PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Sound insulation prediction of single and double CLT panels
Fredrik LJUNGGRENLuleå University of Technology, Sweden

ABSTRACT
Cross laminated timber (CLT) as building material has rapidly gained in popularity in recent years, andthereby also the demand of engineering tools to predict the sound insulation through CLT walls. The soundreduction through walls of single and double panels is predicted and the results are compared with thosefound in the literature as well as with a series of measurements conducted in a test mock-up of two rooms.
Various configurations are considered where the plate thickness, addition of plaster boards and cavity
distance (in case of a double panel) are altered. The prediction of single panel walls is based upon an
established model (by Sharp) for homogenous materials, based upon theory and empirical data. For optimized
application to CLT constructions specifically, the model is modified to some extent. The double panel walls
are analytically modelled under the presumptions of no mechanical connection between the two panels anda cavity filled with mineral wool. The model make use of the results from the developed model for individual
panels. The accuracy of the predicted sound insulation is estimated to be within a couple of dB’s concerning
the weighted sound reduction indexes from 100 and 50 Hz.
Keywords: Sound insulation, Cross Laminated Timber, Modelling

1. INTRODUCTION

The interest to use of CLT – Cross Laminated Timber – in building frames has rapidly increased
over just a few years. CLT panels are in many ways easy to handle, are light (compared to concrete),have high bearing capacity and can handle large spans. Another important aspect is that CLT is asustainable and renewable material.
A CLT panel consists of planks, often 20-30 mm thick, glued together in typical 3-7 layers oforthogonal orientation, see Figure 1.
3-layer5-layer7-layer

Figure 1 – Example of CLT panels.
In this paper, the sound insulation of single and double wall panels is in focus. The purpose is tofind out how accurate established analytical models, slightly modified if needed, can predict theairborne sound insulation.

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2. SINGLE PANEL WALLS
2.1 Model
The calculations originate from Sharps’s model from 1978 (1), a model that is based upon theory
but also to some extent has been adjusted to empirical data. The model is divided into three frequency
regions related to the panel’s coincidence frequency fc ; 1) f below half the coincidence frequency, 2)
f around fc and 3) f above the coincidence frequency. The sound reduction is calculated accordingly:f ≤ fc /2
f = fcf>f

R=20log(Mf)-48
Rc =20log(Mfc )+10log(η)-40
R=Rc+30log(f/f c)

6 dB/octave band
9dB/octave band

where M is the surface weight (kg/m2 ) and η is the loss factor of the panel.
Sharp’s model has in the next phase undergone a couple of modifications in order to work
especially well for CLT panels including better matching against available measurement data. The
idea to several of the modifications are found in (2).
a) For f ≤ fc /2 the constant take the value 48 dB for thicknesses up to 130 mm, for thicknesses
from 180 mm 47 dB is used and between 130-180 mm a successive adjustment of 0,2 dB per
10 mm take place. Within the literature, both 47 (2-3) and 48 dB (1) is reported.
b) In the region fc /2 < f ≤ fc, the sound reduction takes the same value as for fc /2, the so called
coincidence dip thereby gets less pronounced.
c) The sound reduction of twice the coincidence frequency is calculated taking the loss factor
into accountd) For f > 2fc , the slope of curve is 6 dB/octave band
The described adjustments leads to the following set of equation to model the sound reduction:
I.
II.
III.
IV.

f ≤ fc /2
R=20log(Mf)-k*
6 dB/octave band
0 dB/octave bandfc /2<f ≤ fc R=Rc/2
R 2c = Rc/2+10log(η)+23
f = 2fc
f > 2fc
R=R2c+20log(f/2fc)
6 dB/octave band*) k=48 for t ≤ 130 mm, k=47 for t ≥ 180 mm

The sound reduction is thus divided into four frequency regions, shown in Figure 2.
Sound reduction, RFigure 2 – The sound reduction model is divided into four frequency regions.

