Sound absorption coefficient: reading α, αs, αp and αw correctly

The sound absorption coefficient α is the ratio of non-reflected to incident sound energy. A value of 0 means complete reflection; a value of 1 means that none of the incident energy comes back, in other words it is absorbed or transmitted. α depends on frequency: the same material usually absorbs low and high tones very differently. That is exactly why it is measured in one-third-octave bands.

It is important to distinguish two families of definitions. The geometric or angle-dependent absorption coefficient refers to a plane wave striking a surface at a specific angle. It is always smaller than 1.0 and can be expressed as a percentage. The value given in product datasheets, by contrast, is almost always the Sabine absorption coefficient αs from the reverberation room. ISO 354:2003 defines αs as the Sabine absorption coefficient derived from the difference in reverberation times and points out explicitly that αs can take values greater than 1.0 because of diffraction at the specimen edges.

The most important quantities at a glance: αs is the Sabine absorption coefficient measured per one-third-octave band to ISO 354. αp is the practical absorption coefficient, which ISO 11654 forms by averaging three one-third-octave values into one octave value. αw is the weighted sound absorption coefficient, a single frequency-independent number. Alongside them exist the North American single-number ratings NRC and SAA to ASTM C423. These quantities follow different averaging and rating procedures, so they cannot be converted directly into one another. That has practical consequences: NRC and αw often come out differently for the same material, and anyone who equates the labels ends up comparing unlike with unlike.

αs is determined in the reverberation room. The principle under ISO 354:2003 is simple: the mean reverberation time of the room is measured once empty and once with the specimen installed. From the difference of the reciprocal reverberation times, the Sabine equation yields the equivalent absorption area of the specimen AT; dividing by the covered area S gives the absorption coefficient αs = AT / S.

The equivalent absorption area according to Sabine is A = 0.161 · V / T (metric, with V in m³ and T in s). Written more exactly in physical terms it is A = 55.3 · V / (c · T), where c is the speed of sound; at around 20 °C and c of around 343 m/s this gives the 0.161. ISO 354 additionally requires a correction for air absorption via the term 4mV, which is noticeable above all at high frequencies and low humidity. That is why the standard prescribes a climate with a relative humidity between 30 and 90 percent and a temperature of at least 15 °C.

The boundary conditions are strict because the method presupposes a diffuse sound field. The reverberation room must have a volume of at least 150 m³; for new rooms at least 200 m³ is recommended. The specimen of a flat covering should be between 10 m² and 12 m², rectangular with a width-to-length ratio between 0.7 and 1. Measurements are taken in one-third-octave bands from 100 Hz to 5000 Hz to ISO 266, with at least 36 evaluated decays.

The mounting is inseparable from the measured value. ISO 354 regulates several mounting types in its normative Annex B. Type A means mounting directly on the room surface, type J the freely hanging units and sound baffles; in addition there are mountings with a defined cavity behind the specimen and with a perimeter frame. A perforated panel absorber or an acoustic ceiling gains considerably more absorption at low frequencies with a 200 mm cavity than directly on the wall. The mounting and the cavity behind the absorber are therefore always part of the measured value; usual test cavities are 200 mm in ISO practice and 400 mm in ASTM practice. An αs value without the mounting stated is practically worthless, because the same material can differ by whole classes depending on the build-up.

ISO 11654:1997 condenses the measured curve in two steps. First, the practical absorption coefficient αp is formed from the one-third-octave values: for each octave band the arithmetic mean of the three one-third-octave values within it is taken. The result is rounded in steps of 0.05 and, for means above 1.00, capped at αp = 1.00. αp is usually stated for the octave bands 125, 250, 500, 1000, 2000 and 4000 Hz.

In the second step the weighted absorption coefficient αw follows from the αp values. For this a standardised reference curve over the octave bands 250, 500, 1000, 2000 and 4000 Hz is used. The reference curve has the values 0.40 at 250 Hz, 0.60 at 500, 1000 and 2000 Hz and 0.50 at 4000 Hz.

The reference curve is shifted towards the measured curve in steps of 0.05 until the sum of the unfavourable deviations is less than or equal to 0.10. An unfavourable deviation occurs when the measured value lies below the reference curve; only these are counted. αw is then defined as the value of the shifted reference curve at 500 Hz. αw is therefore always a multiple of 0.05.

This reading at 500 Hz is the core of the criticism of the single number: αw condenses a whole curve onto a single support point in the mid-frequency range. Two products with identical αw can lie far apart at 125 Hz or at 4000 Hz. ISO 11654 points out in its scope that the single-number rating does not replace the complete curve and that the complete frequency-dependent data should be consulted for a more precise assessment. Moreover, the rating only starts at the 250 Hz octave band; everything below it is not represented by αw at all.

To recover part of the most important lost information, ISO 11654 has the shape indicators L, M and H. They are placed in brackets after the αw value, for example αw = 0.70 (MH). An indicator is assigned when the practical absorption coefficient αp exceeds the shifted reference curve by 0.25 or more at at least one point.

The assignment is clearly regulated: if the excess occurs at 250 Hz, the indicator is L (low frequencies). At 500 Hz or 1000 Hz it is M (medium, mid frequencies). At 2000 Hz or 4000 Hz it is H (high frequencies). Negative deviations do not trigger an indicator; they are already caught by the 0.10 limit in the shifting procedure.

