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8. ACOUSTICS OF ROOMS AND ENCLOSURES
8.1 Introduction
This section covers the acoustics of enclosed spaces. Upon completion, the reader should have a basic understanding of how to design spaces with suitable acoustic characteristics for a particular use.
The two fundamental qualities that determine a room’s suitability for a particular use are:
- Reverberance or Liveliness: primarily a function of the sound absorption in the room and quantified by the Reverberation Time
- Background Noise Levels: predominantly HVAC noise, quantified by the NC or RC value
Typical applications:
- Acoustical spaces such as concert halls, classrooms, churches, offices, etc
- Industrial Environments - occupied spaces, or enclosures around noise sources
8.2 Sound Fields in a Room
Important Concepts: Near Field Far Field Free Field Reverberant Field Diffuse Field
Figure 1. Sound pressure level variation with distance from the source
8.3 Sound Absorption
As sound strikes a wall, some of it is reflected, while some is absorbed by the wall. A measure
of that absorption is the absorption coefficient αααα , defined as:
incident
incident reflected incident
absorbed
I
I I
I
I −
α = = Equation 1
α = 1 if totally absorptive
α = 0 if totally reflective
α is a function of the material, the frequency, and incidence angle
While some of the absorbed sound is dissipated as heat in the material, some re-radiates from the other side. The amount of energy that gets into the next room is quantified by the transmission coefficient: (more on this in Section 9)
incident
transmitted
I
I
τ = Equation 2
Absorption can be obtained by three primary mechanisms:
- porous materials,
- panel resonators or
- volume resonators:
Porous materials: Energy dissipation occurs due to acoustic pressure fluctuations at the surface which pump air into and out of the material. Friction between this air flow and the tortuous passages of the material dissipate energy as friction, and ultimately heat. Materials in this category include fiberglass, open cell foam, carpet and fabric. The frequency dependence for felt (a common absorption material) is shown in Figure 3.
Iincident
I reflected
I transmitted
Figure 2. Sound striking an absorbing wall
Figure 4. SoundBlox type RSC, a concrete cinder block with enclosed volume resonators for low frequency absorption
SoundBlox (Type RSC) Absorption
0
1
(^12516020025031540050063080010001250160020002500315040005000)
Frequency - Hz
Absorption Coefficient
4" SoundBlox, painted 8" SoundBlox, painted 8" Painted Cinder Block 8" Unpainted Cinder Block
Figure 5. Absorption coefficient of SoundBlox compared to ordinary solid blocks (SoundBlox data from Proudfoot Company).
Published Absorption Coefficient Values Absorption coefficients for commercially available materials are measured and published by manufacturers. A typical tabulation is shown in Table 1. It is possible to have absorption coefficient values greater than 1.0 for finite sized panels due to diffraction effects at the edges, and the additional absorption caused by the exposed area along the sides.
Table 1. Absorption coefficients of common building materials (ref. NIOSH Compendium of Noise Control Materials, 1975)
Figure 6. Impedance tube for measuring normal incidence absorption coefficient
We input a pure tone (or band of noise) using a loudspeaker. The incident wave from the speaker combines with the reflected wave from the end of the tube to form a standing wave. The depths of the minima are directly related to the absorption of the sample at the end of the tube. If the sample were perfectly reflective, total cancellation would occur ¼ wavelength from the end, and a pressure maximum would occur at ½ wavelength. A totally absorptive sample (anechoic) would exhibit a uniform pressure over the entire tube length. So, the difference in the maximum and minimum pressures is an indication of the absorptive characteristics of the sample.
Figure 7. Interaction between incident and partially reflected waves result in a standing wave pattern in an impedance tube. D 1 is the distance from the sample to the first minimum. D 2 is the distance between the first and second minima (equal to 1/2 wavelength)
We experimentally measure the maximum and minimum pressures inside the tube by sliding a microphone along the centerline, from which we can calculate the normal incidence absorption coefficient, αn.
