Chapter 5 Airborne sound insulation

Transcription

1 Chapter 5 Airborne sound insulation Airborne sound insulation is important for noise control in buildings, particularly when the noise source is speech, music or a noise source without mechanical connection to the building structure. A typical noise control application involves a combination of absorption of sound and transmission of sound energy by a variety of airborne and stucture-borne paths

2 Basic Definitions: Transmission Coefficient The transmission coefficient is a frequency-dependent physical property of material = I Transmitted = W Transmitted I Incident W Incident Sound Transmission Loss STL = the log ratio of the incident energy to the transmitted energy STL = 10 log 1/τ

3 A perfectly reflecting material has a transmission coefficient of 0 (STL = ), while the transmission coefficient of an opening is 1.0 (STL=0). It should be noted that typical materials tend to be better at blocking higher frequencies. Transmission loss can be measured directly (but not easily) by mounting a test panel between two reverberation rooms and measuring the sound pressure levels on each side. Other commonly used metrics to describe sound transmission include: NR = Noise Reduction = L 1 - L 2 (easy to measure) Note: NR STL! IL = Insertion Loss = change in sound levels with and without the barrier or treatment in place (easy to measure)

4 Sound transmission between adjoining rooms When the sound pressure levels in source and receiving rooms are L 1 andl 2, respectively, the level difference between the rooms is A 2 L 1 L 2 = R + 10Log 10 S L 1 = L w Log 10 A 1 L 2 = L w + 6 R 10Log 10 A 1 A 2 S (db) (db) (db) where L w = sound pressure level of source S 1 = surface area of the sourceroom S 2 = surface area of the receiving room α = is the average absorption coefficient A 1 = total absorption of the source room A 1 = S 1 α A 2 = total absorption of the receiving room A 2 =S 2 α Figure 6.1 Sound transmission between adjoining ro

5 Sound transmission from outside to inside Assuming that the incident sound on the outside wall is a plane wave whose intensity is I and the wall area is S, with incident sound level L 0. The difference in sound pressure level is L 0 L 2 = R Log 10 A 2 S (db) where L 0 must not include reflections from the wall. Also R 0 should be the value for normal incidence Figure 6.2 Sound transmission from outside to inside

6 Sound transmission from inside to outside When sound intensity I is radiated through the wall to the outside as shownin Figure 6.3, the radiated energy is I. If the source room has the samecondition as in Figure 6.1 and the sound level at the outside of the wall is L 0, L 1 L 0 = R + 6 (db) L 0 = L w 10Log 10 A 1 R (db) where this L 0 value is at the outside surface of the wall and is equivalent to L W. As the sound leaves the vicinity of the wall it spreads outwards. Figure 6.3 Sound transmission from inside to outside

7 B. Composite transmission loss In actual buildings, walls are rarely constructed from a single material but contain windows and doors as well, thus, a wall often includes several components that have different R values. The composite transmission loss denoted by R is expressed by, R = 10log 10 1 τ where τ is the average transmission coefficient,which can be obtained from the transmission coefficients τ i for the area S i τ = S iτ i S i The transmission coefficient τ i for the wall, whose transmission loss is R i, is given by 1 R = 10log 10, τ i = 10 R/10 τ i Figure 6.3 Sound transmission from inside to outside

8 [Ex. 6.1] An exterior wall constructed from reinforced concrete has an area 30 m 2 in which there is a glass window of 10 m 2 and the R values are 50 and 20 db, respectively. Find the composite transmission loss of the wall

9 [Ex. 6.2] Calculate the overall transmission loss at 125 Hz of a wall of total area 10 m 2 constructed from a material that has a transmission loss of 30 db, if the wall contains a panel of area 3 m 2, constructed of a material having a transmission loss of 10 db

10 Measurement of sound transmission loss: reduction index The test specimen is inserted in an opening between two adjacentreverberation rooms as shown in Figure. The sound is generated in oneroom, and the sound pressure levels L 1 and L 2 in both rooms are measuredin the steady state. Then the sound transmission loss R is R = L 1 L 2 10Log 10 A 2 S (db) where S is the area of the specimen, and A 2 is the absorbing area in the receiving room. The measurement instructions are defined in ISO 140 standards

11 Field measurement of airborne sound insulation When measuring airborne sound insulation in an actual building, there areflanking sound transmission paths as well as the direct path through thepartition, as shown in Figure. The value should be calledthe apparent sound reduction index, R. R = L 1 L 2 10Log 10 A 2 S (db)