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The material parameters for a number of modeled panels are presented in Table 1 together withthe calculated coincidence frequency according to equation 1. The CLT density is auumed to be 400kg/m3 and the Young’s modulus (4), Poisson’s ratio (5) and loss factor (6) have been obtained fromthe given references.

𝑓𝑓𝑐𝑐 =

𝑐𝑐2

2𝜋𝜋

�

12𝑀𝑀(1−𝜈𝜈2 )

(1)

𝐸𝐸𝑡𝑡3

Table 1 – Parameters of CLT panels

Thickness (mm)

70

90

120

140

160

180

210

300

Youngs’ m. (GPa)

10,2

10,6

7,86

7,11

9,82

7,86

7,89

8,16

Poisson’s ratio

0,30,30,30,30,30,30,30,3

Loss factor

0,010,010,010,010,010,010,010,01

Weight (kg/m2)

28364856647284

120

Coinc.f. (Hz)

175

134

116

105

78786646

2.2 Results
Examples of sound reduction curves for CLT panels of three different thicknesses; 70,120 and 210
mm are shown in Figure 3. The single number ratings R w and R w,50 (abbreviation for R w + C 50-3150 ) forall modelled configurations are presented in Table 2 and Figure 4. The effect of adding one or twolayer of gypsum board (9 kg/m2 ) is included in Table 2. In the presence of gypsum board, only theadditional mass is considered by the model, possibly influence from other material parameters areoverseen.
Sound reduction, RKL 210

Rw=41

Rw,50=39KL 120

Rw=36

Rw,50=34

KL 70

Rw=31

Rw,50=30

Figure 3 – Sound reduction for CLT panels of three thicknesses; 70, 120 and 210 mm.

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Table 2 – Singe number ratings of single panel walls.
CLTPlate

CLT + 1 gypsum board

CLT + 2 gypsum board

thickness

Rw

Rw,50

Rw

Rw,50

Rw

Rw,50

65

31

30----

70

31303432363490

33

32

35

34

37

35

100

34

33

3634

37

36

120

3634373638371403735

38

37

3938

16038374038

4139

18040

38

41394240

210

4139

4240

4341

240

4240

43414442300

444245

4345

43

320

45

43

----

2.3 Comparisons
The calculated single number ratings are compared with those found from the literature (7-16). Thereferences are a mix of results reported from measurements as from other theoretical models. Overall,
the matching seems satisfactory with most of the references within ±1 dB from the predicted value,
but also note the lack of validation for greater thickness than 180 mm.

Figure 4 – Single number ratings of CLT panels. Open circles are predicted values and filledcolored circles represent verifying data from various references.

3. DOUBLE PANEL WALLS
3.1 Model
The model for the double panel walls start with modelling the individual panels according toprevious section. The special characteristic of a double wall is then applied in accordance to Sharp(1) where the double wall resonance f0 and the limiting frequency fl , equation 2 and 3 respectively,
take a central role.

𝑓𝑓0 =𝑐𝑐2𝜋𝜋�

1,8(𝑀𝑀1−𝑀𝑀2)
𝑑𝑑𝑑𝑑1𝑀𝑀2(2)245𝑓𝑓𝑙𝑙 =𝑐𝑐

(3)

2𝜋𝜋𝜋𝜋

where M1 and M 2 are the weight of the individual panels and d is the free distance in between. The
model assumes a cavity filled with mineral wool and without any sound bridges between the plates,e.g. studs.
The sound reduction is calculated within three frequency regions:
I.
II.
III.

f ≤ f0R=20log((M 1+M 2)·f)-k*
6 dB/octave bandf0 < f < fl R=R1 + R2 + 20log(fd)-29
R= R 1 + R 2 + 6f ≥ fl*) k=48 for t ≤ 130 mm, k=47 for t ≥ 180 mm

where R1 and R2 are the sound reduction from the individual panels.
3.2 Results
The outcome for a number of various wall configurations is summarized in Table 3. All the walls
are symmetric, the single panel thickness range from 70 to 160 mm and the cavity from 45 to 145 mm.
The configurations are modelled with and without complementary gypsum boards.
Table 3 – Data of calculated sound insulation of double CLT walls. Configuration is given as CLTcavity-CLT and G indicates gypsum board.
Config.

f0 (Hz)fl (Hz)Rw

Rw,50

Config.

