PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Sound insulation auralization ﬁlters design for outdoor moving
sourcesImran Muhammad; Anne Heimes; Michael Vorländer
Institute of Technical Acoustics, RWTH Aachen University, Germany

ABSTRACT
Auralization techniques are rapidly attaining importance, mostly due to their applications in building
acoustics and virtual reality. As an application, sound insulation auralization has become a valuable tool toassess the sound insulation of buildings in terms of investigating how the indoor and outdoor noise sources
are inﬂuencing the daily work and live routine of humans. The airborne sound insulation prediction standards
have several simpliﬁcations that are implicit in the formulation on which they are based. Therefore, it isnecessary to develop a model to build up an auralization chain of the sound insulation by taking into accountthe complex wave ﬁelds on the surfaces of the building elements and the spatial and temporal variation of
the sound pressure ﬁeld inside arbitrarily shaped rooms. We investigate the bending (ﬂexural) wave patternson the extended walls of buildings, the directionality of the outdoor moving sound sources to constructperceptually correct binaural ﬁlters. Additionally, we address the problem of synthesizing the room impulse
response from the one-third octave band values of the reverberation times. Our proposed approach increases
acoustic interaction with the virtual environments creating a deeper, more realistic and immersive scene andleading to more accurate perceptual evaluations of sound insulation.
Keywords: Sound Insulation, Bending Waves, Auralization, Noise, Perception

1. INTRODUCTION
The ability to predict sound and vibration transmissions in built-up structures such as buildings,
trains and automobiles is important for human comfort, health and safety. There is a high concern
about steadily growing annoyance due to the noise in private dwellings and the background speech incommercial work sites that leads towards reduced power of concentration during physical or mental
work (1). In this context, in residential and worksite premises, especially in urban area, theinternational standards provided by ISO (International Standards Organization) have reflected thetrend mentioned above, increasing both in number and covering broader aspects (2). However, theseguidelines do not provide the optimal acoustic satisfaction when specific sounds (e.g. conversation
varying in intelligibility) originate from the adjacent office and cause the dissatisfaction in job
performance in one hand and on the other hand, when transient moving sound source from outdoor
are creating annoyance in daily life’s physical or mental work. Therefore, measurement procedures
applied in the laboratory or in the field is just one part of the story. There exist several guidelines andstandards that describe the performance of buildings elements in terms of noise reduction and soundlevel reduction indices in the form of a single number value and/or frequ ency dependent curves.
However, it can be assumed that these quantities are insufficient to describe the real situation for theperception of noise, therefore, it is desirable to have a simulation tool which simulates the sound fieldat the ears of the listener from predicted or measured data using auralization of these noises, which,better consider the subjective impressions of subjects, and psychoacoustic and psychological factors.
The basic principle of building acoustic auralization is to simulate the alteration of a sound signal
from its source to the receiver via transmission through the building structures. The auralization of asituation, whether it is an office-to-office situation or against the outdoor sounds, where either the
speech spoken in one office or the noise produced by an outdoor source, is transmitted throughbuilding structures, requires the source signal modelling sound propagation, i.e. its generation andtransmission form walls and the insulation characteristics of the direct and flanking elements ofdwelling. Both level and spectral characteristics of sources highly depend on the insulation curve of
the building construction separating the source and receiver.
Most of the auralization methods of sound insulation are available in compliance with standardized

1721

data formats (ISO 12354-1 (3), ISO 12354-3 (4), ISO 3382-2 (5)) of sound insulation by calculating
point to point transfer functions from source to the listener. However, due to certain limitations thatare rooted in ISO derivations, it is necessary to address certain important wave phenomenon (such as
bending wave patterns on the building elements) to design these transfer functions accurately forauralization and plausible reproduction of level and coloration. Therefore, there is an opportunity indeveloping a building acoustic auralization framework based on detailed models of ISO standards andavailable up-to-date research (2) and (6-9), to accurately realize the perception and evaluation of noise
and its influences on the humans. Hence, we develop an auralization framework dealing with noiseproducing sources located both inside and/or outside the dwellings. However, in this paper, we present
a part of our model that deals with sound sources against outdoor situations.

