Open windows with better sound insulation

INTER-NOISE 2016 Open windows with better sound insulation Lars Sommer SØNDERGAARD1; Rune EGEDAL2 1,2 DELTA Acoustics, Denmark, Aarhus ABSTRACT Nea...
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INTER-NOISE 2016

Open windows with better sound insulation Lars Sommer SØNDERGAARD1; Rune EGEDAL2 1,2

DELTA Acoustics, Denmark, Aarhus

ABSTRACT Nearly 1/3 of the Danish homes are estimated to be exposed to a road noise level greater than the limit threshold of 58 dB Lden. The Danish Environmental Protection Agency’s guideline from 2007 “Noise from roads” introduces noise limits with open windows (opening area of 0.35 m2) for certain situations. With a moderate/high outdoor noise level from traffic, railway or industry these noise limits cannot be complied with for traditional windows, but requires windows with better sound insulation in open position. For this project three overall window types has been investigated; 1: Further improving the Supply Air Window with special attention to low frequencies, e.g. different types, placement and dimensions of absorbers and resonators have been verified. 2: Double window with focus on the inner cavity between the windows, where different kinds and length of sound barriers have been explored. 3: Single window with different types and placement of (outer) attachments, in the form of sound traps. The project has been initiated by a literature study followed by several laboratory measurement series. Compared to a single window opened 0.35 m2 the sound reduction improvements depending on window type (for Rw+Ctr) are in the magnitude of 18/6/10 dB. Keywords: Open windows, Sound Insulation, Traffic noise I-INCE Classification of Subjects Numbers: 32.4, 33, 51.3

1. INTRODUCTION This project focused on acoustical optimization of open windows is conducted by DELTA in cooperation with HSHansen A/S. This paper addresses some of the results achieved in the project. The project consists of four parts: The three first parts investigates three different solutions and are primarily laboratory studies following (9, 10), initialized by a literature study. The last (fourth) part primarily consists of field measurements and is currently under planning. The project is initiated from (6, 7 and 8). In these guides a relatively new requirement is set that in special situations, where the outdoor noise levels from e.g. road traffic or railroads is high, the indoor noise level in apartments and offices must be under a certain level with open windows, where the opening area is 0.35 m2 for each openable window. The maximum allowable levels for apartments and offices from road traffic are L den 46 dB and 51 dB respectively. Since the introduction of the new guidelines it is regularly stated by authorities, planners and producers, that further knowledge and documentation is needed, as well as more alternative and cheap solutions. They call for a selection of solutions, so it is not necessary to choose a too expensive solution (with better sound insulation than needed) in cases where only a little be tter sound insulation than a regular open window is needed.

2. Inspiration The project was initialized by a literature study. Research in this area is also conducted outside Denmark, but due to the Danish rule of an opening area of 0.35 m 2, the primary relevant sources for this project are Danish and can be seen below. In parallel with the project several student projects regarding Supply Air Windows was conducted, focusing on active noise reduction and angle of incidence (13).

1 2

[email protected] [email protected]

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2.1 Acoustical optimization of Supply Air Windows This project is based on a previous project focused on acoustical optimization of Supply Air Windows, which was also conducted by DELTA in cooperation with HSHansen A/S. The project investigated the primary parameters of significance for the sound insulation of the open window. Compared to a regular open window with the same opening area the Supply Air Window typically had 8-16 dB (R w+C tr ) better sound insulation depending on configuration and dimensions. The project consisted of both laboratory measurements, field measurements and occupant’s response and has been reported in (1 - 5). Beside the good results, it was concluded that it would be suitable to continue the work on the Supply Air Window, especially with regard to improving the sound reduction for the low frequency area (100 – 250 Hz). Furthermore there is a need of developing alternative solutions to the Supply Air Window, because it in some situations has a sound reduction better than needed, and thereby will be an unnecessary expensive solution. 2.2

Experiences with sound insulating open windows in traffic noise exposed residential

areas The Danish Building Research Institute (SBi) has in 2015 concluded a study of experiences with sound insulating open windows in traffic noise exposed residential areas (11, 12). Experience from seven field cases with different solutions has been collected, and additional field experiments have been carried out in a case with transparent external shutters with sound absorbing slits for ventilation along window sides. The SBi project concluded after this papers literature study but is included here since it is a good summary of the major inspirations. In the SBi project it is concluded “that occupants in general are satisfied with the solutions and further development for more general use is recommendable, but investigation of ventilation performance should be integrated in future research”.

