Airborne Sound Insulation of Sustainable Building Facades

Abstract

Two trends are currently leading to an increased risk of indoor noise pollution. Firstly, urban densification causes traffic noise sources to be closer to the building facades which makes them louder at the facades. Secondly, airtightness of buildings, due to energy regulations, leads to the need of natural or mechanical ventilation to ensure a “healthy” indoor air quality, thereby allowing noise to easily pass from outdoors to indoors. In the case of mechanical ventilation, an additional noise source is also created. This study investigates the risk reduction of an indoor noise problem by optimizing the facade elements regarding sound insulation. Noise levels of different transportation noise sources (cars, trucks, trains) are used to calculate the resulting indoor noise levels after passing through the facade elements. The amount of noise transmitted into the indoors is dependent on the frequency spectra of the sources and of the sound reduction properties of the facade elements. Facade elements such as masonry walls, open windows, and ventilators are investigated and modified regarding their sound insulation properties. Through passive means, the weighted sound reduction index of an open window and an open ventilator was increased by 12 dB and 3 dB, respectively. Also, the indoor self-noise of the ventilator was investigated and reduced for different airflow rates.

1 Introduction

In order to promote sustainability by saving energy, regulations force new buildings to be constructed more airtightly. To ensure a “healthy” air quality and to reduce the probability of mold growth, ventilation becomes an essential necessity. Furthermore, urban densification leads to buildings being built closer to streets and rail tracks. Both of these factors (ventilation and densification) can lead to higher noise levels and consequently health issues for the inhabitants of these homes.

The resulting indoor noise levels are dependent on the spectra of the outdoor sources and on the spectra of the sound insulation of the facade elements. So firstly, a closer look is taken at the noise spectra of a set of road and rail traffic noise sources, which were captured in the Stuttgart area. To correlate better to the human perception of noise, the A-weighted levels of these noise sources are discussed. The noise levels of a further noise source, namely, the ventilator used for mechanical ventilation, are also presented at different airflow rates.

In a next step, the sound insulation properties of some selected facade elements are viewed and optimized. These elements include a single and double masonry wall, a box-type window with different opening angles, and an (open) ventilator.

The latter two elements allow for necessary natural ventilation through the facade and are optimized by passive means, in other words by changing the impedances of the boundaries. To better understand the sound insulation of the double facade wall, a simple mass-spring-mass model is used to indirectly calculate the effective stiffness between the inner and outer shell of the facade wall.

Finally, the resulting indoor levels of these selected transportation noise sources are compared, and a conclusion is made on which single number values describing the sound insulation of the investigated facade elements best correlate with the reduction of traffic noise through the respective element.

The authors would like to thank the participating industry partners, Siegenia-Aubi KG, Schüco International KG, Aumüller Aumatic GmbH, and Bundesverband Kalksandstein Industrie e.V., as well as the funding organization of the Federal Ministry of Education and Research (BMBF) for supporting this research.

2 Noise Sources

A selection of noise sources including transportation noise and ventilator noise was chosen for this study. Whereas transportation noises from the sources were simply measured, the radiated noise from the ventilator was optimized through design changes. Both types of noise sources will be discussed for Z-weighted and A-weighted signals. The former is a linear weighting of the frequency components, and the latter simulates the frequency dependency of the average hearing.

2.1 Transportation

Within a former project by Pietruschka et al. (2011) funded by BWPLUS, average levels of various transportation noises (Truck, Car, City Tram, Regional Train, and Freight Train) were collected in a residential area in Stuttgart according to standard DIN 45642 (2004), however using a dummy head. The shape of the measured levels coincides well with the normative traffic noise levels according to the standard DIN EN ISO 717-1 (2019) and DIN EN 1793-3 (1997). All levels used in this paper (see Fig. 22.1) were recorded in front of the building facades, except for the levels of the Freight Train and the Regional Train, which were recorded at a similar distance from the tracks to the buildings, yet not directly in front of the facades due to organizational issues. The used locations are however expected to give comparable levels to those found in front of the nearby buildings.

Fig. 22.1

Outdoor sound pressure levels. Left: linear Z-weighted, right: A-weighted

Looking at the legend, one can see that the Freight Train has the highest overall levels followed by those of the Truck. Looking at the frequency content, the Truck shows higher levels in the low frequency range, whereas the Freight Train shows higher levels in the high frequency range. The source with the lowest overall level is the City Tram. The levels of the City Tram are also the lowest throughout the whole frequency range and are only undercut by the levels of the Regional Train between approximately 80 and 500 Hz.

Going from Z- to A-weighting, the order of the overall source levels changes only between the Car and the Regional Train (see Table 22.1). Hereby, the latter has higher A-weighted levels due to the more pronounced high frequency components, whereby the former has higher linear weighted levels. The levels going from Z- to A-weighting reduce for the five transportation sources, whereby the Car and Truck show the largest reduction of approximately 7–8 dB due to the strong low frequency component.

