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Sound Insulation

J. NEGREIRA, D. BARD

DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY

J. Negreira / Acoustics VTAF05 / 24-Nov-15

Outline

Introduction

Airborne Sound Insulation

Impact Sound Insulation

Conclusions

Analytical models for calculation of Rw in

single and double-leaf walls


Introduction (I)

• Sound transmission

– Airborne

– Structure-borne

• Transmission paths

– Direct transmission (D)

– Flanking paths (Fi)


i Incident wave power

r Reflected wave power

t Transmitted wave power

a Power reduction due to absorption

Introduction (II)


Introduction (III)

Transmission coefficient:

Absorption coefficient:

Reflection coefficient:

[-]

ia

it

[-]

[-]

ir

1


Introduction (IV)

it


Outline

Introduction



Conclusions




References

• ISO 140, Acoustics – Measurement of sound insulation in buildings

and of building elements – Part 3: Laboratory measurements of

airborne sound insulation of building elements (1995).


and of building elements – Part 4: Field measurements of airborne

sound insulation between rooms (1998).


and of building elements – Part 5: Field measurements of airborne

sound insulation of facade – elements and facades (1998).



airborne sound insulation of small building elements (1991)

• ISO 717, Acoustics - Rating of sound insulation in buildings and of

buildings elements – Part 1: Airborne sound insulation (1996).


DEF: Reverberation time

• Reverberation time

– Time for sound to decrease 60 dB from initial level

» “Clarity vs. Intensity” compromise

– Not necessarily coincident with listener feeling

– Why 60 dB?

– Values dependent on ussage

» Ex: general auditorium: 1.5 - 2.5 sec.

– Calculation (Sabine’s law)

i

iieff S

V

A

VT

16.016.060

V: room volume / Aeff: effective absorption area / : individual absorption

coefficients / Si: surface of each element with i

i

https://www.youtube.com/watch?v=gy-ht0GivIY


Nomenclature

• R’w : apparent sound reduction index (in-situ measurement)

• Rw : sound reduction index (laboratory measurement)

• C50-3150 : spectrum adaptation term

• Ctr: spectrum adaptation term due to traffic noise

• D’n , D’n,T , D’w etc. sound level differences (see standards)

Statement of results: R’w(C50-3150 ;Ctr) / Rw(C50-3150 ;Ctr)

”Rule of thumb”: Difference between lab and in-situ ~4 dB!


Measurement sound reduction index (I)

LS : SPL in the sending room [dB]

LR : SPL in the receiving room [dB]

S : wall area [m2]

A : Absorption area in receiving room [m2]

Wall’s reduction index [dB]

(= transmission loss):

A

SLLR RS log10

NOTE: Loudspeaker and microphone positions are defined in the corresponding ISO standard.


Measurement sound reduction index (II)

• Example of measured curve:

‒ High values Better insulation ”Quieter”

63 125 250 500 1000 2000 4000 15

20

25

30

35

40

45

50

55

60

Frequency [Hz]

R [dB]

A

SLLR RS log10

https://www.youtube.com/watch?v=bYRr0JS9WXg


ISO Evaluation of sound reduction index (I)

• Reference curve (ISO 717-1)


ISO Evaluation of sound reduction index (II)

“[…] the reference curve is shifted in

steps of 1 dB towards the measured

one, until the sum of the unfavourable

deviations is as large as possible, but

not more than 32 dB*”

“[…] an unfavourable deviation at a

particular frequency occurs when the

result of measurements is less than the

reference value.”

“[…] the value, in dB, of the reference

curve has at 500 Hz, after shifting in

accordance with this procedure, is R’w.”

*for measurements in 16 one-third-octave band. If measurements are performed in 5 octave bands, the sum should not exceed 10 dB.

Airborne sound insulation – example


DEF: Combined reduction index

...)1010(

1log10

10/

2

10/

121 RR

SSS

R

R1, R2 … individual reduction indexes

S: total area, i.e. S = S1+S2+…

Combined reduction index


DEF: Leakages

• Power of the opening (leakage)

• The reduction index of the wall then becomes

S

Slil

S

SR

S

SR

lR

ewithLeakag

l

i

t

i

tl

10/10log10

log10log10


Example: influence of leakages

Sealing of windows is of crucial importance

3 mm

1

2

30m

m

3 mm

0

5

10

15

20

25

30

35

40

45

10

0

16

0

25

0

40

0

63

0

10

00

16

00

25

00

Re

duk

tions

tal

(dB

)

Frekvens (Hz)

Otätat fönster

Tätningslist vid 2

Tätningslist vid 1och 2


Exercises

2.- What is the influence of a crack in a wall whose dimensions are 1 mm

in width and 1 m in length in a wall of 2.40 m height and 4 m length? The

sound reduction index of the wall without leakage is 50 dB.

How much the combined sound reduction index would be if the sound

reduction index of the wall would increase up to 60 dB?

1.- A 9 m2 facade has a sound reduction index of 60 dB and has installed

a 1,0 m2 double window whose reduction index is 30 dB.

a) What does it mean that the material of the wall has a reduction index

of 60 dB? How much energy does the material let through?

b) Calculate the combined sound reduction index of the facade.


