What Reverberation Time Controls, and What It Does Not

Why this matters

Reverberation time is the one acoustic number a general contractor, an architect and a facility manager are all likely to have heard of, which makes it the number that gets asked for whether or not it is the right one. It is a genuine, measurable, designable property and it answers exactly one question: how long energy takes to decay in a room after the source stops. It does not tell you how loud that room is, it does not tell you whether the neighbour can hear you, and below a frequency you can compute in ten seconds it stops meaning anything at all. What follows is the design sheet you fill in when reverberation time actually is the deliverable, and the arithmetic that decides how much material to buy.

What the number is, exactly

Reverberation time is the time for the sound pressure level in a room to fall 60 dB after the source is cut. It is written T60 and it is frequency dependent, so it is quoted per octave band or per one-third-octave band, never as one number without a band. In practice a decay is measured over a smaller range, commonly 20 or 30 dB, and extrapolated, which is why field reports carry designations such as T20 or T30.

The design relationship, in the classical diffuse-field model, is Sabine's:

T60 = 0.049 x volume / total absorption      (feet and square feet)
T60 = 0.161 x volume / total absorption      (metres and square metres)

Total absorption A is the sum over every surface of its area times its absorption coefficient at that band, plus the absorption of occupants and furnishings. That is the whole design tool. Volume in the numerator is the reason a tall room rings longer than a low one with the same finishes, and it is why volume is a decision, not a given, on a room you are still designing.

The design sheet

Six fields, in the order they get filled and each one for a reason.

1. Band. Pick it from the use, not from habit. Speech rooms design at 500 Hz and 1000 Hz and check 125 Hz. Nothing about this sheet is valid across bands at once.
2. Volume. Interior volume in consistent units. This is the term you cannot buy your way out of later.
3. Total surface area, and the coefficient of each surface at the chosen band. Take the coefficients from the product's own ASTM C423 report with the mounting per ASTM E795, in the editions the specification cites, not from a four-band average; a sibling card covers why an averaged rating hides exactly the band you need, and a coefficient tested in one mounting does not transfer to another.
4. Existing total absorption. Areas times coefficients, summed, including people if the room is used occupied.
5. Target T60, and therefore the total absorption the target requires. Then the deficit.
6. Added absorption, computed as a difference. Panel coefficient minus the coefficient of whatever the panel covers, times panel area. Charging the full panel coefficient counts the covered surface twice.

Then a validity check, which is the field most sheets are missing: if the resulting average absorption coefficient climbs much above 0.2, Sabine's model is no longer the right one and the sheet has to be re-run on Eyring's.

The sheet, filled in

A multipurpose room, 40 ft by 30 ft by 12 ft. Design band 500 Hz. Every coefficient below is at that band.

• Volume: 14,400 ft3.
• Surfaces: 2,400 ft2 of floor and ceiling, 960 ft2 of long walls, 720 ft2 of end walls. Total 4,080 ft2.
• Existing average coefficient: 0.10, so A = 408 sabins.
• Existing T60: 0.049 x 14,400 / 408 = 1.73 s. Loud, echoic, and unusable for speech.
• Target T60: 0.80 s, which is a reasonable speech target for a room this size and is a design choice, not a code requirement.
• Absorption the target requires: 0.049 x 14,400 / 0.80 = 882 sabins. Deficit 474 sabins.
• Correction, printed: added absorption is a difference. Panel coefficient 0.80 at 500 Hz, going onto wall and ceiling surfaces that read 0.05 at that band, so each square foot adds 0.75, not 0.80. Panel area required = 474 / 0.75 = 632 ft2.
• Validity check: new average coefficient = 882 / 4,080 = 0.216, which is past where Sabine's assumptions sit comfortably. The sheet is not finished.

The correction that changes the panel count

Sabine's model assumes absorption is low enough that a sound ray survives many reflections. Once the average coefficient rises, Eyring's form is the right one:

T60 = 0.049 x volume / ( -surface area x ln(1 - average coefficient) )

This is a re-basing, not an added term. It replaces Sabine's A with a different expression for the same physical quantity; you do not compute Sabine and then subtract something.

Run the sheet's own answer through it. With 632 ft2 of panel installed, average coefficient 0.216: -4,080 x ln(0.784) = 4,080 x 0.2434 = 993. T60 = 705.6 / 993 = 0.71 s. Design to Sabine and you land at 0.71 s against a 0.80 s target, a drier room than intended.

Solve for the target on the correct basis. Set 705.6 / (-4,080 x ln(1 - a)) = 0.80. Then -ln(1 - a) = 882 / 4,080 = 0.2162, so a = 0.194 and A = 4,080 x 0.194 = 793 sabins. Deficit from the existing 408 is 385 sabins, and the panel area is 385 / 0.75 = 514 ft2.