Table 22.1 Traffic source levels in dB

2.2 Ventilator

A further investigated noise source, which also contributes to the indoor noise level, is the ventilator. The sound power radiated (into the building) by a standard quality ventilator built into a wall was measured on the basis of DIN EN ISO 3743-1 (2010) with slight deviations. Drechsler and Ruff (2017) showed that this deviation from the standard measurement methods delivers appropriate results. The ventilator was investigated both before (“nor” for normal) and after carrying out some acoustical modifications (“per” for perforation modifications).

In both cases, the ventilator was built into a 150 mm thick calcium silicate brick wall (approximately 350 kg/m²) with thin plastering on the inner side and a thermal insulation composite system on the outer side comprised of 200 mm mineral wool with 12.5 mm gypsum board. In the field, plaster is used instead of gypsum board on the outer side, but the acoustical difference is considered negligible. The opening on the inner side was enclosed with a standard plastic covering spaced a few centimeters away with slits on the cover side to allow air exchange. The plastic tube of the ventilator has a diameter of 160 mm and a length of approximately 380 mm. The acoustically modified ventilator tube has the same dimensions, yet an additional effective perforation of approximately 25–30% at the last 100 mm on the outdoor end at the depth of the mineral wool (see Fig. 22.2). More details on the setup can be found in Ruff et al. (2020).

Fig. 22.2

Ventilator tube with 100 mm of perforation at outer end behind ceramic heat exchanger

The measured Z-weighted and A-weighted total sound power levels L_W for different airflow rates (15 m³/h, 32 m³/h, 45 m³/h and different directions (“in” for inward and “out” for outward)) can be seen in Table 22.2. Note, that the levels do not differ much regarding the direction of airflow for both Z- and A-weighted power levels (sums differ by max. 2 dB). Due to adding the perforation (going from “nor” to “per”), the single number values are reduced by 2–3 dB. The modal behavior of the tube is assumed to be the cause and is explained below.

Table 22.2 A- and Z-weighted sound power levels 𝐿_𝑊 of the ventilator in dB for different airflow rates, directions, and tube types

The cut-on frequency of the tube, at which the first radial mode propagates, is f_c ≈ 2.5 kHz from λ = 2πr/x₀, where λ, r, and x₀ are the wavelength, radius of the tube, and zero of the Bessel function (cylindrical function), respectively. The derivation of the Bessel function of zeroth order J₀(x₀ = k · r), marking the particle velocity at the boundary of the tube, is zero at x₀ = 3.8317. Below this cut-on frequency, plane waves propagate in the tube and lead to strong reflections at the ends, as there is an impedance change (plane waves => spherical waves) when exiting the tube. These reflections further lead to resonances with modal shapes that cause higher sound radiation at these frequencies. These resonances can be seen in Fig. 22.3, which also shows that by increasing the airflow rate, the peak in sound power around 315 Hz increases the most, whereas the levels at the low frequencies only rise slightly.

Fig. 22.3

Sound power levels 𝐿_𝑊 in dB and dB(A) of normal and perforated tubes from ventilator at different airflow rates, direction out, solid line: normal tube; dashed line: perforated tube

As the peak frequency does not shift by increasing the flow rate, it is believed that this resonance is not caused by the blade passing frequency, yet by the resonance along the tube length itself. This tube resonance is however excited by the noise from the blade passing frequency that lies close by. Being that the one end is somewhat closed (unknown impedance due to the covering) and the other end is relatively open (yet with slats), the resonance should lie somewhere between a quarter wavelength (f = 447 Hz–one end rigid and one end fully open) and a half wavelength (f = 223 Hz–both ends fully open). A resonance frequency at f₀ = 315 Hz would mean that the resonance is at 0.35 · λ ≈ 1/3 (>1/4 and <1/2) of a wavelength. A quarter wavelength resonator has its antiresonances and resonances at even and odd multiples of the fundamental frequency, respectively. Being that there is a dip in the levels at approximately double the frequency (f₁ = 2 · 315 Hz), and another local maximum at around three times the frequency f₂ = 800 Hz, supports this theory.

That the latter resonance frequency is slightly lower than three times the frequency is because slightly more than a quarter wavelength fits in this tube as with its not ideally rigid and open ends.

Through the perforation, two things are expected to happen. Firstly, the boundary conditions on the outer side become less defined, thereby spreading out the energy of the resonance to other frequency bands. One can see that the levels are not reduced in all one-third octave bands and even increase at lower frequencies. This supports the assumption that this peak is caused by a tube mode. Secondly, the sound power should get absorbed by the mineral wool. However, the effect is minimal, as otherwise the reduction of the levels at higher frequencies would increase over frequency.

The perforation reduces the peak values for both Z- and A-weighted levels by approximately 6–7 dB for all airflow rates. The overall levels are only reduced by approximately 3 dB. However, being that this peak in the one-third octave band is so high due to the very tonal blade passing frequency, the overall annoyance is reduced by lowering the level at this peak. Tonal sounds are found to be more annoying than stochastic noise according to DIN 45681 (2005).

Depending on the room properties (volume and absorption) and the sound insulation of the facade, these traffic and ventilator noises will be pronounced and disturbing to the occupant.