3. Choice of window types In the project it was chosen to work with three different window types; 1) continued work on the Supply Air Window (with special regard to low frequency sound reduction), 2) “Ordinary window” with internal solution and 3) “Ordinary window” with external solution.

4. Window type 1: Supply Air Window The Supply Air Window is a double construction consisting of two separate parts. Both parts are fitted with a sash that can be opened. For the outer part the sash is fitted in the bottom of the window and for the inner part the sash is fitted in the top of the window. The outer sash is top hung and the inner is bottom hung see Figure 1. The construction is well known and is generally the same as used in previous studies (1-5). The construction is known for its good acoustic properties, this is due to the large vertical channel that the noise has to pass through before it reach es the outlet of the inner part. This alone yields an improved sound insulation. For further improvements of the sound insulation it is possible to fit the cavity with sound absorptive materials of different kind. The double construction of the Supply Air Window introduces a large cavity also when the window is closed. This leads to a very high sound insulation when both sashes are closed. 4.1 Choice of absorbers As concluded by the previous studies conducted on the Supply Air Window the effect of plate absorbers inside the cavity is significant (plate absorbers of the type SUND® Miljöundertak has been used throughout the project). One issue raised is that it is very difficult to improve the reduction of low frequencies. Measurements indicated that the use of a substantially thicker absorber increased the reduction index. However this solution took up a lot of space in the cavity where parts of the window was non-transparent. For this study the aim is to increase the low frequency reduction by introducing absorbers which can handle the low frequencies and at the same time keep the cavity open in order to keep the transparency of the window. Therefore two different types of absorbers were chosen. One based on the Helmholtz resonator, and the other based on perforated plates. These absorbers was chosen because they are easy to work with, they are passive hence they will not introduce any additional electronics and they can be implemented outside of the cavity between the windows.

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Inner service opening

Outer service opening

Inner vent

Outer vent

Figure 1 – Left figure: Principle of the Supply Air Window. Right figure: Principle vertical section of the installed Supply Air Window also showing position of vents and service openings.

Figure 2 – Left figure: Small cavity within the external cavity wall. Right figure: Perforated plates covering the small cavity

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4.2 Possible implementation The two different types of absorbers can both be aimed at reducing low frequencies, although the Helmholtz resonator has a much narrower sound absorptive area than the perforated plate. 4.2.1 Helmholtz resonator The resonator can be constructed in different ways. Introducing the resonator in its traditional form would however take up a lot of space. In the conducted literature study another version of the resonator was found, which had a favorable shape that would fill up less space and provide the same attenuation at a specified frequency. The resonator used for this study is based on (14, 15) and is referenced as the T-shaped resonator. In order to fit the resonators the external cavity wall is opened up, see the left side of Figure 2. A small cavity is built within the external cavity wall and further filled up with mineral wool. The resonator is fitted in to the mineral wool with the opening facing the cavity between the windows. The external cavity wall is then sealed with gypsum board plates with holes at the resonator positions. 4.2.2 Perforated plates The perforated plate is designed to give a wider frequency dampening. In order to facili tate as many implementations as possible the small cavity within the external cavity wall is kept. The small cavity is built all around the window edges, so that it is possible to implement perforated plates both at the top, bottom and sides. The right side of Figure 2 shows the perforated plates mounted on the small cavity. The perforated plates are made of gypsum board plates, with a different perforation grade than shown in Figure 2. The applied perforation grade is 35% and the cavity has a depth of 410m m. 4.3 Laboratory measurements Measurements were conducted on three window sizes (width x height): 1250 mm x 2100 mm (A), 1250 mm x 1500 mm (B) and 900 mm x 2100 mm (C), all with a distance of 210 mm between the inner and outer part. The two different absorbers were implemented as described in the previous section. Different setups were tested with the two absorbers. The T-shaped resonator was tuned in at different frequencies ranging from 80 -315 Hz. The resonators were placed strategically inside the cavity in order to reach maximum effect. Setups with up to 6 resonators tuned to the same frequency were tested. The strategically placement was based o n a quarter wave approach, assuming a closed window. The measurements with resonators were only conducted in the large window size (A). The measurements were conducted in the laboratory with a moving source, but none of the measurements showed significant improvement within the target frequencies. In order to see if the resonators had any impact a measurement was conducted with a static source and narrowband noise at 250 Hz. For this particular measurement 6 resonators tuned at 250 Hz showed some improvement. But for the standard measurement procedure no significant change in reduction index was achieved , and as a result measurements with the T-shaped resonator were not carried out on the other window sizes. The perforated plates were measured with different amounts of mineral wool in the small cavity; no mineral wool, half-filled and full of mineral wool. Further - in order to cover as wide a frequency range as possible - the perforation grade of the plates varied within the cavity. For the perforated plates measurements were conducted on all three sizes of the windows, (A), (B) and (C). In order to enhance the effect of the perforated plates a layer of absorptive material was added to the outside of the plate, covering the perforations, where the idea is to absorb the higher frequencies even more in order to achieve very high performance. A selected number of results are shown in Table 1 and Figure 3. As can be seen the shift from having gypsum board plates with no perforation in the cavity to having gypsum board plates with perforation yields a significant increase in the reduction of the lower frequencies. The difference between Id no. 11, 12 and 13 is most pronounced in the low frequencies, with different degree due to the varying of the perforation grade. As can be seen by these results it is also clear that the perforated plate s has almost no influence on the higher frequencies which are entirely controlled by the amount of absorptive material fitted into the cavity. For the two other window sizes (B and C) an increase of the reduction index is also seen although not as prominent as for the larger window (A).