Outline

Introduction



Conclusions




References



impact sound insulation of floors (1998).


and of building elements – Part 7: Field measurements of impact

sound insulation of building elements (1998).

• ISO 717, Acoustics - Rating of sound insulation in buildings and of

buildings elements – Part 2: Impact sound insulation (1996).


Nomenclature

• L’n,w : weighed normalised impact sound level, (in-situ)

• Ln,w : weighed normalised impact sound level (laboratory)

• Cl,50-2500 : spectrum adaptation term

Statement of results: L’n,w(Cl,50-2500) / Ln,w(Cl,50-2500)

”Rule of thumb”: Difference between lab and in-situ ~4 dB!


Measurement impact sound insulation (I)

Ln : normalised impact sound level [dB]

LR : SPL in the receiving room [dB]

A : Absorption area in the receiving room

10log10

ALL Rn

Impact sound level:

• ISO Tapping Machine

‒ Standardised: 1 hit per 0.1 s

‒ 5 steel cylinders which alternatively hit the floor

NOTE: Tapping machine and microphone positions

are defined in the pertinent ISO standard.

https://www.youtube.com/watch?v=lctdT_8Wvo8


Measurement impact sound insulation (II)

• Example of measured curve:

‒ High values Higher sound transmission ” Noisier”

0

10

20

30

40

50

60

70100

160

250

400

630

100

0

160

0

250

0

Ln

[dB

]

Frequency [Hz]


ISO Evaluation of impact sound insulation (I)

• Reference curve (ISO 717-2)


ISO Evaluation of impact sound insulation (II)

“[…] the reference curve is shifted in

steps of 1 dB towards the measured

one, until the sum of the unfavourable

deviations is as large as possible, but

not more than 32 dB*.”

“[…] an unfavourable deviation at a

particular frequency occurs when the

result of measurements exceed the

reference value.”

“[…] the value, in dB, of the reference

curve has at 500 Hz, after shifting in

accordance with this procedure, is L’n,w”

*for measurements in 16 one-third-octave band. If measurements are performed in 5 octave bands, the sum should not exceed 10 dB.


Sound classes (Sweden)

• Ljudklass A: the soundclass corresponds to very good

acoustic conditions.

• Ljudklass B: it comprises slightly better acoustic conditions

than soundclass C. Certain individuals can still, in some

cases, be disturbed. This sound class are the minimum

requirements if good living environment is requested.

• Ljudklass C: this is the minimum requirements in Swedish

buildings.

• Ljudklass D: Sound class corresponds noise conditions that

are intended to be applied when sound class C cannot be

achieved, e.g. in connection with the refurbishment.


BBR and SS 25267:2004

Ljudkrav för

bostäder

A

[dB]

B

[dB]

C

[dB]

(D)

[dB]

Luftljudsisolering 61 57 53 49

Stegljudsnivå 48 52 56 60

Installationsbuller 22/27 26/31 30/35 30/35

Trafikbuller 22/37 26/41 30/45 34/49

*Installation and traffic noise have not been addressed in this lecture. For more information

about how to measure and evaluate, see the correspondent ISO standards


Example from SS 25267:2004 – Sound class C


Outline

Introduction



Conclusions




DEF: Coincidence – critical frequency (I)

• The wavelength of a bending wave λB is dependent on

frequency, bending stiffness and mass density

• When the wavelength of sound in air coincides with the

structural wavelength Coincidence phenomena

‒ Radiation efficiency becomes very high

‒ Poor insulation


DEF: Coincidence – critical frequency (II)

• Bending wave velocity in a plate

• If f = fc thus cB = co = 340 m/s (fc = critical frequency)

• Or expressed as a function of the coincidence number

42m

BfcB

B

mcfc

2

2

0

h

Kfc

NOTE: The condition for coincidence is that λB=λsin(φ). Therefore, if the incidence angle φ

decreases, the coincidence frequency fc increases according to fc (φ)=fc/sin2(φ). The lowest

frequency at which coincidence occur (critical frequency) occurs at the incidence angle φ=90º.


Critical frequency for common materials

Material Coincidence number Thickness [m] fc [Hz]

Concrete 18 160 110

Light concrete 38 70 540

Gypsum 32 10 3200

Steel 12-13 1 12000

Glass 18 3 6000


Outline

Double-leaf wall

Exact method

Analytical models for calculation of R in


Single-leaf wall

Approximate method


Sound reduction index of single-leaf partitions (I)

• Exact Method

‒ Region I: Stiffness-controlled region (f < f11)

‒ Region II: Mass-controlled region (f11 < f < fc)

‒ Region III: Damping-controlled region (fc< f)


Sound reduction index of single-leaf partitions (II)

• Region I: Stiffness-controlled region (f < f11)

‒ Panel vibrates as a whole (considered thin)