2
min
max
min
max
÷÷
ø
ö
çç
è
æ
P
P
P
P
α (^) N Equation 5
Pmin
D 2 D (^1)
Pmax
Test sample
Additionally, if we measure the distance from the sample to the first minimum D 1 , and the distance between consecutive minima (or consecutive maxima) D 2 , the magnitude of the acoustic impedance can be calculated (ref. pg 57 L,G&E). A good check on the data is that D 2 should be equal to one half of a wavelength.
2
1 max min
max min 0
2
1
2 0 0
2 0 0 2 1 2 cos
1 2 cos D
D
P P
P P
c R R R
R R
u
P
Z
÷÷ =
ø
ö ç
ç è
æ − +
= = Equation 6
8.5 Sabine Absorption Coefficient αααα Sabine
A patch of material is placed in a large, highly reverberant room having a diffuse field. α (^) sabine is calculated from measurements of sound decay (reverberation time) in the room both with and without the material sample in place. It is a better approximation to real installations of absorptive materials, where the incidence angle can be anything.
(reference standards: ISO R354-1963, ASTM C423-84 & AS 1045-1971)
8.6 Room Averaged Coefficient α
Most real rooms have a variety of surfaces with different materials. The total effect of all these surfaces can be approximated by the average:
Equation 7
Assuming a uniform intensity (a diffuse sound field) I α S = I å α i Si
(the absorbed acoustical energy/unit time = the absorbed power)
If the distribution of α is highly uneven, a better approximation is:
averageabsorptionofeach face
where areaofx,y,zfaces
x,y,z
,,
α xyz
z
z y
y x
x
S
S S S
S
Numberofabsorbing surfaces
Areaofthei surface Totalsurfacearea
where: absorptionofthei surface th
1 th
å
N
S S
S
S
i
i
i
N
i
i
8.8 Sound Decay, Reverberation Time
If we now turn off our noise source, the sound level will decay linearly with time. Qualitatively, it’s easy to understand that the more absorption a room has, the quicker the sound will decay. We can (and will) use this decay rate to experimentally measure the overall room absorption.
The time required for the sound level to decay 60 dB is called the reverberation time , or T 60. It is often difficult (particularly at low frequencies) to put enough sound energy into a room to raise the level 60 dB over the background noise. The typical approach is to fit a straight line to the actual decay and extrapolate to 60 dB. Methods to excite the room include impulse sources such as popping balloons (ok for small rooms) or starter pistols; or a steady source – white or pink noise from amplified speakers.
Reverberation time is the single most important parameter for judging the acoustical properties of a room and its suitability for various uses. (Note, RC or NC criteria are measures of the background noise level of a room)
- High reverberation (long T 60 ) is desirable for music (concert halls 1.8 – 2. seconds)
- Low reverberation (short T 60 ) is desirable for speech intelligibility (such as in a classroom, 0.4 - 0.6 seconds)
The reverberation time at 512 or 1000 Hz is typically used as a single number to quantify the acoustic properties of a space. Recommended values for various applications are shown in Figure 9 and Table 2. An equation for calculating the “Optimum” Reverberation Time (according to Stephens and Bate 1950) is T 60 = K[ 0.0118 V1/3^ + 0.1070] Equation 8 V = volume in meters K = 4 for speech, 5 for orchestras, 6 for choirs
Figure 9. Typical decay of sound in a reverberation time test
Background noise level
example V = 1000 m^3 for speech, T 60 = .9 sec
Figure 10. Recommended reverberation times for various uses (reference Lord, Gatley and Evenson)
Table 2. Suitable reverberation times (seconds) for various rooms typically found in educational facilities. (ref. Classroom Acoustics, Acoustical Society of America, 2000) Music Rehearsal 0.6 – 1. Auditoriums 1.0 – 1. Gymnasiums 1.2 - 1. Cafeterias 0.8 – 1.
Figure 11. Attenuation for propagation of sound in air
8.10 Steady State Sound Levels In Enclosures
In a direct field, we already know that the intensity varies with distance.
where: directivity factor
θ
Q
Q
r
W
I
and where :^2 meansquaresound pressure
2
p
c
p I
In a reverberant field, the intensity is constant everywhere and is related to pressure by:
c
p I (^) rev 4
2
= Equation 12
Note that the intensity in a diffuse (reverberant) field is only ¼ that of a plane wave.