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Figure 3 – Sound reduction index for: Left figure: Laboratory results for type A. Right figure: Laboratory results for type B and C Table 1 – Overview of Figure 3 – all values given as a percentage indicate the degree of perforation of the gypsum board plates. Openings refer to the sashes at the top and bottom. For Id no. 6 the extra absorber is fitted opposite of the sash. All results are for open windows unless otherwise indicated. Id. No.

Rw

Rw+Ctr

Description

1

18

16

Only gypsum board plates (A)

2

24

20

40 mm frame absorber (A)

3

24

22

3.14 % 40 mm frame absorber (A)

4

25

22

3.14 % and 34.9 % 40 mm frame absorber (A)

5

29

24

As Id no. 4 with 20 mm absorber on openings (A)

6

30

26

As Id no. 5 with 80 mm top and 40 mm bottom (A)

7

55

50

Closed window (A)

8

16

15

Only Gypsum board plates (B)

9

20

19

3.14 % and 34.9 % 40 mm frame absorber (B)

10

23

20

As Id no 9 with 40 mm absorber on openings (B)

11

20

18

Only Gypsum board plates (C)

12

26

23

3.14 % and 34.9 % 40 mm frame absorber (C)

13

28

24

As Id no 12 with 40 mm absorber on openings (C)

14

59

57

Closed window (C)

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5. Window type 2: “Ordinary window” with internal solution The basic idea of this window type is to increase the sound insulation within the limits of a standard sized window. The main purpose is that this window type should be easily incorporated into already existing buildings and should be less expensive than the Supply Air Window. 5.1 Development of solution The solutions are based on a standard sized window (width x height): 1230 mm x 1480 mm. Two mockup constructions are devised with an internal sound absorptive solution. The distance between the inner and outer part was varied between 210 mm and 290 mm. Results showed that it did not substantially change the sound reduction.

Figure 4 – Sketches of the two mockup solutions: Left: Mockup solution A. Right: Mockup solution B 5.1.1 Mockup solution A The solution is based on a side hung double construction with a sound absorber in between. The window is split into two equal parts with a plywood plate, one part which is closed and another which is open. For the open part a plywood plate is situated in between the double construction in order to create a longer path for the sound. The size of the plywood plate is varied between 200 mm and 460 mm, absorptive material was added to the plywood plate and the frame . A sketch of the mockup is shown in the left side of Figure 4. Table 2 – Overview of the left side of Figure 5 Id. No.

