ACOUSTICS OF THE ROOMS
This science studies, as its name indicates it, the emission perception and especially the absorption of sounds (music, noise) in a building. The experience made it possible to model and thus to establish a rather reliable theory of the various phenomena in acoustics, notemment with Sabine.
In the sound study of a room, modeling will make it possible thanks to a diagnosis to cure of the various problems such as sound-proofing. A too noisy room where one owes shout to hear the interlocutor is a typical case of negligence in terms of acoustics; it is also the case in a large majority of establishments (restaurants, shopping centers, public buildings, etc). The bad design of these various buildings and the feeling of faintness for the people proved that it is harmful for health. European standards are spirit to set up itself to regulate this type of problems in the future.
Physical study of the phenomenon
Time of reverberation
By the experience, one defines the time of reverberation like the time put by the waves for deaden after reflexion on the walls of the room. This atenuation decreases as a logarithm.
During the emission of a sound, this one is broken up into direct sounds and reflected sounds . The direct sounds are perceived in the first : they move in straight line. they are of a low intensity. The sounds reflected follow the direct sounds and then the sounds more reflected after reflexion on the walls of the studied room.
Finally there is a atenuation of the emitted sound, by absorption in the air and the walls.
One can measurement this atenuation thanks to a sonometer.
One defines the time of Tr reverberation as a fall of the loudness of 60dB. This Tr varies according to the geometry and the coating of the room.
In a very sound room the sounds mix, in a not very sound room the sounds one of the evil has to be perceived... it is necessary to find a happy medium.
Modeling
A modeling (semi-empirical) of the phenomenon draws up a relationship between the average absorption coefficient of the walls, the surface and the volume of the room:
Tr = F (V, S, K) where F is a function compared to the Volume of the room, its side Surface and K, coefficient absorption of the walls. For K = 0 step of absorption (100% reflecting)
K = 1 : 100% of absorption (0% reflecting)
Side surface is taken as the assessment of absorbing surfaces ex: glaze = 0% of absorption
Index I is established: If and Ki are the absorption surface and coefficient respectively of the hardware in question. It is deduced that the sum of If is not different than side surface. Total surface, summons Si*Ki product is called the surface of Sabine.
Formulate of Sabine
According to the experience, one could determine in an approximate way time of reverberation of an acoustic room. This formula was established by Sabine:
Tr = 0.16 * V / Aire de Sabine
= 0.16 V/S i(Ki*Si)
Tr = 0.16 * V / Surface of Sabine
V: volume of the room (in m3)
Surface of Sabine: S i (Ki*Si) (en m²) K not having a unit
This formula does not take charge of the mobillier nor possible people who can be in the room. It is necessary to add to the surface of Sabine an equivalent. One can calculate the coefficient of obsorption and surface averages of a person... and then after multiplying this Sabine unit obtained by the number of witnesses. One will more precisely see it in the example.
Types of materials used
One distinguishes 3 types of materials used in the construction of an acoustic room.
The porous materials are used for the absoption. They are particularly effective for absorb the high frequencies. The small pores absorb the short wavelengths.
The diaphragm is designed to stop the low frequencies and to deaden them. Materials like the isorel (compacted paperboard, plywood) are effective for frequencies going up to 500 Hz. Another method implies the suspension of materials in question by leaving a space of air inside. The air plays in this case a role of piston.
The resonators (material assembly of absorption) are used to treat the peaks of resonance. For this technique there is a selective absorption in a frequency band suitable for the frequency of the room.
Some practical rules
Examples of application
Example 1 We want to envisage a studio of recording of 200m 3 envisaged for a formation of jazz. The time of optimal Tr reverberation to 1000Hz of 0,7s is maintained for all the frequencies.
Surface of Sabine: S i Si*Ki + equivalent
According to the formula of Sabine; Tr = 0.16*V/(surface of Sabine)
Surface of Sabine = 0,16 * V / Tr = 0.16 * 200 / 0.7 = 46m²
One must thus envisage materials to approach this value to obtain desired acoustics.
Hard Isorel in diaphragm with 50mm and teases mineral
Let us determine the surfaces of Sabine A for 3 critical frequencies:
It was seen that the isorel is effective for the absorption of serious sounds: for a frequency of 125Hz the absorption coefficient is worth 0.32. For acute sounds, the absoption of this hardware falls in K=0,09 (1000Hz and 4000Hz).
The mineral wool (here one has 45m²) is particularly absorbing for frequencies bordering the 1000Hz, for that frequency coeffient it K=0.96. For the low sound, with 125Hz, K=0.27. Finally, for an acute sound (4000Hz) K = 0.76
While recapitulating:
| frequency | 125Hz | 1000Hz | 4000Hz |
| surface/material | coeff / A | coeff / A | coeff / A |
| 80m²/ isorel | 0.32 / 25.6 | 0.09 / 7.2 | 0.09 / 7.2 |
| 45m²/ mineral wool | 0.27 / 12.15 | 0.93 / 41.85 | 0.76 / 34.2 |
| Total/Sabine unit | 37.75 | 37.75 | 41.40 |
To finish, it is necessary to add remaining surfaces of the room, such as glass (panes) and plasters it. These materials will increase little the result.
| frequency | 125Hz | 1000Hz | 4000Hz |
| Surface of Sabine Total + other surfaces |
45 |
55 |
50-55 |
Example 2
One wants to improve the acoustic of a concert hall of capacity 3000 witnesses. One will put all the parameters in the form of table:
Volume of the room: 11400m3
| Material |
Surface |
Coefficient |
Sabine Unit |
| Plaster | 22000m² | 0.033 | 73 |
| glas | 17m² | 0.027 | 0.5 |
| wood | 235m² | 0.061 | 14.4 |
| hanging | 80m² | 0.250 | 20 |
| witnesses* | 1500m² | 0.440 | 660 |
| Orchestrates | 80m² | 0.440 | 35.2 |
| TOTAL | 11400m² | 803.1 |
* here it is supposed that a person occupies 1m². In this case, the room is with empty half
From where, the formula of Sabine is applied:
Tr = 0.16 * 11400 / 803.1 = 2.27s (for the room with empty half)
According to the practice, the ideal time of reverberation must be between 1.2s and 1.7s
For a full room, one displays Tr=3.86s which is strong.
For the empty room, Tr=10s
To improve acoustics of this room materials are treated. In this case one increases absorption to lower the time of reverberation. Obviously one treats the plaster by perforating it, one adds perforated flagstones, synthetic materials, resonators which deaden the effect.
In result one finds for the plaster:
Surface coefficient Sabine unit 2200m² 0.4 880
One thus finds Tr = 1,131 if the room is half-empty. the result proves that one is under the ideal conditions