12 Field measurement of airborne sound insulation This value may be used for comparison with the laboratory measured value of R. In order to evaluate the airborne sound insulation between rooms in the field, the level difference is used. D=L 1 L 2 (db) However, the receiving sound pressure level is inversely proportional tothe sound absorption area in the receiving room. So, the normalised level difference, with reference absorption 10m 2, is given by A 2 D n,10 = L 1 L 2 10Log (db)

13 Generally, this formula is used for the sound insulation of small structural elements (area of about 0.2m 2 or less), e.g. a fresh air vent in a facade, is defined by Normalised unit insulation D n,e : D n,e = L 1 L 2 10Log 10 A 2 A 0 (db) where A 0 = 10 m 2 and A 2 = absorption area of the receiving room. The definition means that the sound insulation of small elements is normalised to correspond to 10 m 2 wall area; this is done becauseusing the real area S of the element in the calculation would lead tovery low sound insulation values which would be miss-leading whencompared to the sound insulation of a wall structure

14 Alternatively, normalising the measured reverberation time T 2 in the receiving room to a reference value of 0.5 s, which is typical of domestic rooms, D n,0.5 = L 1 L 2 10Log 10 T (db) This equation is adopted and called the standardised level difference bythe International Standards Organisation

15 Weighted sound reduction index The value of the reference curve at 500 Hz, R w (or Rw) is called the weighted sound reduction index (or weighted apparent sound reduction index)

16 Weighted sound reduction index Weighted sound reduction index R w is a single-number quantity which is determined R w from the measured or calculated sound reduction index according to ISO between one-third octave bands Hz. Reference curve (ISO 717-1) is moved with 1 db steps to such a position that the sum of unfavourable to the reference curve is as large as possible but not more than 32,0 db (when measurement has been done in 16 one-third octave bands) or 10,0 db (when the measurement has been done in 5 octave bands) Unfavourable deviation: measured or calculated sound reduction index is smaller than the value of the reference curve at a certain frequency R w corresponds to field measurement and R w to laboratory measurement Terminology in English R w : apparent weighted sound reduction index R w : weighted sound reduction index 16

17 Determination from the reference curve

18 Determination from the reference curve

19 Field vs. laboratory measurement The sound reduction index measured in the field (R w ) is in practice always lower than that measured in laboratory (R w ), because: In a building sound traverses not only through the separating structure, but also via flanking structures as flanking transmission Holes and other sound leaks due to, e.g., installation errors deteriorate sound insulation Difference between R w and R w : As large as 20 db, if the structure contains sound leaks 5-10 db if flanking transmission is high below 1 db, if structures are properly sealed and flanking transmission has been eliminated

20 Field vs. laboratory measurement Example: double leaf wooden door measured in the filed and in Laboratory Difference in sound reduction index caused by poor sealing

21 Spectrum adaptation terms The shape of ISO reference curve is based on the variation of hearing sensitivity at different frequencies and the spectrum of speech Thus the weighted sound reduction index R w primarily describes the ability of structure to isolate speech! in order to describe sound insulation against, e.g, traffic noise other descriptors are needed because traffic noise has more sound energy at lower frequencies Spectrum adaptation terms: C tr : traffic noise C: railway and airplane traffic

22 Spectrum adaptation terms R w + C tr : weighted sound reduction index against road traffic noise R w + C: weighted sound reduction index against railway / airplane traffic noise These describe quite well how many decibels the structure is able to cut from the A-weighted traffic noise level The values are needed in the design of facade (and roof) sound insulation

23 ISO definition

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25 Basic structural types

26 Mass law for sound insulation of a single wall A. Normal incidence mass law When a plane wave, whose angular frequency is ω =2π f, is incident normally on an infinitely wide thin wall, some of the wave is reflected and some transmitted

27 The transmission loss for this system after some aproximation is R 0 10Log 10 wm 2ρc 2 = 20Log 10 f. m 43(dB) which is proportional both to frequency and the surface mass m of the wall. This is called the mass law for airborne sound insulation. Doubling the weight of the wall or the frequency gives an increase of 6 db in R

28 B. Random incidence mass law When the incident angle is θ, then the transmission loss equation can be derived as follows R θ 10Log 10 1 τ θ = 10Log wmcos(θ) 2ρc Log 10 1 τ θ 2 If we are calculating the average value in the range θ= , the equation is transformed as the random incidence mass law R random = R 0 10Log R