Rw

Rw+Ctr

Description

15

7

6

Single window

16

56

45

Closed added absorption

17

17

14

Mockup solution A, 290 mm plate, added absorption

18

16

13

Mockup solution A,200 mm plate, added absorption

19

15

12

Mockup solution A, 290 mm plate, no absorption

20

18

16

Mockup solution B, 290 mm plate, added absorption

21

23

19

Mockup solution B, 510 mm plate, added absorption

5.1.2 Mockup solution B The solution is based on a side hung double construction, only this time the window is hung from the middle of the construction, creating an illusion of a side hung window. A plywood plate is situated in between the double construction in order to create a longer path for the sound. The size of the plywood plate is varied between 290 mm and 700 mm, absorptive material was added to the plywood plate and the frame. A sketch of the mockup is shown in Figure 4.

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5.2 Laboratory measurements on mockup Both of the mockup solutions were installed in the laboratory and a large number of measurements were conducted. A selected number of results are shown in Figure 5 and Table 2. As a reference, a measurement with only an open single window is performed, and as expected with very poor results. For the following curves the double construction is used, but with the two different mockup approaches. For the other results it is seen that introducing a double construction with a prolonged way for the sound increases the reduction of especially higher frequencies and adding absorption increases it further but with the cost of transparency. Furthermore it is seen that there is a quite large difference between Mockup A and B for frequencies around 125 Hz. This difference is caused by the geometry of the cavity when it is separated into two equal parts. Additionally a measurement with an all-closed double window is shown, and as seen for the Supply Air Window the closed version has a significant sound reduction.

Figure 5 – Sound reduction index for: Left figure: Laboratory results for window type 2, mockup solutions. Right figure: Laboratory results for window type 2, prototype solution 5.3 Development of prototype Based on the results and on the convenience needed for everyday use the model selected for prototyping is mockup solution A, even though it was not the most effective solution. Based on the mockup HSHansen developed a prototype solution with a sliding window in between the double construction. This solution secures an agile system where it is possible to set th e window in any position and still have the benefit of transparency. The prototype can be seen in Figure 6. 5.4 Laboratory measurements on prototype A number of laboratory measurements were conducted on the prototype. A selected number of the measurements can be seen in the right side of Figure 5 supplemented with a short description in Table 3. As can be seen the reduction is primarily due to the double construction, adding absorption to the frame only increases the sound reduction by 1 dB. Measurements with perforated plates were tested as they were for the Supply Air Window, but it did not improve the sound reduction. It did however shift the weighting of the spectrum towards a lower frequency.

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Figure 6 – Photo from the laboratory of the prototype. Left figure: Window wide open for adjustment of the sliding window. Right figure: The window adjusted to 0.35m2 opening area. Table 3 – Overview of the right side of Figure 5 Id. No.

Rw

Rw+Ctr

Description

22

7

6

Single window

23

52

41

Prototype, closed window, added absorption frame

24

15

12

Prototype, 290 mm, added absorption frame

25

13

11

Prototype, 290 mm, no absorption frame

26

14

12

As Id no 24 with perforated (34.9 %) plate at entrance

6. Window type 3: “Ordinary window” with external solution The focus for this window type is to investigate an added external solution and is to be used for both new buildings and renovated buildings. The work package is divided in first a mockup part followed by a prototype part. 6.1 Development of solution Based on a brainstorm different solutions were suggested. In the end it was decided on focusing at three mockup constructions, all external solutions added to a two -winged window with standard size (width x height): 1230 mm x 1480 mm: 6.1.1 Mockup solution A This mockup solution can be described as a plywood box (or sound trap) with the dimensions (width x height x thickness): 1850 mm x 1640 mm x 160 mm. The box is closed in top and bottom, but open in each of the sides. Extensions were added in each side for some of the measurements resulting in dimensions: 2250 mm x 1640 mm. The solution was tested with an inward opening single window. For an eventual final solution the surface in parallel with the window will also be a window as sketched in the left side of Figure 7. However for the measurements this part was plywood too . The parts shown as plywood in Figure 7 (sides, top and bottom) were for some of the measurements covered by absorption (20 – 40 mm thickness) in order to increase the sound insulation. 6.1.2 Mockup solution B This mockup solution can be described as a plywood box (or sound trap) with the dimensions