In practice a shape indicator is a warning sign from the standard to the planner: here there is a pronounced strength outside the mid range that the bare αw value swallows. If an indicator is present, the complete absorption curve should be consulted, which is what the standard intends. An L indicator, for instance, can make an otherwise mediocre αw value considerably more interesting for a room with a low-frequency problem than the class would suggest.

Annex B of ISO 11654 assigns a sound absorption class to every αw value. This annex is informative, so it is not a binding requirement of the standard, but it has established itself as the language of marketing and specifications. Class A stands for the highest absorption.

The limits are: class A covers αw from 0.90 to 1.00 (that is 0.90, 0.95, 1.00). Class B covers 0.80 and 0.85. Class C covers 0.60 to 0.75 (0.60, 0.65, 0.70, 0.75). Class D covers 0.30 to 0.55. Class E covers 0.15, 0.20 and 0.25. Values from 0.00 to 0.10 are not classified.

A class bundles a whole span of αw values, and each of these values in turn hides a whole curve. Class C runs from 0.60 to 0.75; two class C products can therefore already differ by 0.15 in αw. Even with exactly the same αw = 0.90 (both class A), the frequency responses can differ strongly. One product shines at 2000 to 4000 Hz and fails below 250 Hz, the other is balanced across the whole band. The datasheet says class A in both cases. The class answers the question of the total amount of absorption. In which frequency range that absorption lies, it does not say.

In North America, measurements follow ASTM C423 and are rated with different single-number values. The NRC (Noise Reduction Coefficient) is the arithmetic mean of the absorption coefficients at 250, 500, 1000 and 2000 Hz, rounded to the nearest multiple of 0.05. The SAA (Sound Absorption Average) is the mean of the twelve one-third-octave bands from 200 Hz to 2500 Hz, rounded to 0.01, and thus more finely resolved than the NRC.

The methodological difference from αw is fundamental. NRC and SAA are pure means over a fixed frequency range. αw arises from shifting a reference curve and reading at 500 Hz, so it implicitly weights differently and penalises dips below the curve. That is why NRC and αw often do not agree. For materials with pronounced high-frequency absorption, the NRC or SAA tends to be higher than αw, because the averaging counts the high bands in full while the reference curve weights them less. It is precisely in such cases that ISO 11654 typically assigns an H shape indicator. The direction of this deviation is well documented; its size depends on the individual product.

For comparison this means: NRC, SAA and αw cannot be converted directly into one another. Anyone comparing a North American product with a European one should bring both back to the common basis, that is to the one-third-octave or octave curve. A serious data platform therefore puts the raw αs curve in the foreground and derives the single-number ratings from it transparently, instead of placing incomparable labels side by side.

Datasheets occasionally give αs values such as 1.05 or 1.15. That does not violate the law of conservation of energy. It is a well-known artefact of the reverberation room measurement. ISO 354 names this effect explicitly: αs can take values greater than 1.0 because of diffraction effects.

The cause is the edge effect. A specimen of finite size, 10 to 12 m², has free edges at which sound is diffracted into the specimen. Cox and D'Antonio (Acoustic Absorbers and Diffusers) explain this with the impedance discontinuity at the specimen edges: the effectively absorbing area is larger than the geometric area S that stands in the denominator of αs = AT / S. Typically, a strongly absorbing specimen can behave acoustically like a somewhat larger area, from which values above 1.0 arise arithmetically, for example around 1.08 to 1.17. This range is a worked example and not a standard value, since the effect depends on material, geometry and reverberation room.

The effect grows with the ratio of edge length to area and with the absorption strength of the material. Small or narrow specimens, highly absorbing foams and freely hanging absorbers show it particularly clearly. In practice an αs above 1.0 means two things: first, the material really is very strongly absorbing. Second, the numerical value should be treated with caution, because it depends on specimen geometry and reverberation room and cannot be transferred one to one to a full-area covering in a real room. For the formation of αp and αw, ISO 11654 caps such values at 1.00 anyway.

Selection begins with the question of which acoustic problem in the room is to be solved. A room for speech to DIN 18041 (the German standard for reverberation time targets; room group A, use type speech) needs above all uniform absorption in the speech range of 250 to 4000 Hz. A recording studio or a room with booming bass needs low-frequency absorption below 250 Hz, which is exactly where αw and the classes are blind. In that case an L shape indicator or the αp values at 125 Hz matter more than the class.

Three pieces of information therefore always belong together: first the frequency-resolved curve (αs per one-third-octave band or αp per octave band), second the mounting and construction depth, third the measurement source together with the standard. Without the mounting the curve is not reproducible; without a test report the origin is unclear. The single number αw and the class are useful for a rough preselection and for specification texts. As the sole basis for a decision they are not fit for purpose.

If you lay the αs curves of many manufacturers side by side over the same one-third-octave bands, it becomes immediately visible that class A comprises a whole family of very different frequency responses. A comparison at curve level, filtered by mounting and frequency emphasis, corrects the misleading impression that all class A products are the same. Anyone planning should select by the shape of the curve that suits the room and treat the class only as a rough indicator of quantity.