Airborne sound insulation, enclosures and booths
Airborne sound insulation explained: mass law, R and Rw, D and DnT,w, flanking and leaks, and what speech level reduction (ISO 23351-1, DS,A) measures.
Acoustics
Absorption and insulation are easily confused, and they do different jobs. Absorption reduces the sound reflected inside a room: it shortens the reverberation and lowers the level of the reverberant field. Insulation reduces the sound passing from one room to another through walls, floors, doors and windows. A soft absorbing panel improves the acoustics of the room it hangs in and adds little to the insulation of the wall behind it, because it is light and porous and sound passes through it easily. Absorption is covered in the articles on random incidence and absorption ratings. This one deals with airborne sound insulation and with small enclosures, where both matter at once.
Transmission and the sound reduction index
When sound strikes a partition, a fraction τ of the incident sound power passes through. τ is the transmission coefficient, and the sound reduction index is
R = 10 · lg(1 / τ) dB
A wall that lets through one thousandth of the incident power has R = 30 dB; one that lets through one millionth has R = 60 dB.
R is measured in a laboratory with two reverberation rooms separated by the test element, according to the ISO 10140 series. A loudspeaker creates a diffuse field in the source room, so sound strikes the partition at random incidence, and
R = L1 − L2 + 10 · lg(S / A)
where L1 and L2 are the average levels in the source and receiving rooms, S is the area of the partition and A is the equivalent absorption area of the receiving room, found from its reverberation time. The test facility is built so that sound reaches the receiving room only through the test element.
Mass law, coincidence and double walls
For a single limp panel, insulation is governed by its mass per unit area, m, in kg/m². The field-incidence mass law gives approximately
R ≈ 20 · lg(m · f) − 47 dB
with f in hertz. Each doubling of the mass, or of the frequency, adds about 6 dB. A panel of 10 kg/m² at 500 Hz gives R ≈ 20 · lg 5000 − 47 ≈ 27 dB; doubling the mass to 20 kg/m² gives about 33 dB. This is why heavy masonry insulates well and light materials on their own insulate poorly.
Real panels are also stiff. At and above the critical frequency, the bending waves in the panel can match the trace of the incident airborne waves, sound couples efficiently into the panel, and the insulation falls into a dip, the coincidence dip, deepest near the critical frequency and rising again above it. For thin panels such as glass and plasterboard this dip lies in the upper part of the speech range; for heavy masonry it lies at low frequencies.
Double constructions, two panels with an air space between them, can perform far better than the same total mass in one layer, above a certain frequency. Below the mass-air-mass resonance the two panels move together as one; around the resonance the insulation is poor; above it the insulation rises steeply. For panels of masses m1 and m2 and an empty cavity of depth d in metres, the resonance lies at roughly
f0 ≈ 60 · √((1/m1 + 1/m2) / d)
Two panels of 10 kg/m² with a 100 mm cavity give f0 ≈ 60 · √2 ≈ 85 Hz. Heavier panels and deeper cavities move the resonance lower. Porous material in the cavity damps it, and any rigid connection between the two panels, such as shared studs or ties, bridges the cavity and spoils much of the gain.
Laboratory and field
In a building the separating element is never the only path. Sound also travels through the flanking structures: along floor slabs, through façades and lightweight walls that run continuously past the partition, through ducts, ceiling voids and service runs. Flanking transmission is the main reason a wall with a high laboratory rating performs worse in a building. The prediction methods of ISO 12354 estimate field performance from laboratory data by adding the flanking paths.
Field measurements to ISO 16283-1 therefore use quantities of their own.
| Quantity | Definition | Where it applies |
|---|---|---|
| R and Rw | Sound reduction index of the element alone, and its single-number rating | Laboratory (ISO 10140, rated to ISO 717-1) |
| R′ and R′w | Apparent sound reduction index, flanking included | Building (ISO 16283-1) |
| D | Level difference, L1 − L2 | Building |
| Dn | D − 10 · lg(A / A0), normalised to A0 = 10 m² of absorption | Building |
| DnT and DnT,w | D + 10 · lg(T / T0), standardised to T0 = 0.5 s, and its rating | Building |
| DS,A | Speech level reduction of an enclosure or furniture ensemble | Laboratory (ISO 23351-1) |
Rw is found as described in ISO 717-1. A reference curve is shifted against the measured one-third-octave values from 100 Hz to 3150 Hz until the sum of the unfavourable deviations is as large as possible without exceeding 32 dB, and Rw is the value of the shifted curve at 500 Hz. Two spectrum adaptation terms often accompany it. C relates to sources with a fairly even spectrum, such as speech, radio and television and many everyday activities. Ctr relates to urban road traffic and other sources rich in low frequencies, among which the standard lists disco music. A rating written Rw (C; Ctr) = 45 (−1; −5) dB tells the reader that the element is noticeably weaker against bass-heavy sound than its main number suggests.