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(width x height x thickness): 1850 mm x 1640 mm x 270 mm. The solution was tested with an inward opening single window. The box is closed in top, bottom and one side, but open in the other side. An extension was added in the open side for some of the measurements resulting in dimens ions: 2050 mm x 1640 mm. For an eventual final solution the surface in parallel with the window will also be a window as sketched in the middle side of Figure 7. However for the measurements this part was plywood too. The parts shown as plywood in Figure 7 (sides, top and bottom) were for some of the measurements covered by absorption (20 – 40 mm thickness) in order to increase the sound insulation. 6.1.3 Mockup solution C This mockup solution can be described as an on-the-side sound trap or open plywood box with the dimensions (width x height x thickness): 590 mm x 1480 mm x 270 mm. The solution was tested with an outward opening single window. The box is closed in top and bottom, but open in each side. The idea is that the window opens outwards and “locks” to the box. Additionally a n extension was added in the open side for some of the measurements resulting in dimensions: 1090 mm x 1480 mm. In the box absorption is added in order to increase the sound insulation. A sketch of the principle is shown to the right in Figure 7.

Figure 7 - Sketches of the three mockup window solutions: Left: A, Middle: B, Right: C 6.2 Laboratory measurements on mockup Each of the mockup solutions was installed in the laboratory and a large number of sound reduction measurements were performed. A selected number of results are shown in Figure 8 and Table 4. Table 4 – Overview of the left side of Figure 6. Id. No.

Rw

Rw+Ctr

Description

27

7

7

Window without added external solution

28

11

10

Mockup solution A, short box, no added absorption

29

22

18

Mockup solution A, long box, added absorption

30

14

13

Mockup solution B, short box, no added absorption

31

26

22

Mockup solution B, short box, added absorption

32

10

9

Mockup solution C, short box, no added absorption

33 24 19 Mockup solution C, long box, added absorption Besides the measurements with the added external solutions a measurement of the “ordinary window” has also been performed as a reference. As expected the sound reduction is very low for this measurement. For the remaining six curves it is here chosen to show two types of result; First: a measurement without the box extension (denoted “short box”) and without added absorption material. Secondly: a measurement with the box extension (denoted “long box”) and with a dded absorption material. The point of this is to indicate the sound reduction range for each of the mockup solutions. As can be seen the short box results without added absorption are relatively similar to the ordinary

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window. With extended box and added absorption the results vary much from the ordinary window – especially for frequencies above 250 Hz. Especially solution B show some promising results, which approaches the results of the Supply Air Window.

Figure 8 – Sound reduction index for: Left figure: Laboratory results for window type 3, mockup solutions. Right figure: Laboratory results for window type 3, prototype solution 6.3 Development of prototype The results of the measurements with the mockup solutions were evaluated in order to select one of them for prototyping. Solution C was chosen primarily since it was the most innovative of the solutions, even that it was not the one with the highest sound reduction. Based on the mockup HSHansen developed a 2mm aluminum prototype with a detachable bird grid, which is shown in Figure 9.

Figure 9 – Photo from the laboratory showing the external solution prototype. Left figure: Photo taken slightly above, with the window closed. Right figure: Photo taken from the right side without bird grid, with added absorption and with the window open.

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6.4 Laboratory measurements on prototype A number of laboratory measurements on sound insulation were performed with the prototype. A selected number of the measurements are shown graphically in the right side of Figure 6 supplemented by a short description of each measurement together with single number values in Table 5. As can be seen added absorption is very important for this solution. Meas urements with added bitumen were also performed in order to check the influence of added sound insulation/weight to the aluminum construction. As can be seen the added bitumen had nearly no effect. For some of the measurements the absorption thickness was varied. As it can be seen the absorption thickness has an influence on most frequencies and increases the single number sound reduction by 3 dB. Finally a measurement with closed window was performed. It can be seen that the sound reduction is not as large as for window type 1 and 2, which primarily is due to that the “ordinary” window for window type 3 is only a single window, which in general will have a sound reduction similar to the sound reduction of the “ordinary window”. Naturally window type 3 can be used for a double window as well with increased sound reduction with both open and closed window. Table 5 – Overview of the right side of Figure 6. Id. No.