3 Sound Insulation

The sound insulation most often described by the sound reduction index, R_tot of the facade, is the energetic sum of the sound insulation of its elements (wall, window, ventilator) weighted by their areas:

$$ {R}_{\mathrm{tot}}=-10\log \sum \limits_{i=1}^{n=3}{10}^{-0.1{R}_{i,\mathrm{area}}},\mathrm{with}\ {R}_{i,\mathrm{area}}={R}_i-10\ \log \frac{S_i}{S_{\mathrm{tot}}}, $$

(22.1)

where S_tot is the total area of the facade, S_i is the area of the element i, and R_i,area is the sound reduction index of the element weighted by its area to the total area. In general, the sound reduction index describes ten times the logarithmic ratio of the incident sound power to the radiated power of the element. In this investigation, it was measured according to DIN EN ISO 10140-2 (2020). The total sound reduction index of the facade, R_tot, will not be discussed much further in this paper, as there exist so many possible permutations of wall, window, and ventilator elements. Yet, in a later section, the sound reduction index, R_i,area, normalized to the same overall area will be compared between the elements. However, firstly, the sound reduction index, R_i, of the elements as they were measured is looked at more closely.

3.1 Wall

Only two of the nine walls that were investigated in the iCity project are presented here. The one wall is a double wall (DW) built of an inner shell (brick wall), cavity (thermal layer), and outer shell (brick wall). The other wall is a single wall (SW) of the same inner shell (brick wall) on its own. They were chosen to demonstrate the effects of the anchors between shells. Due to wind loads, it is important to fasten the outer shell of a facade wall to the inner shell with metal anchors. These anchors, which are set in plastic plugs, however diminish the sound reduction of the wall relative to the same wall without anchors. One goal of this partial study is to find a simple formula to describe the effect of the outer shell fastened by different means and thereby to be able to predict the total sound reduction index before constructing the wall. This will ensure a healthy indoor environment and reduce cost due to over-designed constructions.

The base 175 mm thick calcium silicate brick wall (SW–single wall) has a mass per area of approximately 340 kg/m² (see Fig. 22.4). The other wall system (DW—double wall) is comprised of the base wall, also called inner shell (IS), plus 200 mm of mineral wool cavity insulation, and an external outer shell (OS) constructed of 115 mm thick calcium silicate block bricks with a mass per unit area of approximately 198 kg/m². Nine anchors per square meter were installed. A more detailed description of the setup can be found in Schneider et al. (2018).

Fig. 22.4

Inner shell of calcium silicate brick wall covered with insulation, anchors (marked with white circles), and first rows of outer shell

Although the system is quite complex as seen in a modal analysis (not shown here) with coupled modes beginning at 30 Hz, it was decided to firstly model the double wall as a simple mass-spring-mass system. For double walls filled with air or fibrous material, the stiffness of the cavity is well known and predictions of transmission can be made. However, the added anchors complicate matters and at low frequencies add an extra stiffness compared to just air, thereby increasing the mass-spring-mass frequency. The anchors also introduce structure-borne bridges at higher frequencies, which reduce the sound reduction index. The latter effect falsifies the simple estimation using the mass-spring model at higher frequencies.

Although estimates are false at high frequencies, a way was found to extract the effective stiffness of the cavity by comparing the theoretical differences between the sound reduction index of the single wall (𝑅_SW) and the double wall (𝑅_DW) utilizing the difference in velocity on the one side, IS, (𝐿_𝑣1) of the double wall and on the other side, OS, of the wall (𝐿_𝑣2) (see Fig. 22.5) when exciting the IS with a loudspeaker.

Fig. 22.5

Sketch of walls defining quantities. ΔR = R_DW − R_SW and ΔL_v = L_v1 − L_v2, and equivalent mass (m₁, m₂), spring (s), and damper (d) elements

3.1.1 Mass-Spring-Mass System

How the theoretical quantities of 𝑅_DW, 𝑅_SW, 𝐿_𝑣1, and 𝐿_𝑣2 can obtained by a simple mass-spring-mass system is shown here. They are all dependent on the impedance of the wall (𝑧_𝑊), meaning the ratio of exciting force 𝐹₁ and resulting velocity 𝑣. The relationship between the force and velocity of a mass-spring-mass system can be described by the following matrix equation:

$$ F=\left[\begin{array}{c}F1\\ {}0\end{array}\right]=N\cdotp \frac{1}{j\omega}\left[\begin{array}{c}{v}_1\\ {}{v}_2\end{array}\right] $$

(22.2)

where F₁ is the force exciting the wall, $j=\sqrt{-1}$, ω is the angular frequency, and v₁ and v₂ are the velocities of the inner and outer shells, respectively. The stiffness matrix, N, is defined as

$$ N=\left[\begin{array}{cc}s& -s\\ {}-s& s\end{array}\right]+ j\omega \left[\begin{array}{cc}d& -d\\ {}-d& d\end{array}\right]-{\omega}^2\left[\begin{array}{cc}{m}_1& 0\\ {}0& {m}_2\end{array}\right] $$

(22.3)

The stiffness and damping of the cavity are described by s and d, whereas the masses of the inner and outer shells are defined by m₁ and m₂.