29 However, in an actual sound field, using the range of θ= , is more realistic and the following approximate formula is obtained R field =R 0 5dB which is recognized as closer to reality and called the field incidence mass law. Figure shows these theoretical curves

30 Coincidence effect on sound transmission The mass law has been derived on the assumption that the walls are set in uniform piston motion. However, flat plates are accompanied by bending vibrations, which cause significant decreases in R values. Coincidence occurs when the longitudinal sound wave in air hitting the plate at a certain angle and the bending wave in the plate are in phase, and thus sound penetrates the structure easily

31 When a plane wave whose wavelength λ is incidenton a wall at angle θ, a pattern of alternating sound pressure movesalong the wall with a wavelength of B = sin θ Therefore, the wall is excited by a bending vibration, which produces abending wave that propagates along the wall surface. The propagation speed c B of the bending wave ofa plate, whose thickness is h, can be derived from the theory of bending vibration of a bar. c B = 2πhf E 12ρ(1 σ 2 ) 1/2 where ρ is the density of the plate, E is the Young s modulus of the plate material and σ Poisson s ratio. c B an be seen to increase with frequency

32 In Figure 6.11 we can find the condition where the value of c B satisfies equation c B = c sin θ At this frequency, the bending vibration is such that its amplitude may become comparable to the incident sound wave, resulting in a serious decrease insound insulation. This frequency is called the coincidence frequency. This phenomenon is called the coincidence effect, as distinct from resonance

33 The coincidence frequency is f (θ) = c 2 2πhsin 2 (θ) 12ρ(1 σ 2 ) E The lowest coincidence frequency when θ=90 is given by f c c2 2πh 12ρ where σ =0.3 (leading to an approximation (1 σ 2 ) 1) and c s is the soundspeed in the solid material. f c is called the critical frequency. Critical frequency is the lowest frequency at which the coincidence phenomenon occurs. Any lower frequency than this yields c B <c resulting in an absence of coincidence, while at any higher frequency than f c, coincidence will occur. Coincidence occurs at the higher frequency, the more perpendicular to the plate is the sound incidence angle E

34 In Figure 6.12, the relationship between the material thickness h and f c for various materials is shown. The higher f c with smaller h the less the effect, but with larger h, f c decreases to the middle or lower frequency range essential for good sound insulation and, so, the transmission loss is seriously decreased. The length and width of the panel should be at least 20 times the panel thickness (Watters 1959). For a given material, the coincidence frequency is inversely proportional to the panel s thickness. Therefore, the coincidence frequency can be raised by decreasing thickness. The higher the frequency, the greater the transmission loss, or in other words, the better the wall is as a barrier to outside noise

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36 Frequency characteristics of a single wall We have considered the infinitely wide wall for the mass law and the effect of coincidence on the sound transmission

37 Frequency characteristics of a single wall In region I in Figure, below tthe lowest resonance f rl, the wall is generally controlled by its stiffness and edge condition. In the second region, higher resonances are controlled, not only by the mass but also by internal energy losses and losses at the boundaries. At frequencies two to three times f rl up to and near the critical frequency f c, is the mass controlled region III. In region IV, there is multi-coincidence, which is controlled by both stiffness and resistance. It is very difficult to estimate the sound transmission in the lowest frequency region I, but easier to make approximations in the higher frequency regions as mentioned above

38 Sound insulation of double-leaf walls According to the mass law, the transmission loss of a single wall increases by only 6 db for a doubling of the wall thickness, i.e. twice the mass. Also, when the thickness increases, the coincidence effect may cause undesirable results. This suggests that sound insulation of a single wall has its limitations. In order to isolate the structural coupling, the leaves should be mounted on staggered studding with a resilient connection between stud and leaf. Also, in order to reduce the acoustic coupling through the air, the air space should be increased as much as possible and absorptive treatment introduced into the cavity between the leaves

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40 Double structures Structural types

41 Double structures Structural types

42 In the case of a fixed double- or tripleglazed window, since absorptive treatment in the air space is limited to the reveals as shown in Figure. It is recommended that the air space should be enlarged to increase the absorptive area and its absorption characteristic tuned to the resonance frequency of the air space. There are also techniques for reducing the effects of coincidence by using different thicknesses of glass for the two panes and attenuating welldefined resonances by slanting one pane with respect to the other