2. AIRBORNE SOUND INSULATION AGAINST OUTDOOR SOUND
Sound transmission from an outdoor source, (e.g. a moving vehicles), into a building is a complex
process. The moving sources are directional sound sources with strong low frequency soundcharacteristics. There exist multiple propagation paths from these sources to several parts of a building
including reflections from the ground and other surround buildings. Sound transmission throughexterior walls of a building becomes more complicated because of the varying angles of incidence ofthe source, the multiple transmission paths within the building and the fact that these phenomena allvary greatly with the frequency of the sound source. In this paper, we introduce a procedure for
estimating indoor sound levels from outdoor noise sources. The procedure for the filter designs ofsound levels should cover sound transmission loss of exterior walls, roof construction s, windows, andsome doors.
2.1 Sound Insulation Model
Our first model for outdoor sound insulation prediction is based on the filter design techniques
described in the previous work (10, 14, 16, 17). However, the procedures of filter design for soundlevels should cover sound transmission loss of exterior walls, roof constructions and windows.
Therefore, we begin with a new idea of segmenting the building elements into finite size patches
known as secondary sound sources (SS), because generally the exterior walls of common buildings
are consist of an assembly of two or more parts or surfaces (e.g. windows etc.). ISO 12354-3, provides
basic guidelines for airborne sound insulation against outdoor sound source , which are based on
diffuse field theory. The diffuse sound field approximations are very advantageous for the indoor cases
where the adjacent rooms are assumed to be diffuse. This is not the case for outdoor environments.
Hence, we take into account only the direct part of the sound filed hitting the surfaces of the building
elements exposed. We consider direct sound transmission paths ‫݀ܦ‬, through each small part of theelement (secondary sources) because it is assumed that the transmission for each secondary source isindependent from the transmission of the other (4, 6). Therefore, for a direct sound field the soundtransmission coefﬁcient of a plane wave depends on the angle of incidence ߠ, between the directionof propagation of the incident plane wave and the normal to the plane of the exterior elements (i.e.
walls). Furthermore, there are certain building acoustics parameters for which, normally, the spatiallyaveraged values are used for indoor cases such as; vibration velocities on the surface of elements,
radiation efficiencies and bending wave transmission across the junctions. However, we consider theangle of incidence dependent radiation efficiencies ߪሺߠሻ , to get angle dependent transmission
coefficients. The angle dependent transmission coefficient is denoted as ߬ሺߠሻ and is given by,ଶͳ߬ሺߠሻ ൌ ተተܼሺߠሻ  ߠ
ͳ൅
ʹܼ଴

(1)

ܼ଴ is impedance of free medium (i.e. air). The bending wave impedance of the wall ܼሺߠሻ, is given
by Equation 2.
݂ ଶܼሺߠሻ ൌ ݆߱ ቈͳ െ ൬ ൰ Ǥ ሺͳ ൅ ݆ߟ௧௢௧ ሻ ସ ߶቉݂௖(2)Here, ݂௖ is the critical frequency and ߟ௧௢௧ is the loss factor of element. The single sided radiation
efficiency ߪሺߠሻ, for infinite plate is given by Equation 2 (for ݂ ൐ ݂௖ ).

1722ߪሺߠሻ ൌ

ͳ
 ߠ

(3)

Therefore, Equation 1 can be rewritten as,ଶ߬ሺߠሻ ൌ ተ

ͳ
ተ
ܼሺߠሻ
ͳ൅
ʹߩܿǤ ߪሺߠሻ

(4)

After simplifications, we finally get the angle dependent transmission coefficient given by,߬ሺߠሻ ൌͳଶଶଶ݂݉ߨ ߟ ‫ ݎ‬ଶ ସ ߠ݂݉ߨ ଶ݂൬ͳ ൅ ߩܿ Ǥ ௧௢௧൰ ൅൬൰ ቆͳ െ ൬ ଶ ߠ൰ ቇ݂௖ߩܿǤ ߪሺߠሻ
ߪሺߠሻ(5)

