What Speech Intelligibility Depends On

Why this matters

The most common fix applied to a room where people cannot follow each other is more level: a louder talker, a bigger speaker, a microphone. That fix works against one of the two things limiting intelligibility and does exactly nothing against the other, because the second one scales with the talker. In the worked room below, six more decibels of vocal effort buys six decibels of signal-to-noise ratio against the mechanical background and moves the late-energy fraction by zero. Knowing which limiter you are looking at is the difference between a job that lands and one where the customer says it sounds louder and is still no easier to follow.

Intelligibility is a ratio, and it is a ratio of two things at once

Ratio one: signal to noise, at the listener, in the speech bands. Speech information lives mostly in the 500, 1000, 2000 and 4000 Hz octave bands. Consonants carry nearly all of the intelligibility and they are the quiet, high-frequency part of speech. Vowels are loud, low and carry very little information. That is why a background noise that is loudest at low frequency can leave speech "audible" and unintelligible at the same time: you hear the vowels and lose the consonants.

The ratio is stated as A-weighted sound pressure level of speech minus A-weighted sound pressure level of background, both re 20 micropascals, overall, at the listener's ears. ANSI/ASA S12.60 Part 1, a voluntary consensus standard that binds only where a state or district has adopted it or a specification calls it out, is built around a signal-to-noise ratio of at least +15 dB at the child's position and a background of 35 dB, A-weighted, one-hour average, in core learning spaces under 20,000 cubic feet.

Ratio two: early energy to late energy. The ear integrates reflections that arrive within roughly the first 50 milliseconds of the direct sound into the direct sound; they add to the useful signal. Reflections arriving later smear one syllable across the next and act as noise generated by the talker. This is what people mean when they say a room is "live."

An intelligibility metric such as the Speech Transmission Index, measured to IEC 60268-16 in the edition your specification names, combines both ratios into one number from 0 to 1. It exists because neither ratio alone predicts the outcome.

What does not appear in either ratio

This is where the money goes wrong.

• The talker's absolute level, once the room is the limiter. Both the direct sound and the reverberant tail come from the same mouth. Raising vocal effort by 6 dB raises both by 6 dB and leaves early-to-late unchanged.
• Overall A-weighted background alone. Two backgrounds at the same overall A-weighted level can differ by 10 dB or more in the 2000 Hz octave band, which is the band that eats consonants. The per-band spectrum is the thing, and a criterion curve comparison is how you look at it.
• Room volume by itself. A large room with short reverberation is easier than a small hard one. What matters is absorption relative to volume, not either alone.
• A ceiling tile called "acoustic." A tile has an absorption coefficient per octave band from an ASTM C423 test on a stated mounting. Some are absorptive; some are mostly a facing. Read the report.
• Low-frequency absorption. A 1 or 2 inch porous panel does most of its work above about 500 Hz. It helps speech and does very little for a 125 Hz rumble, which is a different complaint with a different fix.

Telling the two limiters apart in the field

Two checks, and neither needs an analyzer.

Move closer. If intelligibility improves sharply as the listener halves the distance to the talker, the direct sound is still winning at that distance and the room is not yet the limiter. If halving the distance changes very little, the listener is well beyond critical distance, which is the distance at which the direct sound and the reverberant field are equal, and level is not your lever.

Turn the mechanical off. If the complaint largely goes with the air handler, the limiter is signal-to-noise and the fix is on the noise side. If the complaint survives with the fan off, the limiter is the room's own late energy and the fix is absorption placed where reflections arrive late.

Worked example: why the far end of the table is hard to follow

The same conference room used in the absorption-or-isolation article: 20 ft by 14 ft by 9 ft, 2,520 cubic feet, 1,172 sq ft of surface, painted gypsum walls and ceiling over carpet on slab. Total absorption at the 500 Hz octave band is 142.6 sabins, giving 0.87 seconds of reverberation. After 72 sq ft of 2 inch panels are added, absorption is 207.4 sabins and reverberation is 0.60 seconds.

Critical distance, before treatment. Room constant R = total surface x average absorption coefficient, divided by (1 minus that coefficient). Average coefficient = 142.6 / 1,172 = 0.122, so R = 142.6 / 0.878 = 162 sq ft. Critical distance = 0.141 x the square root of (directivity x R), and this relationship is derived for a point source in a diffuse room, holding source directivity constant. Taking a talker facing the listener as a directivity of 2: 0.141 x square root of (2 x 162) = 0.141 x 18.0 = 2.5 ft.

After treatment: average coefficient 0.177, R = 207.4 / 0.823 = 252 sq ft, critical distance = 0.141 x square root of 504 = 3.2 ft.

Everyone past the first seat is in the reverberant field, before and after. That single number explains the complaint.

