University of Windsor S2014/Lecture 26 2014 92-455.pdf · Noise, Vibration, Harshness –Sound...

Noise, Vibration, Harshness – Sound Quality Research Group

Copyright 2014 by Robert Gaspar. All rights reserved no part of this publication may be reproduced or distributed in any formor by any means, or stored in a data base or retrieval, without the prior written permission of the author.


University of Windsor

Sound AbsorptionCopyright ©2014, Robert Gaspar. Some material taken from MIT OCW Room Acoustics


Introduction• Reverberation time was introduced during the presentation about

anechoic rooms.

• The RT60 measurement is the time required for a generated constant sound level to decrease by 60 dB when the source of sound generation is shut off.

• Wallace Sabine is considered to be a pioneer in architectural acoustics. In 1900, he published the results of experiments that he started in 1898.

• He used the Fogg lecture room at Harvard, to investigate changes in the acoustic characteristics of the lecture room by adding and removing materials such as seating.

Lecture 26 2


Sabine’s work

• Sabine derived an expression for the duration T of the residual sound to decay below the audible intensity, starting from an initial intensity that was 1,000,000 time higher:

• T = 0.161 V/A

• where V is the room volume in cubic meters, and A is the total absorption in square meters.

• Although this was n empirical formula, Sabine's formula is still used to estimate the reverberation time in rooms.

• To honor his work, the unit of sound absorption if called the Sabin.

Lecture 26 3


The Sabine

• The unit of sound absorption is measured in square meters, and is referenced to the area of open window.

• This unit stems from the fact that sound energy travelling toward an open window in a room will not be reflected at all, but completely disappear in the open air outside.

• The effect would be the same if the open window would be replaced with 100 % absorbing material of the same dimensions.

Lecture 26 4


Total Room Absorption

• While Sabine’s formula is still used, further studies have expanded on the idea to account for frequency dependency and multiple surface areas.

• This has lead to the following equation for total room absorption:

• A = S1 α1 + S2 α2 + .. + Sn αn = ∑ Si αi

whereA = the absorption of the room (m2 Sabine)Sn = area of the actual surface (m2)αn = absorption coefficient of the actual surface

Lecture 26 5


Room Acoustics

Lecture 26 6

0 2 4 6 8 10Time [s]

1.5

1.0

0.5

0.0

-0.5

-1.0

Inte

nsi

ty

0

-20

-40

-60

-80

-100

Sou

nd

leve

l[d

B]

Intensity

Sound level

Sound On

Sound source in a room• Intensity increases quickly to

equilibrium:• Switched off then gradual decay• Reverberation time RT60

• intensity ↓ by factor 106

• sound level ↓ by 60 dB• At equilibrium the energy

produced by the sound source is absorbed by the room

PA = ∑(αsiSi)

i

= 4Iequil whereA

MIT OCW Room Acoustics


Mean Absorption Coefficient• The mean absorption coefficient for the room can be expressed as:

• am = A / Swheream = mean absorption coefficientA = the absorption of the room (m2 Sabine)S = total surface in the room (m2)

• For any room, the acoustic characteristics can be calculated with the formulas above

• Or estimated using typical rooms and their acoustics as a basis.

Lecture 26 7


Absorption Coefficients of Materials

Lecture 26 8

Floor materials 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 4 kHzcarpet 0.01 0.02 0.06 0.15 0.25 0.45Concrete (unpainted, rough finish) 0.01 0.02 0.04 0.06 0.08 0.10Concrete (sealed or painted) 0.01 0.01 0.02 0.02 0.02 0.02Marble or glazed tile 0.01 0.01 0.01 0.01 0.02 0.02Vinyl tile or linoleum on concrete 0.02 0.03 0.03 0.03 0.03 0.02Wood parquet on concrete 0.04 0.04 0.07 0.06 0.06 0.07Wood flooring on joists 0.15 0.11 0.10 0.07 0.06 0.07



Lecture 26 9

Seating materials 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 4 kHzBenches (wooden, empty) 0.10 0.09 0.08 0.08 0.08 0.08Benches (wooden, 2/3 occupied) 0.37 0.40 0.47 0.53 0.56 0.53Benches (wooden, fully occupied) 0.50 0.56 0.66 0.76 0.80 0.76Benches (cushioned seats and backs, empty) 0.32 0.40 0.42 0.44 0.43 0.48Benches (cushioned seats and backs, 2/3 occupied) 0.44 0.56 0.65 0.72 0.72 0.67Benches (cushioned seats and backs, fully occupied) 0.50 0.64 0.76 0.86 0.86 0.76Theater seats (wood, empty) 0.03 0.04 0.05 0.07 0.08 0.08Theater seats (wood, 2/3 occupied) 0.34 0.21 0.28 0.53 0.56 0.53Theater seats (wood, fully occupied) 0.50 0.30 0.40 0.76 0.80 0.76Seats (fabric-upholsterd, empty) 0.49 0.66 0.80 0.88 0.82 0.70Seats (fabric-upholsterd, fully occupied) 0.60 0.74 0.88 0.96 0.93 0.85