From this matrix equation, the velocities, v₁ and v₂, can simply be calculated as

$$ {v}_1= j\omega {F}_1\frac{s+ j\omega d-{\omega}^2{m}_2}{\det (N)} $$

(22.4)

$$ {v}_2= j\omega {F}_1\frac{s+ j\omega d}{\det (N)} $$

(22.5)

which can be converted into drive point and transfer impedances dividing by the excitation force, F₁, respectively.

As the cavity “springs” (air, mineral wool, anchors) are all in parallel, their stiffness per area must be added, leading to a total stiffness of ${s}_{\mathrm{tot}}^{\prime \prime }={s}_{\mathrm{air}}^{\prime \prime }+{s}_{\mathrm{mineral}}^{\prime \prime }+{s}_{\mathrm{anchor}}^{\prime \prime }$, with ${s}_{\mathrm{air}}^{\prime \prime }=\rho {c}^2/d=1.2\cdotp {340}^2/0.2\ \mathrm{N}/{\mathrm{m}}^3$, ${s}_{\mathrm{m}\mathrm{ineral}}^{\prime \prime }=4.8\times {10}^6\ \mathrm{N}/{\mathrm{m}}^3$, and ${s}_{\mathrm{anchor}}^{\prime \prime }={E}_{an}\cdotp {n}_{an}\cdotp {A}_{an}/{l}_{an}=2\times {10}^{11}\cdotp 9\cdotp 2\cdotp \pi \cdotp 2\times {10}^{-3}\cdotp 0.21\ \mathrm{MN}/{\mathrm{m}}^3$. Assuming the shells of the wall are limp masses, and neglecting the influence of damping, the resonance frequency of the mass-spring-mass system can be calculated as ${f}_0=1/\left(2\pi \right)\sqrt{s\left(1/{m}_1+1/{m}_2\right)}$. This means that if the wall had no anchors, the resonance frequency would be lower, as the total stiffness s″_tot would be lower. A lower resonance frequency is better for the sound insulation, as above it there is an improvement of the sound insulation (see Fig. 22.6). In other words, adding the anchors reduces the performance of the wall, yet they are needed to resist the wind loads. The sound reduction index of this simplified wall can be estimated by

$$ R\left(\varphi \right)=20\log \left|\frac{\frac{z_w}{\cos \varphi }+2{z}_p}{2{z}_p}\right| $$

(22.6)

with z_w being the impedance of the wall and z_p = ρc the impedance of a plane wave. For purpose of simplification, a mean incident angle is selected (φ = 45 deg) to simulate the outdoor (traffic) noise. The impedance of the single mass wall is z_w1 = jωm and of the mass-spring-mass wall is ${z}_{w12}={F}_1/{v}_2=\frac{1}{j\omega}\frac{\det (N)}{s+ j\omega d}$ (see Eq. 22.5).

Fig. 22.6

Left: Sound reduction index, 𝑅. Solid–measured, dashed–calculated/predicted from IS-measurement plus improvement from mass-spring-mass approach. Right-top: Improvement of 𝑅 due to adding OS, Δ𝑅, and velocity level difference of both shells, Δ𝐿_𝑣. Right-bottom: Difference between Δ𝑅 and Δ𝐿_𝑣 for measured (solid) and calculated (dashed) cases

The theoretical improvement in sound reduction index by adding the outer shell is ΔR = R(z_w12) − R(z_w1). The expected sound reduction index of the DW can be calculated by adding ΔR, and the improvement due to the increase of the total mass (ΔR_mass = 20 log 10((m_IS + m_OS)/m_IS) ≈ 4 dB) to the sound reduction index of measured SW. This leads to the trend seen in the left graph of Fig. 22.6 (dashed line).

Note that the theoretical resonance frequency at 151 Hz (see dip in dashed line of left graph) is higher than measured and that the theoretical improvement with 40 dB/Oct is steeper than measured in the high frequencies due to the missing effect of structural bridging. Even though the slope is steeper adding the theoretical improvement, the single number rating is lower than the measured wall due to the resonance dip being too high. The reason for the excessively high resonance frequency is due to the fact that the stiffness of the plastic wall plugs, in which the anchors sit, was not considered.