We now calculate this angle dependent transmission coefficient (Equation 5) for the small segments(finite patch), which is a function of angle dependent radiation efficiency ߪሺߠሻ. However, due to theassumption of infinite size plates, important discrepancies may be found between predicted andexperimental data (18). To remove these discrepancies, we adopted spatial windowing techniquewhich is introduced by Villot et al. in (8), where, he showed that the results are much closer tomeasurement results than other simple procedures. Hence, we implement this technique for finite size
secondary sources (ܵܵ) and hence calculate the corresponding transmission coefficients. In spatial
windowing technique, the idea behind is to compute the radiated power where only a small area ܵௌ(of length ‫ܮ‬௫ and width ‫ܮ‬௬ ) of an infinite structure contributes to the sound radiation, as shown in
Figure 1.

Figure 1 – Exterior wall between source and receiver, segmented into patches (SS)
Assuming a propagating structural wave of wave number ݇௣ , the velocity field in the wave number
domain is defined by taking the spatial Fourier transform, giving,‫ݒ‬ො൫݇௫ ǡ ݇௬ ൯ ൌ ‫ݒ‬ොǤ ‫ܮ‬௭ ‫ܮ‬௬

‫ܮ‬௬
‫ܮ‬
 ቆ൫݇௫ െ ݇௣  ߰൯ ௫ ቇ Ǥ  ቆ൫݇௬ െ ݇௣  ߰൯ ቇ
ʹ
ʹ
‫ܮ‬௬
‫ܮ‬
ቆ൫݇௫ െ ݇௣  ߰൯ ௫ ቇ Ǥ ቆ൫݇௬ െ ݇௣  ߰൯ ቇ
ʹ
ʹ

(6)

Where, ߰ is the azimuth angle for ݇௣ . This result is used to calculate the radiated power (withreference to Fahy (15)) and is giving,

1723

ଶ

ܹ൫݇௣ ǡ ߰൯ ൌߩ଴ ܿ଴ ௞బ ଶగ ห‫ݒ‬ො൫݇௫ ǡ ݇௬ ൯หන න݇଴ ݇௥ ݀߶ ݀݇௥ ͺߨ ଶ ଴ ଴ඥ݇ ଶ െ ݇ଶ௥(7)଴With ݇௫ ൌ ݇௥ ሺ߶ሻ and ݇௬ ൌ ݇௥ ሺ߶ሻ. The radiation factor (8, 15) is then calculated by double
integral, which may be written as,ߪ൫݇௣ ǡ ߰൯ଶଶܵ ௞బ ଶగ  ቀ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௫ ቁ Ǥ  ቀ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௬ ቁൌ ଶන නଶଶߨ ଴ ଴ൣ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௫ ൧ ൣ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௬ ൧݇଴ ݇௥ൈ ݀߶݀݇௥
ඥ݇଴ଶ െ ݇ଶ௥(8)