Lecture 26 10

Reflective wall materials 125 Hz250 Hz500 Hz1 kHz 2 kHz 4 kHzBrick (natural) 0.03 0.03 0.03 0.04 0.05 0.07Brick (painted) 0.01 0.01 0.02 0.02 0.02 0.03Concrete block (coarse) 0.36 0.44 0.31 0.29 0.39 0.25Concrete block (painted) 0.10 0.05 0.06 0.07 0.09 0.08Concrete (poured, rough finish, unpainted) 0.01 0.02 0.04 0.06 0.08 0.10Doors (solid wood panels) 0.10 0.07 0.05 0.04 0.04 0.04Glass (1/4" plate, large pane) 0.18 0.06 0.04 0.03 0.02 0.02Glass (small pane) 0.04 0.04 0.03 0.03 0.02 0.02Plasterboard (12mm (1/2") paneling on studs) 0.29 0.10 0.06 0.05 0.04 0.04



Lecture 26 11

Reflective wall materials 125 Hz250 Hz500 Hz1 kHz 2 kHz 4 kHzPlaster (gypsum or lime, on masonry) 0.01 0.02 0.02 0.03 0.04 0.05Plaster (gypsum or lime, on wood lath) 0.14 0.10 0.06 0.05 0.04 0.04Plywood (3mm(1/8") paneling over 31.7mm(1-1/4") airspace) 0.15 0.25 0.12 0.08 0.08 0.08Plywood (3mm(1/8") paneling over 57.1mm( 2-1/4") airspace) 0.28 0.20 0.10 0.10 0.08 0.08Plywood (5mm(3/16") paneling over 50mm(2") airspace) 0.38 0.24 0.17 0.10 0.08 0.05Plywood (5mm(3/16") panel, 25mm(1") fiberglass in 50mm(2") airspace) 0.42 0.36 0.19 0.10 0.08 0.05Plywood (6mm(1/4") paneling, airspace, light bracing) 0.30 0.25 0.15 0.10 0.10 0.10Plywood (10mm(3/8") paneling, airspace, light bracing) 0.28 0.22 0.17 0.09 0.10 0.11Plywood (19mm(3/4") paneling, airspace, light bracing) 0.20 0.18 0.15 0.12 0.10 0.10



Lecture 26 12

Absorptive wall materials 125 Hz250 Hz500 Hz1 kHz 2 kHz 4 kHzDrapery (10 oz/yd2, 340 g/m2, flat against wall) 0.04 0.05 0.11 0.18 0.30 0.35Drapery (14 oz/yd2, 476 g/m2, flat against wall) 0.05 0.07 0.13 0.22 0.32 0.35Drapery (18 oz/yd2, 612 g/m2, flat against wall) 0.05 0.12 0.35 0.48 0.38 0.36Drapery (14 oz/yd2, 476 g/m2, pleated 50%) 0.07 0.31 0.49 0.75 0.70 0.60Drapery (18 oz/yd2, 612 g/m2, pleated 50%) 0.14 0.35 0.53 0.75 0.70 0.60Fiberglass board (25mm(1") thick) 0.06 0.20 0.65 0.90 0.95 0.98Fiberglass board (50mm(2") thick) 0.18 0.76 0.99 0.99 0.99 0.99Fiberglass board (75mm(3") thick) 0.53 0.99 0.99 0.99 0.99 0.99Fiberglass board (100mm(4") thick) 0.99 0.99 0.99 0.99 0.99 0.97Open brick pattern over 75mm(3") fiberglass 0.40 0.65 0.85 0.75 0.65 0.60Pageboard over 25mm(1") fiberglass board 0.08 0.32 0.99 0.76 0.34 0.12Pageboard over 50mm(2") fiberglass board 0.26 0.97 0.99 0.66 0.34 0.14Pageboard over 75mm(3") fiberglass board 0.49 0.99 0.99 0.69 0.37 0.15Performated metal (13% open, over 50mm(2") fiberglass) 0.25 0.64 0.99 0.97 0.88 0.92