To find the effective stiffness per area of the cavity including all effects, the velocity level (L_v) difference between the IS and OS when exciting the IS was measured and simulated with the same mass-spring-mass system as described above (see right diagrams in Fig. 22.6). In the upper right graph, the measured and predicted improvement in sound reduction index, ΔR, and the difference in velocity level, ΔL_v, are shown. The predictions unfortunately do not coincide with the measurements. However, if the difference between the deltas ΔR(meas) − ΔL_v(meas) and ΔR(calc) − ΔL_v(calc) is calculated (lower right graph), it can be seen that the predicted and measured have the same trend and differ by less than 5 dB throughout the whole frequency range. Note that to achieve these close results, the theoretical effective stiffness per area was reduced to ${s}_{\mathrm{tot}}^{\prime \prime}\approx 37\ \mathrm{MN}/{\mathrm{m}}^3$. This means that the plastic wall plugs have effectively reduced the ${s}_{\mathrm{tot}}^{\prime \prime }$ from 113 MN/m³ to a third and control the stiffness between the shells. As the wall plugs are situated in a different plane than the other “springs,” the reciprocal of the total stiffness is the sum of the reciprocal stiffnesses, leading to a stiffness of the wall plugs of 56 MN/m³. The total stiffness is lower than the smallest stiffness. Note that the mass-spring-mass resonance frequency thereby reduces from 151 to 87 Hz ($f=1/2/\pi \sqrt{s{{\prime\prime}}_{tot}\left(1/{m}_1+1/{m}_2\right)}$).

Overall, it can be said that the OS increases the sound insulation from above 63 Hz starting at 4 dB due to the mass increase (dashed horizontal line). A steady improvement up to 20 dB is achieved until 500 Hz where the slope levels off due to structural bridging. The weighted sound reduction index calculated according to the standard increased by adding the OS R_w(SW) = 54 dB to R_w(DW) = 65 dB, a 10 dB increase. If the wall plugs could be made less stiff, a larger increase in sound reduction index would be expected.

3.2 Ventilator

The setup of the ventilator was already described earlier. In contrast to the wall, the improvement of sound insulation through modifications will be investigated regarding the sound reduction index of small elements using 𝐷_𝑛,𝑒 instead of 𝑅, yet also according to DIN EN ISO 10140-2 (2020).

The dashed-dotted line in Fig. 22.7 depicts the sound insulation of the test wall without a ventilator and hole. The sound insulation drops drastically by incorporating the ventilator, especially around the tube resonance frequency (approximately 250–315 Hz) determined earlier. During times when no ventilation is needed, the tube can be closed upon which the sound insulation increases by approximately 10–15 dB. The improvement due to adding the perforation to the tube, as described earlier, can be seen in the right graph. Unlike the reduction in sound power due to the perforation, the sound insulation also improves at higher frequencies by approximately 2–3 dB. The perforation leads to a similar magnitude in improvement if the tube is open or closed. However, when closed a new peak is introduced at lower frequencies. This supports the earlier assumption that tube modes have the most influence on the radiation and insulation properties. If one side of the tube is closed, the tube acts more like a 1/4 wavelength resonator than a 1/2 wavelength resonator increasing the wavelength at the resonance and reducing its frequency. At these resonance frequencies, the particle velocity at the perforated end has a maximum, whereby through friction much sound energy is transformed to thermal energy increasing the sound insulation.

Fig. 22.7

Left: Sound reduction index of small elements, 𝐷_𝑛,. Solid–normal (nor), dashed–perforated (per), o–closed, no marker–open. Right: Improvement due to adding perforation for 𝐷_𝑛, (left axis) and 𝐿_𝑊 (right axis)

Comparing the reduction of radiated sound power, one can see that the highest improvement of both is around as much as the first and second resonance frequency of the tube between 250 and 500 Hz.

3.3 Window

Two different box-type windows were investigated in this iCity project. One was placed in a real office room and studied regarding natural ventilation (Chap. 21) and sound insulation. The other, installed in the acoustic facilities, with a depth of 0.15 m, a height of 1.312 m, and a width of 1.062 m, is discussed in this chapter (see Fig. 22.8) with the focus on sound insulation. A box-type window, such as the “Hamburger Hafencity Fenster,” was chosen because of its high sound insulation in the closed state. It was also chosen to warrant an increased sound insulation when tilted by making the sound enter the one side, in this measurement setup at the top of the box-type window, and travel through the height of the window, before exiting on the bottom half of the other side. For the presented data, the width of opening gaps (upper left and lower right) was always the same (0 mm, 20 mm, 40 mm, or 60 mm).

Fig. 22.8

Setup of box-type window with Helmholtz absorbers–black circles are openings

The measured weighted sound reduction index of the closed window is 𝑅_𝑤 = 51 dB. However, when tilted open for natural ventilation, the sound reduction reduced to 𝑅_𝑤 = 21 dB or 24 dB depending on the gap width of the openings (here 60 mm and 20 mm, respectively). The sound reduction index, 𝑅, of the non-treated window can be seen in the left graph of Fig. 22.9. The case with the largest gap has the worst sound insulation. At very low frequencies, the decrease in 𝑅 due to opening the windows is approximately 10 dB. The sound waves with very long wavelengths at those frequencies do not “see” the gap in the box-type window and still get reflected strongly. Between 80 and 400 Hz, the decrease in 𝑅 is approximately 15 dB, and 𝑅 runs almost parallel to the case with the closed box-type window. Above 400 Hz, the wavelength gets in the range of the gap length (width of the box-type window), and 𝑅 stays almost constant or independent of the frequency and the same amount of sound transmits through the box-type window.