Rw

Rw+Ctr

Description

27

7

7

Window without added external solution

34

10

9

Prototype, no added absorption

35

21

17

Prototype, added 40mm absorption

36

18

14

Prototype, added 20mm absorption

37

10

9

Prototype, no added absorption, bitumen added

38

38

31

Prototype, no added absorption, close window

7. CONCLUSIONS Three window types with a large number of solutions has been investigated and documented, to be used for different applications and problems. For window type 1 (the Supply Air Window) the low frequency sound reduction has been improved resulting in an open window sound reduction comparable with the sound reduction for a closed regular window (with low sound reduction). For window type 2 and 3 several solutions has been empirically investigated both as mockup solutions and prototype solutions. A summary of benefits and downsides for each of the three window types is shown in Table 6. Additionally the improved sound reduction (expressed as R w+Ctr ) is shown comparing each of the window types to a regular open window (all with an opening area of 0.35 m 2 ). Table 6 – Summary Window type 1

∆ Rw+Ctr

18

Downsides

Upsides

Double construction -> expensive

Very good sound reduction when open

Need to be high to “work”

Very good sound reduction when closed

Nearly fixed formats

Nearly no visual impact

Double construction -> expensive 2

6

Slightly improved sound reduction when open

3

10

Nearly no visual impact Good sound reduction when closed

Visual impact

Good sound reduction when open

Need special closing mechanism

Do not need to be made in glass

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ACKNOWLEDGEMENTS The project is partly financed by the Danish Ministry of the Environment under the development program “Grøn Teknologi 2013” (Green Technology 2013).

REFERENCES Notice that reference 1, 2, 3, 5, 6, 7 and 11 are only available in Danish. 1. Legarth SV, Søndergaard LS. Spørgeskemaundersøgelse og lydmålinger af Russervinduer monteret i Kollektivhuset, Hans Knudsens Plads 1, 1. sal, København Ø. (Questionairy and sound measurements of the Supply Air Window mounted in Kollektivhuset, Hans Knudsens Plads 1, 2. floor, Copenhagen East). DELTA, 2013 2. Søndergaard LS, Olesen HS. Designguide for bestemmelse af "Russervinduer" lydisolation. (Design guide to determine sound insulation of Supply Air Windows). DELTA, 2011 3. Søndergaard LS, Olesen HS. Lydmæssig optimering af "Russervinduer" - Miljøprojekt nr. 1417, 2012 (Acoustical optimization of Supply Air Windows - Environment project no. 1417, 2012). DELTA/Danish Ministry of the Environment, 2012 4. Søndergaard LS, Olesen HS. Investigation of sound insulation for a Supply Air Window. Proc. 43rd Forum Acusticum; 27 June - 1 July 2011; Aalborg, Denmark 5. Søndergaard LS, Legarth SV. Investigation of sound insulation for a Supply Air Window – field measurements and occupant response. Proc. 43rd International Congress on Noise Control Engineering , Inter-noise; 16 - 19 November 2014; Melbourne, Australia 6. Danish Ministry of the Environment, 2007, Vejledning 4/2007, Støj fra veje (Guidance 4/2007 Noise from roads) 7. Danish Ministry of the Environment, 2007, Tillæg til vejledning nr. 5/1984: Ekstern støj fra virksomheder (Addition to guidance 5/1984: Environmental noise from plants) 8. Danish Ministry of the Environment, 2007, Tillæg til vejledning nr. 1/1997: Støj og vibrationer fra jernbaner (Addition to guidance 1/1997: Noise and vibration from railroads) 9. ISO 10140:2010, Acoustics - Laboratory measurement of sound insulation of building elements - Part 1, 2 4 and 5 10. ISO 717-1:2013, Acoustics – Rating of sound insulation in buildings and of building elements – Part 1: Airborne sound insulation. 11. Rasmussen B, Erfaringer med lydisolerende åbne vinduer i trafikstøjbelastede boligområder (Experiences with sound insulating open windows in traffic noise exposed residential areas), Danish Building Research Institute, (2015). www.sbi.dk/SBi2015:08. 12. Rasmussen B, Experiences with sound insulating open windows in traffic noise exposed housing, Proc. 44th International Congress on Noise Control Engineering , Inter-noise; 9 - 12 August 2014; San Francisco, USA. 13. Hansen MB, Investigating the impact of noise incidence angle on the sound insulation of a supply air window, Proc. 44th International Congress on Noise Control Engineering , Inter-noise; 9 - 12 August 2014; San Francisco, USA 14. Cheng LL, Yu GH, Vipperman KS, Noise control in enclosures: Modeling and experiments with T-shaped acoustic resonators, Acoustical Society of America, 2007, Pages 2615-2625 15. Li D, Vipperman JS, On the design of long T-shaped acoustic resonators, Acoustical Society of America, 2004, Pages 2785-2792

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