2

22

38

2

2

2

11

)1(768

4

1lnlog101

log10

baEh

C

CcfK

KK

R

s

sFFS

S

S

Cs: Mechanical compliance for a rectangular plate

E: Young’s modulus of the material the wall is made of

h: wall thickness

a, b: plate dimensions

: Poisson’s ratio of the wall

: Density of the surrounding fluid (F), i.e. air

cF wave propagation speed in the fluid (F), i.e. air

cLplate wave propagation speed in the plate (longitudinal wave)

F

2211

11

34 bahcf Lplate

For a simply supported plate


Sound reduction index of single-leaf partitions (III)

• Region II: Mass-controlled region (f11 < f < fc)

‒ Transmission loss independent of stiffness (controlled by mass inertia)

‒ Some energy transmitted and part reflected at panel surface

dBc

fmR

FF

5''

1log10

2

m’’= h is the surface mass of the panel

NOTE: Although the above equation is valid for frequencies up to fc, it yields only accurate

results for f ≤ 0.5fc . The mathematical expresion around fc is mathematically cumbersome

and rarely used, its being the reason why approximate methods were developed.

Mass law >>1


Sound reduction index of single-leaf partitions (IV)

• Region III: Damping-controlled region (fc< f)

‒ Curve “dip” controlled by internal material damping

‒ Important for design (low insulation)

2

''1log10)(

7.5log22.33)log(10)(

FF

cc

c

c

c

mffR

dBf

ffRR

is the total loss factor or damping of the panel

Lplate

Fc

hc

cf

32


Outline

Double-leaf wall

Exact method



Single-leaf wall

Approximate method


Sound reduction index of single-leaf partitions (I)

• Approximate method

‒ Region I: Mass-controlled region (f < f1)

‒ Region II: “Plateau” (f1 < f < f2)

‒ Region III: Stiffness-controlled region (f2< f)

Hyphotesis: Infinite panel and diffuse field excitation


Sound reduction index of single-leaf partitions (II)

• Region I: Mass-controlled region (f < f1)

‒ Transmission independent of panel stiffness

dBc

fmR FFn 5log20log20´´log20


Sound reduction index of single-leaf partitions (III)

• Region II: “Plateau” (f1 < f < f2)

‒ Governed by internal damping

‒ Height of the plateau depends on material

‒ f1 and f2 are the lower and upper limits of the plateau

» Calculated with expresions of adjoining regions


Sound reduction index of single-leaf partitions (IV)

• Region III: Mass-controlled region (f2 < f)

‒ Governed by stiffness of the panel

2

log22.33)( 2 f

f

n fRR

NOTE: The slope of the expression (10 dB/octave) should just be used

only for the 2 octaves above f2. For the following octaves, one should use

a slope equal to 6 dB/octave, i.e. “20log(f/f2oct)” instead of “33.22log(f/f2)”,

where f2oct is the frequency where the 3rd octave above f2 start.


Outline

Double-leaf wall

Exact method



Single-leaf wall

Approximate method


Introduction

• Double-leaf wall literature rather extensive

– Theoretical analysis, less developed due to complexity

– Analyses often carried out using FEM, SEA.

• Several theoretical derivations of sound transmission

– Double-leaf wall without mechanical coupling

– Double walls with structural connections

– …


Sound reduction index of double-leaf walls

• Approximate empirical model for a double leaf wall without structural

connections, with cavity filled with porous absorber (Sharp 1978)

S

ARRR

A

SLLR

A

SLLR

A

SLLR

DoubleWall

DoubleWall

221

3

31

3

322

2

211

log10

log10

log10

log10

d

d

M

ffdBRR

fffdBdfRR

ffR

R

;6

;29)log(20

;

21

021

0

21

0

11

2 mmd

cf F

dfd

55

RM denotes the mass law with M=m1+m2

R1 and R2 denote the individual sound reduction index for each leaf

d: distance between the two leaves i.e. (cavity thickness)

NOTE: Diffuse field assumed in both rooms


• Improvement in the sound reduction index of a double-leaf wall

respect to a single wall, and also when including insulation in

the cavity.

Examples (I)


Examples (II)

0

10

20

30

40

50

60

70

80

50 80 125 200 315 500 800 1250 2000 3150

frekvens [Hz]

Reduktionstal [dB]

R3 R2 R1

135 mm

Gipsplatta, 13 mm

Mineralull

Stålreglar c/c 600

mm R1= tomt hålrum

R3 = 140 mm mineralull

R2 = 30 mm mineralull

Rw [dB]

R3: 55

R2: 49

R1: 43

• Variation in the sound reduction index of a double-leaf wall

when varying parameters in the cavity (inclusion of insulation

and its thickness).


Examples (III)


Examples (IV)


Examples (V)


Examples (VI)

“Rule of thumb”: decoupled structures perform much better

acoustic bridges eliminated


Outline

Introduction



Conclusions




Conclusions

• ISO procedures (acoustic insulation)

– Airborne sound insulation

– Impact sound insulation

• Analytical calculation methods of reduction sound index

– Single-leaf wall

» Exact method

» Approximate method

– Double-leaf wall

NOTE: Check out the acoustic glossary

http://www.acoustic-glossary.co.uk/

Thank you for your attention!

[email protected]