DnT,w is the quantity building regulations usually address, because it describes what occupants experience between two rooms: the level difference adjusted to a standard reverberation time in the receiving room. It depends on the partition, the flanking paths and the size of the rooms, so the same wall gives different DnT,w values in different rooms.
Leaks
Sound passes through gaps far more easily than through any wall. For a partition made of parts with different transmission coefficients, the total transmission is the area-weighted average of their τ values, and the weakest part dominates. Take a wall of R = 50 dB, τ = 0.00001, with an open gap covering 1 % of its area, τ = 1 for the gap. The combined transmission coefficient is about 0.01 and the composite R about 20 dB. With a gap of 0.1 % of the area it is about 30 dB. Neither figure depends much on how good the wall is. Narrow slits can transmit even more than their area suggests, especially at frequencies where they resonate.
Door seals, cable entries, ventilation openings, gaps around frames and the joints between a partition and the floor or ceiling therefore deserve as much attention as the partition itself.
Small enclosures and booths
A small enclosure, a booth for one or two people standing inside a larger room, combines all of these issues in a demanding form. Its walls are usually light, because it has to stand on an ordinary floor and may need to be moved. Glazing is common, and glass has its coincidence dip in the speech range. It has a door whose seals must work every time it closes. And it needs ventilation, since a closed box with a person inside soon warms up and the air goes stale. Each ventilation path is an opening, which needs attenuating ducts or baffles. Inside, the volume is so small that the space behaves modally over much of the speech range, and absorption on the inner surfaces is needed to stop speech sounding boxy and to keep the level inside from building up.
Classic sound reduction indices fit such an object poorly. It is a free-standing body in a room, leaking sound in all directions, and the practical question is how much less a neighbour hears of a voice inside.
ISO 23351-1 answers that question with the speech level reduction, DS,A. In outline, a loudspeaker reproducing a standardised speech spectrum is placed inside the enclosure where a user's mouth would be, and the A-weighted speech level is measured at a set of positions around it. The enclosure is then taken away and the measurement repeated with the source in the same place. DS,A is the difference, in decibels, between the speech levels without and with the enclosure. The standard covers furniture ensembles, such as high-backed seating groups and screened work points, as well as closed enclosures. Because DS,A is A-weighted and based on speech, it relates directly to privacy and distraction, the subjects of speech in open-plan rooms.
Why the laboratory value and the experience differ
The same enclosure can feel better or worse in use than its laboratory number suggests.
Background noise. Privacy depends on how far the leaked speech lies below the background noise. A given DS,A gives more privacy in a busy room than in a silent one.
The room around it. A real room may be more reverberant than the test room, letting leaked speech build up, or may put a hard wall or a window right beside the enclosure, reflecting sound towards listeners.
Voices. The test uses a standard speech level. People on calls, in heated discussion or wearing headphones often speak louder, and the leaked level rises with them.
Ventilation and doors. Fans add noise inside and sometimes outside, vents are designed openings, seals age, and doors are sometimes left ajar. It is worth checking how the ventilation was set during the test.
Direction of listening. DS,A describes sound going out. The user inside is concerned with sound coming in and with how the small space itself sounds, which also depends on the noise of the surrounding room and on the absorption inside.
Spectrum. A single A-weighted number summarises a whole spectrum. Two enclosures with the same value can differ at low frequencies, which matter for deep voices and for music, or at high frequencies, which carry much of the information in consonants.
The same distinctions apply to larger rooms for sound. A rehearsal or recording room needs insulation in both directions, to keep music in and to keep outside noise away from the microphones. Several studios appear in the recording chronology, among them the BEX-Studio in Cologne for RA 010 and AirWave Recording Studios in Chicago for RA 023; the release pages say nothing about how those rooms were built. The inside of such rooms is the subject of recording rooms, and the section index lists all six articles.
Key terms
- Sound reduction index (R): 10 · lg(1/τ), the insulation of a building element measured in the laboratory, in dB.
- Weighted sound reduction index (Rw): the ISO 717-1 single-number rating of R, read at 500 Hz from a shifted reference curve.
- Standardised level difference (DnT,w): the weighted field level difference between two rooms, adjusted to a reverberation time of 0.5 s.
- Flanking transmission: sound travelling between rooms through paths other than the separating element.
- Mass law: the rule that the insulation of a limp single panel rises by about 6 dB per doubling of mass or frequency.
- Speech level reduction (DS,A): the ISO 23351-1 reduction in A-weighted speech level provided by an enclosure or furniture ensemble.