43 Depending on the coupling type, the following rules of thumb can be given of the factors that affect sound insulation. The sound insulation of a non-coupled double-leaf partition Total mass increases (amount of plates) Thickness of air space increases Amount of absorption material in air space increases The sound insulation of a coupled double-leaf partition improves when; Amount of couplings (studs, railings) decreases Flexibility of couplings increases, i.e., their dynamic stiffness decreases Attachment of plates to studs weakens (amount of screws decreases and/or the screwing tension decreases)

44 Theoretical values of double-leaf wall transmission loss is, R 02 = 10Log 10 w 3 m 2 d 2c 3 ρ 2 2 = 2R01 +20Log 10 2kd where R 01 is the transmission loss of a single wall given

45 Practical sound insulation of double-leaf walls A dip may occur in the R curve around the resonance frequency f rm, beyond which the curve slopes up by about 10 db oct 1 to higher frequencies. The peaks and dips due to f rd and due to f rd, may not appear distinctly, but the fall at 4 khz coincides with the critical frequency f c of a single plywood wall. Therefore, sometimes different panel thicknesses are employed so that the values of f c for each panel are different. There are two ways of increasing the R of this type of wall, as shown in the figure. One is by inserting absorbing material into the air space and the other is by underlining the outer skin with plasterboard. It can be seen that in (a) the effect of glass fibre is larger in the case of a lightweight partition, while in (b) inadequate application of plasterboard does not work so well

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47 Sandwich panels As an application of the above mentioned double-leaf wall construction, filling the air space with other materials, thus creating a sort of triplelayer wall, can be considered in order to increase thermal insulation or for other purposes. Theoretically, in place of the air spring previously discussed, the core material is thought of as acting as an elastic spring or resistance in the analogous electrical circuit. If the core material is glass fibre, for example, it acts as a resistance that improves the sound insulation, while an elastic material such as sponge or foamed plastic may produce more peaks and troughs in the frequency characteristics, thus decreasing sound insulation. Therefore, careful selection of material with reference to measured data is essential

48 Sound insulation of sandwich structures

49 Composite Wall with Air Space The double-wall construction, consisting of two panels separated by an air space, is often used as a barrier to reduce noise transmission. For this construction, the overall transmission loss is influenced by the air mass in the space, in addition to the effect of the transmission loss for each separate panel. The behavior of the TL curve for the composite wall may be divided into three regimes. Regime A, the low-frequency regime, occurs for closely spaced panels. When the two panels are placed very close together, the panels act as one unit, as far as the sound transmission is concerned

50 The air space between the panels has a negligible effect. This behavior occurs for the frequency range, as follows The frequency f o is the resonant frequency of the two panels coupled by the air space The transmission loss for Regime A is given by the following:

51 As the panels are moved farther apart, standing waves are set up in the air space between the panels, and Regime B behavior is observed. This regime occurs for the frequency range, as follows: The transmission loss in Regime B is given by the following: When the panels are moved sufficiently far apart, the two panels act independently, and Regime C behavior is observed. The air space between the panels acts as a small room. This behavior occurs for the frequency range, f > (c/2 π). The transmission loss in Regime C is given by:

52 Sound transmission through openings and cracks When a porous material or one with cracks is used, the transmission loss may be greatly reduced from the value estimated on the basis of the mass law, because sounds leak through the pores or cracks. If a fairly large opening is provided, the composite transmission loss should be calculated using a transmission coefficient τ =1 (R=0 db) for the opening area. Where a small opening exists, diffraction may occur. There is a complicated relationship between the wall thickness and the sound wavelength and in some cases τ >1 at the resonance frequency. Therefore, even with a tiny opening there might be an unexpectedly large sound transmission so that insulation may be seriously decreased

53 Example: Two panels of glass, each having a thickness of 6mm are to be used to reduce the sound transmission through an opening 1.00 m high and 2.00 m wide. The panels are spaced 75mm apart, and the air around the panels is at 248 o (758F), for which ρ = 188 kg/m 3 and c = 345.6m/s. The surface absorption coefficient for the glass is = 0:03. Determine the transmission loss at the following frequencies: (a) 250 Hz, (b) 1000 Hz, and (c) 4kHz