If we assume steady state conditions and a diffuse field, the amount of energy absorbed by the walls must equal the reverberant power supplied. The reverberant power is the sound power of the source minus the sound power absorbed in the first reflection,
W ( 1 − α ST ). The absorbed power is Irev ( S α ST ).
The reverberant intensity is then:
R
W
S
W
I
ST
ST
rev =
α
Equation 13
Where R is called the room constant, ST
R S ST
Equation 14
In most cases of low absorption, we typically simplify by assuming:
R ≈ S α ST and α ST ≈ α SABINE
A real room is somewhere between a diffuse and a free field. Therefore the total pressure is the sum of the direct and reverberant fields.
úû
ù
êë
é
r R
Q
p cI cIrev W c
π
ρ θ ρ ρ θ
and in terms of levels:
ú
û
ù
ê
ë
é
r R
Q
L P LW
10 log 102
θ Equation 15
The quantity Lp – Lw is plotted in Figure 12. In the reverberant field, the sound pressure level is independent of location. Note that in a highly reflective room (low R), the reverberant field is very large, and begins very close to the source.
The change in a room’s SPL due to changing its absorption is called the Noise Reduction, NR:
1 1
2 2
1 2 10 log( 2 / 1 )^10 log α
S
S
NR = LP − LP = R R = Equation 16
In order to get a decrease of 6 dB, the room absorption must be increased by a factor of
- (that’s a lot !)
Direct Field
Reverberant Field
8.11 Effect of Mounting
The more area an absorbing material presents to incident sound, the more energy is absorbed. In addition, it is possible to make a material more effective at low frequencies by mounting it with an air space between it and the adjacent wall or ceiling (see Figure 13 and Table 4).
Figure 13. Methods of mounting absorbing panels on walls or ceilings: a) hard mounted b) hanging baffle c) air space behind panel
Table 4. Effect of mounting on a 24” x 48” x 1.5” thick fiberglass panel on total absorption (absorption in Sabins) (data from NIOSH Compendium of Noise Control materials) Frequency - Hz Mounting Configuration 125 250 500 1000 2000 4000 Hanging baffle 4.3 6.6 9.8 13.3 13.6 10. Hard mounted on rigid wall (#4 mount) 1.5 3.5 6.2 7.4 6.5 6. 16” air space (#7 mount) 7.2 6.4 6.0 7.2 6.2 3.
Air space (^) 16”
8.13 Standing Waves
Room modes Placement of sound sources and absorbing material Modal density
8.12 Anechoic Rooms
Effectiveness of wedges
8.12 Reverberation Rooms
8.15 Summary
Adding absorption is only justifiable if the reverberant field is dominant. Absorption on walls or ceilings will have little or no effect in the direct field, i.e. in the immediate vicinity of a noise source.
Design guidelines:
- To have the greatest effect on total absorption (and the reverberation time), add absorption to the least absorptive areas first.
- Distribute absorption around the room as much as possible to minimize local effects.
- Avoid having two parallel walls that are both highly reflective. This can cause a flutter echo.
- Low frequency absorption (< 250 Hz) is difficult to achieve with porous materials of reasonable thickness. To be effective at low frequency, porous materials must be thick, Material thickness ≥ 1/4 λ for anechoic (α ≈ 1.0)
- Low frequency absorption of porous materials can be increased by mounting them with an airspace behind them.
- Design the room with non-parallel walls wherever possible to break up standing waves and flutter echo.
- Absorption or a diffusing element on the back wall of a room (the wall directly opposite to the sound source or speaking person) is highly desirable
- Mount absorbing panels so as to maximize the area exposed to incident sound
8.16 References
- Compendium of Materials for Noise Control, NIOSH, 1975, HEW Publication No. 75-
- Sonic and Vibration Environments for Ground Facilities – A Design Manual, NASA , NAS8-11217.
- Classroom Acoustics, Acoustical Society of America, Architectural acoustics technical committee, August 2000.