What distance actually costs, after treatment. Level at a distance follows the direct term (directivity divided by 4 pi r squared) plus the reverberant term (4 divided by R), with r in feet and R in square feet so the units cancel in the ratio:

• At 3 ft: direct 2 / (4 x pi x 9) = 0.01768; reverberant 4 / 252 = 0.01587; total 0.03355
• At 10 ft: direct 2 / (4 x pi x 100) = 0.00159; reverberant 0.01587; total 0.01746
• Difference: 10 x log10 (0.03355 / 0.01746) = 10 x log10 (1.921) = 2.8 dB

Free-field intuition says 20 x log10 (10/3), which is 10.5 dB. The room delivers 2.8 dB. The person at the far end is barely quieter and much harder to follow, which is the observation that sends people looking for a hearing problem that is not there.

Signal to noise at the far seat. Normal vocal effort is published in the range of roughly 55 to 60 dB, A-weighted sound pressure level re 20 micropascals, overall, at 1 m on axis. Take the low end, 55 dB, because assuming a quiet talker is the conservative direction for a design that has to work for quiet talkers. Diffuser noise measured at the far seat is 42 dB, A-weighted, overall, equivalent-continuous over 5 minutes.

Speech at 10 ft, after treatment, is 2.8 dB below the near-seat value. Taking 1 m as approximately the 3 ft near-seat distance, which is worth about two tenths of a decibel in this room and is stated rather than folded in, and working from 55 dB there: 52.2 dB, A-weighted, overall. Signal-to-noise ratio at the far seat is 52.2 minus 42, which is +10.2 dB. Positive, comfortably audible, and below the +15 dB that the classroom standard treats as the design target.

Late energy, before and after. In a diffuse field decaying exponentially, energy falls 60 dB in one reverberation time, so the decay constant is 13.8 divided by the reverberation time, and the fraction of the reverberant energy still arriving after 50 milliseconds is e raised to the power of minus 13.8 times 0.05 divided by the reverberation time. This treats only the reverberant field and holds the direct sound out of it.

• At 0.87 seconds: e to the minus 0.793 = 0.45. Forty-five percent of the reverberant energy arrives too late to help.
• At 0.60 seconds: e to the minus 1.15 = 0.32. Thirty-two percent.

Now price the two fixes against those numbers.

• Six more decibels of vocal effort: signal-to-noise ratio goes from +10.2 to +16.2 dB, past the target. Late fraction stays at 45 percent, because the tail rose 6 dB with the voice.
• The 72 sq ft of absorption: late fraction goes from 45 percent to 32 percent, a real gain on the smearing. Signal-to-noise ratio changes only slightly, because absorption pulls the reverberant contribution of speech down along with everything else.

Neither fix alone addresses both limiters, and that is the whole point. In this room, if the complaint is "I can hear them but I cannot make out words," the late energy is the limiter and absorption is the work. If the complaint is "I cannot hear them at all," the background is the limiter and the diffuser is the work.

Sibling-rule check. Every level above carries quantity, weighting, reference, bandwidth and time basis. The critical distance relationship carries its geometry (point source, diffuse room, stated directivity of 2) and the level-versus-distance arithmetic is a ratio in consistent feet, so no unit constant is smuggled in. The absorption values and the resulting reverberation times are the same figures the absorption-or-isolation article derived at the same 500 Hz octave band, and this article states the same direction: absorption lowers reverberant level, raising background lowers intelligibility. The vocal effort figure was taken at the low end of its published range rather than the middle, which is the conservative direction. The Sabine-derived numbers are stated at one octave band and are not carried to another.

Verifying you called it right

Word-score test, free and honest. Pick a list of unrelated two-syllable words, have a talker read twenty of them from the far position at normal effort with the listener facing away so lip reading is out, and score. Do it before the work and after, at the same seat, with the mechanical in the same state. A jump from a poor score to a good one at unchanged vocal effort is the absorption doing the work.

Where a specification or a dispute is involved, the measurement is a Speech Transmission Index to IEC 60268-16 or a reverberation time to ISO 3382-2, at the octave bands the specification names, and it is worth saying up front which standard and which edition the acceptance is being judged under.

The failure mode: treating a signal-to-noise problem with absorption. Absorption lowers the reverberant contribution of speech and of the mechanical background together, so it does not reliably improve the ratio between them. A room where the fan is the problem gets quieter and no clearer, and the panels were the wrong purchase.

References

• ANSI/ASA S12.60 Part 1 for classroom background and signal-to-noise design targets, binding only where a state, district or specification has adopted it, in the edition adopted.
• IEC 60268-16 for the Speech Transmission Index and ISO 3382-2 for reverberation time, in the editions the specification names.
• ASTM C423 for absorption coefficients and NRC, including the mounting used in the test; the tested product's own report owns the number.
• See related: How to Decide Whether a Room Needs Absorption or Isolation; What Background Noise Does That Is Actually Useful; What a Noise Criterion Curve Is For.