Fig. 22.9

Left: Sound reduction index of the box-type window, 𝑅, with different gap widths. Right: Average improvement of 𝑅 for all gap widths (left axis) and for absorption coefficient (gray–right axis) due to adding Helmholtz and porous absorbers

In this project, two similar measures were taken to increase the sound insulation of the tilted box-type window at low and high frequencies by incorporating, first, Helmholtz absorbers (tuned to 125 Hz) and, second, porous absorbers of 40 mm thickness onto the top/bottom and both side window reveals, respectively. The weighted sound reduction index for all four cases (with and w/o Helmholtz absorber and with and w/o porous absorber) is listed for all of the four opening gaps in Table 22.3.

Table 22.3 Weighted sound reduction index, 𝑅_𝑤, in dB of windows with various opening gaps and absorber configurations

Note that the Helmholtz absorber has little influence on the single number value, R_w, which rises at most by 1 dB. The porous absorber also has little influence on R_w for the closed box-type window; however, a large influence of approximately 12 dB when the window is tilted open. The box-type window with a gap of 20 mm and with both Helmholtz and porous absorber has a quite high weighted sound reduction index of R_w = 36 dB. The absorption coefficients of the two absorbers, measured in an impedance tube, can be seen in the right graph (right axis) of Fig. 22.9.

The Helmholtz absorber theoretically tuned to 125 Hz has its maximum of α = 0.81 at 125 Hz. The porous absorber reaches its maximum of α = 0.98 at about the frequency corresponding to a quarter wavelength f = c₀/(4 · 0.04 m) = 2125 Hz, where c₀ = 340 m/s is the propagation speed in air.

The Helmholtz absorber does have a larger influence when looking at the sound reduction index, R. The improvement of sound reduction index, ΔR, can be seen in the right graph of Fig. 22.9. At the tuned frequency of 125 Hz, the improvement is approximately 5 dB for both, the case with and w/o porous absorber. At higher frequencies, however, there is a negative improvement with a negative peak at 400 Hz and 800 Hz depending on w/o or with porous absorber, respectively. This suggests that the improvement is not only due to the absorption of sound, but also that the impedance of the box-type window reveals changes now allowing more sound to pass. The worsening of R at higher frequencies due to the Helmholtz absorber is higher with the additional porous absorber in place. Hence, the improvement of R due to the porous absorber increases toward higher frequencies as expected.

The improvement for duct acoustics predicted according to Piening found in Möser (2009) and VDI 2081 (2019) is quite a bit lower than measured. Assuming the duct has the full width of the box-type window and the absorbers cover the reveal of the full height of the window, the maximum reduction for the porous absorber is 3.5 dB at 2000 Hz and for the Helmholtz absorber is 2.9 dB at 125 Hz. These values are lower than measured, because Piening only captures the losses along the duct walls and not at the openings at which absorbers are also implemented in these windows. In Fig. 22.9, one can see that the frequency ranges of improvement and high absorption coefficient coincide quite well. At higher frequencies, the improvement due to the porous absorbers declines when half a wavelength fits in the duct depth (f_ray = c₀/(0.15 m/2) = 1133 Hz) due to the sound then traveling more focused as a ray.

4 Indoor Levels

As the indoor sound pressure levels from the ventilator and traffic sources are dependent on the volume of the room, the equivalent absorption area therein, and the areas of the different facade elements, a facade-room scenario was chosen to allow the comparison between them. As a further simplification, the receiving room will be assumed to have a diffuse sound field (Fig. 22.10).

• Facade width w = 5 m.

• Facade height h = 2.5 m

• Facade area S = 12.5 m²

• Ventilator S_vent = 0.02 m²

• Window S_wind = 1.56 m²

• Wall S_wall = 10.92 m²

Fig. 22.10

Sketch of facade scenario. Wall: dark gray, window: medium gray, ventilator: light gray

• Room depth d = 4 m

• Room volume V = 50 m³

• Reverberation time T = 0.5 s (common value for living spaces)

The equivalent absorption area, A, can be calculated according to Sabine as A = 0.163 · V/T = 16.3 m².

4.1 Sound Transmission Through Single Elements and Ventilator Levels

As a first step, the element sound reduction index, D_{n, e}, is converted into a sound reduction index as follows: R = D_n,e + 10 log (S_vent/A). Furthermore, the sound reduction indices will be normalized to the chosen scenario by R_i,area = R − 10 log(S_i/S_tot). The indoor levels produced by the traffic noise source j through facade element i are then approximated by L_ij = L_p,j − R_i,area + 10 log(S_tot/A), where L_p,j is the level of the source j measured in front of the facade and R_i,area is the area of normalized sound reduction index of the facade element i.

The noise from the ventilation at different speeds and for different modifications can be calculated as L_p = L_W − 10 log(A) − 6 dB which is also shown in Table 22.4. For a selected set of elements, it can be seen in Fig. 22.11 that the A-weighted indoor levels lie between 10 and 60 dB(A) depending on the facade element (wall, vent, wind) and the traffic source, or they are dependent on the ventilator speed. As the direction of ventilation has little effect on the levels, only levels of inward ventilation are presented.