54 Example: Two panels of glass, each having a thickness of 6mm are to be used to reduce the sound transmission through an opening 1.00m high and 2.00m wide. The panels are spaced 75mm apart, and the air around the panels is at for which ρ = kg/m 3 and c =345.6m/s.The surface absorption coefficient for the glass is α = Determine the transmission loss at the following frequencies: (a) 250 Hz, (b) 1000 Hz, and (c) 4kHz

55 Figure. Example of transmission loss for circular hole 55

56 Sound insulation of windows and doors The sound insulation of windows and doors depends not only on the insulation of the fittings but also upon the sealing around their perimeters. The sound insulation of fittings is evaluated in the same way as for a single- or double-leaf wall, also taking into effect small cracks. Even though the R value of the door panel is increased, the insulation may not improve unless the gaps at the perimeter are minimised

57 Figure: Example of measured composite transmission losses of walls with slits; wall size: 1.9m 1.9m, slit located at centre; slit length: 1.9 m; solid line: measured value by 1/2 octave band; broken line: calculated value assuming slit R = 0; dash-dotted line: theoretical value of pure tone

58 Sound insulation of windows and doors The first door has a gasket for sealing the edge of the door, and also absorptive treatment at the perimeter. It is essential to minimise the gap. The second door has a drop-bar, which automatically seals the gap when the door is in a closed position. This is very useful where a flat floor is required even under the door. In some cases, doors are weighted with dry sand or consist of dense boards and porous materials. When an R value of more than 30 db is required, it may be advantageous to employ a double-door arrangement with absorbent lining to the walls and ceiling between the doors as a sound-lock

59 Figure: Examples of sound-insulating doors

60 Sound insulation of windows and doors The first door has a gasket for sealing the edge of the door, and also absorptive treatment at the perimeter. It is essential to minimise the gap. The second door has a drop-bar, which automatically seals the gap when the door is in a closed position. This is very useful where a flat floor is required even under the door. In some cases, doors are weighted with dry sand or consist of dense boards and porous materials. When an R value of more than 30 db is required, it may be advantageous to employ a double-door arrangement with absorbent lining to the walls and ceiling between the doors as a sound-lock

61 Flanking transmission The sound transmission between two rooms in a building depends not only on the dividing construction, wall or floor, but the flanking building constructions can also give very important contributions to the transmission. If the rooms are further apart and have no common wall, it is obvious that the sound transmission is entirely flanking transmission. In some cases, flanking transmission can reduce the sound insulation seriously

62 Transmission paths in a building

63 Phenomenon and meaning Laboratory measurement yields the sound reduction index of a single building element (partition etc.) In a building sound is transmitted between spaces not only directly through the separating structure, but via flanking structures as flaking transmission This phenomenon is called structural flanking transmission. The greater the sound insulation requirement between spaces, the more effect flanking has on sound insulation and the more the design of sound insulation becomes minimizing of flanking transmission

64 There are three basic principles to avoid flanking transmission. 1. Heavy flanking construction In buildings with heavy constructions, like concrete or masonry, the flanking transmission is a minor problem if the flanking constructions are sufficiently heavy, i.e. having a surface mass at least 70 80% of that of the dividing construction. The heavy flanking construction means that the vibrations created by the incident sound have a very small velocity and, thus, the sound energy that can be transmitted to the next room is very limited

65 2. Separation of flanking constructions The best way to avoid flanking transmission is often to disconnect the flanking structure at the point where it passes the dividing construction. However, in practice it is not always so easy, and some kind of resilient layer can be the solution instead of a gap. Such solutions may put high demands on the materials and on the correct execution. Some examples are shown in below Figure

66 Examples of separation to avoid flanking transmission. (a) Concrete wall connected to a facade of sandwich-elements. (b) Concrete wall connected to ceiling elements of lightweight concrete; elastic sealing and mineral wool in the gaps. (c) Floating floor with a gap under a light partition wall

67 3. Treatment to reduce sound radiation The vibrations generated in the flanking construction may not necessarily radiate much sound energy if the construction is a panel with a sufficiently high critical frequency. A gypsum board with thickness 13mm or less is a typical example of such a panel. At frequencies below the critical frequency the vibrations in the panel are travelling at a lower speed than the sound in the air, and thus the sound radiation is not efficient. Some examples are shown in below Figure

68 Figure: Examples of flanking constructions with reduced sound radiation. (a) Light wooden facade elements connected to a massive partition wall. (b) Same as (a) but improved to avoid leakage problems. (c) Lightweight concrete facade with internal treatment of 9mm gypsum board on laths