of the assembly's rating, not a finishing detail, and omitting it costs more than any material substitution would.
Vibration isolation: too little deflection makes it worse
An isolator under a machine is a spring, and the system it forms has a natural frequency set by how far that spring deflects under the load it carries — more deflection, lower frequency. Isolation begins only when the driving frequency is above about 1.4 times that natural frequency, and it improves from there.
Below that ratio the isolator does not merely fail to help: it AMPLIFIES, transmitting more force than a rigid mounting would, with the worst case exactly at resonance. An isolator chosen too stiff for a slow-running machine is a fault that is easy to introduce, hard to see and makes the problem it was bought to solve measurably worse.
So the design quantity is static deflection rather than a product name, and the check is against the lowest driving frequency present — usually the shaft speed, not the blade-pass or electrical frequency. The other half is the structure underneath: an isolator is only as good as the floor it stands on, and a springy long-span floor can have a natural frequency close to the isolator's, at which point the two interact and the calculation on the isolator alone no longer describes anything.
Reverberation: how long a room holds its own sound
Inside a room the question is not what gets through the walls but how long a sound lingers before the surfaces soak it up. Reverberation time is the number of seconds a sound takes to fade by sixty decibels once its source stops, and Sabine's formula ties it to two things: the room's volume, and its total absorption.
Each surface's absorption is its area times its absorption coefficient, the share of the sound energy striking it that it does not send back: close to nothing for glazed tile or plastered masonry, close to all of it for an acoustic tile hung on a deep suspension. Coefficients change with frequency, carpet taking little of a low note and a good deal of a high one, so the time is worked one octave band at a time, and a standard that sets a single figure, as the UK's school standard BB93 does, averages the middle bands.
Because the absorption sits below the line, the time falls in proportion as absorption is added: double a room's absorption and its reverberation time halves. That is how a hard classroom is brought down to a usable time with an acoustic ceiling, and it is also the reason the same ceiling does nothing for the sound reaching the next room, which is the rest of this page's subject.
- T
- reverberation time in seconds, for the octave band the coefficients describe
- V
- the room's volume
- A
- total absorption: each surface's area S_i times its absorption coefficient α_i, added up (sabins)
Silencers, absorption and what has to be measured
A duct silencer trades pressure drop for insertion loss, and both come from the same test. More absorptive length and narrower airways attenuate more and cost more fan energy; beyond a point the extra resistance also generates SELF-NOISE at the silencer itself, which sets a floor on how quiet the outlet can be no matter how much attenuation is added upstream.
Absorption inside a room is a different quantity from transmission between rooms and is frequently confused with it. Acoustic clouds, reflector panels and applied absorbers change reverberation and clarity in the space they are in; they do essentially nothing for what the neighbour hears. A complaint about noise from next door is not answered by absorption, and a complaint about a room being harsh is not answered by a heavier partition.
Ratings themselves are measurements. Transmission loss, insertion loss, absorption coefficients and impact ratings all come from standardised laboratory tests, and the honest use of the estimators here is to place an assembly in the right region before a specification is written or a consultant is engaged. Where the acoustic performance is contractual, it is verified by a field measurement in the finished building — which is also the only test that includes the flanking paths this page is mostly about.
Calculators that use this method
Basis
- ASTM E90 (laboratory airborne sound transmission loss) and ASTM E413 (the STC single-number rating fitted to sixteen one-third-octave bands).
- ASTM E336 and E413/E1332 for field measurement, and the distinct field metrics that exist so laboratory and in-situ results are not compared directly.
- ASTM E492 and E989 for impact insulation, the companion problem to airborne transmission through floors.
- ASTM E477 for duct silencer insertion loss, pressure drop and self-noise measured together on the same specimen.
- ASTM C423 for sound absorption coefficients and the NRC rating — a room property, not a partition property.
- Sabine's equation T = K V / A with K = 0.161 s/m (0.049 s/ft): S. Errede, University of Illinois Physics 406 lecture notes, Auditorium and Room Acoustics, after Backus, The Acoustical Foundations of Music; absorption coefficients of common materials in octave bands, Approved Document E (2003 edition incorporating 2004, 2010, 2013 and 2015 amendments), Table 7.1; BB93 (2015) for the mid-frequency average.
- Gypsum Association GA-600, Fire Resistance and Sound Control Design Manual, for tested partition assemblies and their ratings.
- ASHRAE Handbook, HVAC Applications, chapter on Noise and Vibration Control — isolator selection by static deflection, the amplification region below resonance, and floor flexibility.
- Beranek, L. and Ver, I., Noise and Vibration Control Engineering, for the mass law, the coincidence effect and composite transmission loss.