Table 22.4 Indoor sound pressure levels, 𝐿_𝑝, of ventilator in dB(A) for normal (nor) and perforated (per) tube for both operating directions outward (out) and inward (in)

Fig. 22.11

Top: A-weighted indoor sound levels from ventilator and traffic sources through selected facade elements according to facade and room configuration. Bottom: Reduction of A-weighted levels from outdoor to indoor due to facade elements

The WHO-Europe World Health Organization (2018) recommends levels below 40 dB(A) to ensure a healthy night’s sleep. Higher levels can cause the occupant to awake constantly, which could lead to a health hazard.

As expected, the indoor dB(A) levels through the wall and through the closed box-type windows are the lowest. More interesting is the fact that the order of loudest to quietest source changes depending on which element the sound transmits through. Outdoors, the sources showed the following order from loudest to quietest:

• 1. Freight Train–88.6 dB(A).

• 2. Truck–80.8 dB(A).

• 3. Regional Train–78.9 dB(A).

• 4. Car–77.3 dB(A).

• 5. City Tram–71.7 dB(A).

Yet, going through the wall (with nine anchors and an outer shell), for example, the order changes to:

• 1. Truck–27.6 dB(A).

• 2. Car–25.1 dB(A).

• 3. Freight Train–20.1 dB(A).

• 4. City Tram–11.6 dB(A).

• 5. Regional Train–11.0 dB(A).

This is due to the spectra of the sources and the sound insulation of the elements. The Freight Train level falling from first to third place is because the source has high levels between 1 and 2k Hz (see Fig. 22.1), which are highly attenuated by the wall with an outer shell (see Fig. 22.6).

The dB(A) level of the Car on the other hand is not very strongly attenuated by the wall with the outer shell, because its spectrum has a strong low frequency content (see Fig. 22.1) around the dip in sound insulation of the wall at the mass-spring-mass resonance (see Fig. 22.6), meaning those important frequencies are not reduced.

Furthermore, the top graph in Fig. 22.11 shows that the open windows, even after modifications, lead to the highest indoor levels. It can also be seen that the ventilator produces levels that are lower than all the transportation noises transmitted through the ventilator itself when running with a flow rate below 32 m³/h. The transmitted Freight Train noise is even louder than the ventilator at a flow rate of 45 m³/h. The ventilator at the middle flow rate produces levels similar to the transmission of the Tram.

To understand the reduction of A-weighted levels due to the facade better, the difference between the out- and indoor levels are plotted for the same element-source pairs in the lower graph of Fig. 22.11. As it was noticed in the upper graph of absolute levels, the wall and closed box-type window achieve the highest reduction in levels of around 60 dB. This corresponds to a subjective perception of 1/64 = 1/2^60dB/10 as loud. Again, the reduction depends largely on the spectra of noise source and sound reduction index of the element.

It can be seen that the spread of indoor levels between the different traffic sources is largest for the wall (≈ 15 dB), lower for the closed box-type window (≈ 10 dB), and smallest for the ventilator and open box-type window (≈ 5 dB). The wall shows the largest reduction, ΔL_p, for the trains, because the sources have strong higher frequency components, which are strongly attenuated by the wall. The Car and Truck show the lowest reduction by the wall due to the low sound reduction index of the wall at low frequencies and the high levels of the sources at low frequencies. This order of spread can be seen for the other facade elements as well. Adding the Helmholtz resonators to the open box-type window leads to an improvement for the Car and Truck sources, with their low frequency content, and leads to a worsening for the City Tram, because adding the Helmholtz absorber reduced the sound insulation at high frequencies (9), where the City Tram has high levels.

Seeing all this different behavior begs the question, if the weighted sound reduction index, which does not consider the different source spectra, is the proper measure to use for a facade. Please note that this is not a new finding, but has been investigated by many already and is captured, for example, as spectrum adaption terms in the standard DIN EN ISO 717-1 (2019).

4.2 Which Single Number Value Best Represents dB(A) Reduction?

For this same reason, different single number values (SNV) have been developed, some called spectral adaption terms, which as the name says, make corrections according to the assumed source spectra. Many such SNV have been developed over the years, some through subjective studies as in Hongisto et al. (2018), in which subjects are played back recordings of outdoor noise transmitted to the indoors and asked to rank the signals relative to their annoyance. As this type of study is out of the scope of this research, it is assumed that the A-weighted indoor levels sufficiently correlate with the human perception of annoyance and comparisons are made between the reduction of A-weighted sound level, Δ𝐿, from outdoors to indoors and a selected five of the standard SNV as they exist in DIN EN ISO 717-1 (2019) (R_w, R_w + C, R_w + C_tr, R_w + C_{50 − 3150}, R_w + C_{tr50 − 3150}). The latter two will for short be named Rw + C₅₀, Rw + C_tr50.

The spectrum adaptation terms C, C_tr go from 100 Hz to 3150 Hz in one-third octave bands and put more emphasis on the lower frequencies. The terms with the added 50 Hz do the same, however also considering sounds one octave lower down to the 50 Hz band.