What that is worth. 632 ft2 against 514 ft2 is 23 percent more panel than the room needs, bought and installed, to overshoot the target. Which of the two governs is not a judgement call: at an average coefficient above roughly 0.2, Eyring governs and Sabine is the approximation.

Held constant, stated. Both forms assume air absorption is negligible, which is true at 500 Hz and stops being true above about 2000 Hz in a large room, where a term proportional to volume has to be added. Both assume a diffuse field, which requires the absorption to be reasonably distributed. Putting all 514 ft2 on one surface of a six-surface room is concentrated absorption and returns less than either model predicts, so distribute it across at least two planes.

Sibling-rule check, printed. Coefficients taken per named octave band rather than from a four-band average, per the absorption-rating card: yes. Added absorption computed as panel coefficient minus covered-surface coefficient: yes. The model's validity condition checked against the post-treatment figure rather than the pre-treatment one, and the sheet re-run when it failed: yes. The correction identified as a re-basing rather than an addition, with the governing form named: yes. Panel quantity rounded up rather than down, which is away from the flattering direction.

When you go to measure the result, the impulse source is a real hazard and it gets treated as one. A blank-firing pistol or a burst balloon can produce peak sound pressure levels approaching or exceeding the 140 dB peak figure that the footnote to Table G-16 at 29 CFR 1910.95(a) states should not be exceeded. Everyone in the room wears hearing protection, nobody stands close to the source, and a firearm of any kind is not brought into an occupied building without the owner's written agreement. An interrupted-noise decay from a loudspeaker avoids the whole question and is what most field work uses.

What reverberation time does not predict

How loud the room is. T60 depends on volume divided by absorption. Steady-state level depends on absorption, distance and directivity, and volume is not in it. Two rooms with identical T60 can be far apart in level.

Take the room above at its 882 sabins and 0.80 s, room constant R = 882 / 0.784 = 1,125. Now a small office, 20 ft by 15 ft by 12 ft, so 3,600 ft3 of volume and 1,440 ft2 of surface, with 220 sabins. Its T60 = 0.049 x 3,600 / 220 = 0.80 s, identical. Its room constant is 220 / 0.847 = 260. The reverberant term is 4/R in both cases, so the same source produces a reverberant level 10 log10 (1,125 / 260) = 6.4 dB higher in the small room. Same reverberation time, two thirds of the way to twice as loud. A sibling card owns why the same machine reads differently in two rooms; the point here is that T60 is not the number that tells you.

Whether the neighbour hears you. That is transmission across a boundary and it is a property of the partition and the paths around it, not of either room's decay. Two sibling cards own it.

Whether a listener can follow a talker. Intelligibility depends on the ratio of direct to reverberant energy at that listener's position and on the background level, both of which depend on distance and on the source. A room can meet a T60 target and still fail a talker at the back.

Where the statistical model stops applying

Below a certain frequency a room does not have a reverberant field at all; it has individual resonances, and a decay measurement there is measuring one or two modes rather than a statistical average. The crossover is estimated by the Schroeder frequency, approximately 2,000 times the square root of T60 divided by volume with volume in cubic metres, or approximately 11,900 times the same square root with volume in cubic feet.

• Multipurpose room above: 11,900 x square root of (0.80 / 14,400) = 89 Hz. The statistical model is usable through the whole speech range.
• Small office above: 11,900 x square root of (0.80 / 3,600) = 177 Hz. Everything at and below the 125 Hz octave band in that office is modal, and a reverberation time quoted there describes a couple of resonances, not a room.

That is the honest limit of the whole tool, and it explains a recurring field result: a small room treated to a correct T60 target that still sounds boomy. The treatment worked in the bands the model covers, and the complaint lives below them. Whatever you install to fix it, install it under the same rules as any other interior finish, meaning a surface burning characteristics class suitable for the occupancy and location tested to ASTM E84 in the edition the adopted code references, clear of sprinkler heads under NFPA 13 in the edition your authority having jurisdiction adopted, and anchored to structure rather than to ceiling hanger wire.

References

• ASTM C423 and ASTM E795 for absorption coefficients and mounting; ASTM E84 for surface burning characteristics; in the editions the specification or adopted code cites, since consensus standards bind through that reference rather than on their own
• NFPA 13, in the edition adopted by the authority having jurisdiction, for sprinkler coverage and obstruction
• 29 CFR 1910.95, including the 140 dB peak figure in the footnote to Table G-16 at (a), for occupational noise exposure in general industry
• See related: What Absorption Does That Blocking Cannot; What an NRC Rating Actually Tells You; Why the Same Machine Reads Differently in Two Rooms; What Speech Intelligibility Depends On