Lecture 26 13

Ceiling material 125 Hz250 Hz500 Hz1 kHz 2 kHz 4 kHzPlasterboard (12mm(1/2") in suspended ceiling grid) 0.15 0.11 0.04 0.04 0.07 0.08Underlay in perforated metal panels (25mm(1") batts) 0.51 0.78 0.57 0.77 0.90 0.79Metal deck (perforated channels,25mm(1") batts) 0.19 0.69 0.99 0.88 0.52 0.27Metal deck (perforated channels, 75mm(3") batts) 0.73 0.99 0.99 0.89 0.52 0.31Plaster (gypsum or lime, on masonary) 0.01 0.02 0.02 0.03 0.04 0.05Plaster (gypsum or lime, rough finish or timber lath) 0.14 0.10 0.06 0.05 0.04 0.04Sprayed cellulose fiber (16mm(5/8") on solid backing) 0.05 0.16 0.44 0.79 0.90 0.91Sprayed cellulose fiber (25mm(1") on solid backing) 0.08 0.29 0.75 0.98 0.93 0.76Sprayed cellulose fiber (25mm(1") on timber lath) 0.47 0.90 1.10 1.03 1.05 1.03Sprayed cellulose fiber (32mm(1-1/4") on solid backing) 0.10 0.30 0.73 0.92 0.98 0.98Sprayed cellulose fiber (75mm(3") on solid backing) 0.70 0.95 1.00 0.85 0.85 0.90Wood tongue-and-groove roof decking 0.24 0.19 0.14 0.08 0.13 0.10



Lecture 26 14

Miscellaneous surface material 125 Hz250 Hz500 Hz1 kHz 2 kHz 4 kHzPeople-adults (per 1/10 person) 0.25 0.35 0.42 0.46 0.50 0.50People-high school students (per 1/10 person) 0.22 0.30 0.38 0.42 0.45 0.45People-elementary students (per 1/10 person) 0.18 0.23 0.28 0.32 0.35 0.35Ventilating grilles 0.30 0.40 0.50 0.50 0.50 0.40Water or ice surface 0.008 0.008 0.013 0.015 0.02 0.025www.sae.edu/reference_material/pages/Coefficient%20Chart.htm


Other Reverberation Time Models

• For very absorbent rooms, Sabine’s formula fails.

• For a room that is 3.0 m x 3.7 m x 2.4 m with an absorption coefficient of α = 1.0

RT60 = 0.161 V/A = 0.161*3.0*3.7*2.4/{2*(3.0*3.7+3.0*2.4+3.7*2.4)}

RT60 = 0.079 seconds but this value should be zero

• Eyring-Norris Equation:

• αaverage is the average absorption coefficient ∑ Si αi / ∑ Si

• For average absorption coefficients of 0.25 or less, the results are the same as Sabine’s prediction Lecture 26 15

60

average

0.161VRT =

-S ln(1-α )


Other Reverberation Time Models

• For very large rooms the passage of the sound through the air can add absorption to the room.

• This lowers the reverberation time and is taken into account by adjusting the A effect by adding 4mV to it. i.e.

RT60 = 0.161 V/(A + 4mV)

• Air absorption is only significant above 2 kHz

• m = 0.009 @ 2 kHz, 0.025 @ 4 kHz, and 0.080 @ 8 kHz measured in Sabines per square metre.

Lecture 26 16


Designing for Room Acoustics

•Good acoustics•Low background noise, loud wanted sound•Well diffused sound field•No echoes or acoustic distortions•Appropriate RT60

Lecture 26 17


Designing for Room Acoustics

•Good acoustics

•Geometrical acoustics• Avoid large planar surfaces facing each other (fluttering

echo)• Avoid concave surfaces (focusing)

Lecture 26 18

Focusing (bad) Distribution (good)

Bad

Good

MIT OCW Room Acoustics


100%

90%

80%

70%

60%

50%

40%

0 1 2 3 4 5

Reverberation Time [s]

Room Acoustics and Intelligibility

• Intelligibility and sound• high sound level → low A → high RT → lower intelligibility

•Recommended RT60

Lecture 26 19MIT OCW Room Acoustics

Inte

ligib

ility

2.5

2.0

1.5

1.0

0.5

0.0

200 500 1000 2000 5000Room volume [m³]

10000 20000

Op

tim

alre

verb

erat

ion

tim

e[s

] MusicSpeech

Image by MIT OCW.


Room Acoustics and Intelligibility

• Intelligibility as a function of delay• Direct sound → path l• Reflected sound → path l’

•Delay• Δt = (l’ - l) / 340 [m/s]• Speech: Δt = 35 ≤ ms i.e. l’ - l ≤ 12 m (130 ms per syllable)• Music: Δt = 44 ≤ ms i.e. l’ - l ≤ 15 m

• If critical• Change room geometry• Add absorbing panels


Image by MIT OCW.


Room Acoustics and Nature of Sound

•Wave nature of sound• Standing wave if L = n ½ λ

• Proper frequency fn = c / λn = n c/(2L)

→ no rational relationship between lengths

→ non-rectangular plan


W

B S

L

L = 1.2W

Image by MIT OCW.

n = 1

n = 2

n = 3 λ/2

Image by MIT OCW.

L

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