Rw

Rw,50

70-45-70

1021200

46

43

G70-45-70G

51

48

70-70-70

81780

50

46

G70-70-70G

54

51

70-95-70

70

580

52

49

G70-195-70G

57

53

70-120-70

62

460

54

50

G70-120-70G

59

55

70-145-70

57

380

56

51

G70-145-70G

61

56

120-45-120

78

1200

53

49

G120-45-120G

56

52

120-70-120

62

780

57

52

G120-70-120G

60

55

120-95-120

53

580

59

55

G120-95-120G

62

58

120-120-120

47

460

61

57

G120-120-120G

64

60

120-145-120

43

380

63

58

G120-145-120G

66

61

160-45-160

67

1200

56

51

G160-45-160G

58

53

160-70-160

54

780

60

54

G160-70-160G

62

56

160-95-160

465806356

G160-95-160G

65

58

160-120-160

41

460

65

58

G160-120-160G

6760

160-145-160

37

380

66

60

G160-145-160G

69

62

3.3 Comparisons
Reported values for this specific type of walls are limited in the literature. A few references (9, 1213) referring to measurements in laboratory are valid for comparisons, see Table 4.

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Table 4 – Comparisons of single number ratings of double panel walls.
Configuration

LAB.MEASUREM.

MODELLING

DIFFERENCE

Rw

Rw,50

Rw

Rw,50

Rw

Rw,50

65-100-65

55

52

54

50

-1-2100-60-100

52-52

49

0-100-110-100≥ 55

≥ 53

56

52

≈1

≈-1

G100-110-100G

≥ 56

≥ 55

6055

≈4

≈0

Another comparison is done from horizontal measurements conducted inside a two room test
mockup (17), Table 5. As the measurements includes flanking transmission of the mockup, the soundreduction should take a lower value compared to the calculations, and a difference of 1-4 dB is noticed
for most of the configurations. However, focusing on the difference between the configurations, thedifference in sound insulation is rather similar for measurement and calculation for many of theconfigurations.
Table 5 – Comparisons of single number ratings of double panel walls.
Configuration

MOCK-UP MEASURE.

MODELLING

DIFFERENCE

Rw

Rw,50

Rw

Rw,50

Rw

Rw,50

70-70-70

50

45

50

46

0

1G70-70-70G

56

50

54

51-2

1

G70-145-70G

59

55

61

56

2

1120-70-120

53

50

57

52

4

2

G120-70-120G

58

53

60

55

2

2120-145-120

59

56

63

58

4

2G120-145-120G

61

58

66

61

5

3160-45-160

53

49

56

51

3

2G160-45-160G

56

52

58

53

2

1G70-70-160G

58

54

59

54

104. DISCUSSION AND CONCLUSIONS

The modelled sound insulation for single CLT panels showed in terms of single number ratings (R wand R w,50 ) good agreement with corresponding values found from literature references. The proposedmodel, a modified version of Sharp’s approach, may therefore serve as an engineering tool in
predicting the sound insulation performance. The deviation between measured and predicted ratings
was within ±2 dB in all cases but typically ±1 dB.
When it comes to walls of double CLT panels, the results indicate a fairly agreement with available
data for validation. But due to the limited amount of reference data, it is hazardous to quantify theuncertainty until further validating measurement results are found. The results indicates that a double
CLT panel wall, with appropriate combination of plate thickness and cavity depth, will serve as a goodalternative in terms of sound insulation when it comes to partitions between apartments.

ACKNOWLEDGEMENTS

The work has been financially supported by Wood Centre North (TCN) – Luleå University ofTechnology.

247

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