The procedure to calculate the spectrum adaption terms is the same as explained in Sect. 22.4.1, yet now the A-weighed source levels are normalized to zero dB(A) meaning the A-weighted indoor levels and the A-weighted level reductions are the same. Furthermore, the room scenario for the adaption terms is nonexistent, or in other words, the assumption is made that the element surface, 𝑆_i, is the same as the equivalent absorption area in the room, 𝐴. These differences in the calculation methods mean that compared with the level reduction calculated here, there would be an offset even if the same source spectra in both cases would be used.

So, the question addressed here is, which SNVs are most representative to describe the reduction in A-weighted outdoor to indoor levels (Δ𝐿_p) in these studies, with these spectra and these facade elements, and do they coincide with those suggested in the standards? The most appropriate SNVs to use for different traffic situations would be the ones that show the least variation relative to Δ𝐿_𝑝. For example, Meier (2021) suggests to use 𝑅+𝐶 for outdoor noise and traffic noise outside of built-up areas and 𝑅+𝐶_𝑡𝑟 within built-up areas.

To give an idea of the variation between the different SNVs, a subset of the elements and sources are displayed in Fig. 22.12. The standard deviations listed in the legend are calculated for all elements presented earlier (2 × Walls, 4 × Vents, 16 × Windows). This means that because there were many more open box-type window cases, those are weighted more than, for example, the walls. Yet, this is found to be acceptable, because most facades incorporate a window, which often delivers the lowest reduction of A-weighted levels and thereby controls the overall insulation. In the future, it might be more appropriate to select multiple facade variants with different types and sized elements and compare the SNV of the overall sound reduction with the indoor levels on whole ΔSNV = SNV − ΔL.

Fig. 22.12

ΔSNV: Difference between single number values (SNV) and A-weighted reduction of sound levels Δ𝐿_𝑝 for three sources (Truck, Car, and City Tram). Dashed line is mean value and standard deviation is in respective legend

As mentioned earlier, an offset is expected due to the added room and facade assumptions in this study, meaning that the mean value is not as representative as the standard deviation. As expected, the variation of ΔSNV is the largest for the wall with the outer shell regarding both displayed sources. The standard deviations can be found in all sources and SNVs in Table 22.5. For the selected scenarios, the table suggests that 𝑅_𝑤 + 𝐶₅₀ is best suited for the Truck, 𝑅_𝑤 + 𝐶_𝑡𝑟 for the Car and Regional Train, 𝑅𝑤 for the City Tram, and 𝑅𝑤 + 𝐶 for the Freight Train. This would correlate with the normative recommendation, suggesting the use of 𝑅_𝑤 + 𝐶 for the Freight Train and 𝑅_𝑤 + 𝐶_𝑡𝑟 for the Car and Truck. The latter only if going down to 50 Hz was not an option.

Table 22.5 Standard deviation of ΔSNV: Difference between single number values (rows) and A-weighted reduction of sound levels from outdoors to indoors for all sources (columns)

If only one SNV should be suggested to be used for the rail vehicles, this study would recommend 𝑅_𝑤. One SNV for the Trucks and Cars could be either of these

$${𝑅}_{\text{𝑤}}+{𝐶}_{\text{𝑡𝑟}},{𝑅}_{\text{𝑤}}+{𝐶}_{50},\text{or}{𝑅}_{\text{𝑤}}+{𝐶}_{\text{𝑡𝑟50}}.$$

5 Conclusion and Outlook

Within the framework of the iCity research project, the sound insulation of several facade elements was improved by passive means. The weighted sound reduction index of the wall, for example, was improved by 11 dB through adding an outer shell to the inner shell. More importantly, the effective stiffness of attachment anchors was estimated indirectly through vibration and sound insulation measurements, thereby revealing more potential for further improving the walls.

The sound reduction and weighted sound reduction index of the ventilator was improved by 7 dB in one-third octave bands and by 3 dB, respectively, through the simple addition of perforation on the last section of the ventilator tube.

The sound reduction index and weighted sound reduction index of the open box-type window was improved by 6 dB and 1 dB, respectively, by adding Helmholtz absorbers in the box-type window reveals and by 15 dB to 12 dB, respectively, by adding a porous absorber. As shown by others, it was confirmed that the A-weighted indoor levels greatly depend on the spectra of the noise source levels and of the sound reduction index of the facade elements. Although the weighted sound reduction index by adding the Helmholtz absorber only increased by 1 dB, the indoor levels decreased by 3 dB for the Car and Truck sources. The indoor noise level created by the self-noise of the ventilator in the chosen “standard” room was of a similar magnitude as the traffic noise transmitted through it for the medium and high airflow settings.

A multidimensional calculation showed that there exist no correct single number values (SNV) that can be utilized for all scenarios. Even the two SNVs suggested in the standards were not necessarily the best for these noise source-facade element scenarios.

A possible way forward could be to better capture the actual source spectra outdoors for specific areas, for example, through citizen science noise sensors (https://luftdaten.info/einfuehrung-zum-laermsensor/), and then select the suitable facade elements to optimize for the overall indoor level in that area.