Villot (8), found that the dependence of the radiation efficiency (Equation 7) on the angle ߰ isslight. Therefore, in order to condense the results and present the variation of the radiation efficiency
as a function frequency and angle of incidence ߠ, the radiation efficiency is averaged over ߰.
‫ߪۃ‬൫݇௣ ൯‫ۄ‬టଶଶగ ௞బ ଶగ ଶ ቀ൫݇  ߶ െ ݇௥௣  ߰൯‫ܮ‬௫ ቁ Ǥ  ቀ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௬ ቁܵൌ ଷන න නଶଶʹߨ ଴ ଴ ଴ൣ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௫ ൧ ൣ൫݇௥  ߶ െ ݇௣  ߰൯‫ܮ‬௬ ൧݇଴ ݇௥ൈ ݀߶݀݇௥ ݀߰ඥ݇଴ଶ െ ݇ଶ௥(9)Furthermore, Fahy (15) and Villot (8) observed that for ݇଴ ‫ ܮ‬൏ Ͷ, the radiation efficiency of thefinite structure (e.g. ͳǤͶ ൈ ͳǤͳ ݉) using spatial windowing filtering is lower than that of the infinite
system for any angle of incidence and does not significantly vary with the angle of incidence ߠ,
whereas, for ݇଴ ‫ ܮ‬൐ Ͷ, radiation efficiency of the finite structure increases with the angle of incidence
ߠ, following the radiation efficiency of the infinite system, up to a certain incidence angle and does
not significantly vary afterwards. For an acoustic wave, the wave number ݇௣ is related to the incident
angle ߠ, by ݇௣ ൌ ݇଴  ߠ. Therefore, the transmission coefficient given in Equation 5 can now be
determined for small size secondary source (denoted by ߬ௌ ሺߠሻ) by inserting sigma from Equation 9
for frequencies greater than critical frequency. Below the critical frequency, the sou nd transmission
coefficient is calculated using the average diffuse field single sided radiation efficiency approachgiven in (3), while the bending stiffness is ignored.
The idea is now to apply the spatial windowing to the radiation process and also to f ind the effectof spatially windowing on the incident pressure field, there by correcting the transmission factor of
the infinite structure to obtain the corresponding transmission factor of the finite structure ߬ௌ ሺߠሻ, thus
using Equation 9 into Equation 5, we can get the final transmission coefficient for a single secondary
source. Another approach proposed by Vigran in (18) to obtain the transmission coefficient ߬ௌ ሺߠሻ, forfinite plate (i.e. in our case secondary source), is to calculate the transmission coefficient ߬௜௡௙ ሺߠሻ forinfinite plate and then use Equation 10 to get finite ߬ௌ ሺߠሻ . The term ݁ ௝ఉሺఏሻ is the phase of thesecondary source radiation, which depends on the incidence angle of the wave and time of arrival ofwave at secondary source. In this paper, we are not discussing on the phase part of Equation 10.
߬ௌ ሺߠሻ ൌ ߬௜௡௙ ሺߠሻሺߪሺ݇଴  ߠሻ  ߠሻ݁ ௝ఉሺఏሻ

(10)

2.2 Filters Design TechniqueSound insulation filters are designed based on the above presented model , where at the first place,
we consider the sound source directivities. Secondly, the sound insulation transfer functions fromsource to the receiving rooms are calculated for extended walls by using concept of dividing theindividual building element into a multitude of secondary sound sources. The elements may be1724homogeneous (e.g. a single homogeneous wall element) or consisting of an assembly of two or moreparts or surfaces (e.g. doors, windows). Thirdly, the receiver room acoustics is implemented in a waythat it includes the receiving room reverberation based on room geometry, absorption and binauraltransfer functions between secondary sound sources and the receiver. Moreover, the room impulse
responses (RIRs) are synthesized from one-third octave band values of the reverberation times of thereceiving room.
To proceed for the filters design procedure, let us take a sound source with directivity, ܳௌ and theacoustics power ܲ௔ ൌ ͳͲିଵଶ ͳͲି଴Ǥଵ௅ೈ (in Watts). Then the mean squared sound pressure at any point
at a distance ‫ݎ‬, from the source in energetic notation is given by Equation 11.
ܳௌ‫݌‬ௌଶ ൌ ߩ଴ ܿ ή ൬൰Ͷߨ‫ ݎ‬ଶ(11)

The sound power on the external surfaces of the building elements can be calculated with a simple
modification to the stationary sound fields in the ordinary room that is to separate the direct soundfield and the reverberant part. Therefore, under free field conditions the direct incident sound power
on a secondary sound source ‘݅’ of a surface area of ܵௌ , denoted by ܹௌǡ௜ is given by Equation 12,
where ‫ݎ‬௜ is the distance from the source acoustic centre to the infinitesimal elemen t ݀ܵ and ߠ is theincidence angle. The quantities ܳௌ , ‫ݎ‬௜ and ߠ depend on the element geometry.
ܹௌǡ௜ ൌܲ௔ܳௌȁ  ߠȁ݀ܵනͶߨ ௌ Ͷߨ ή ‫ݎ‬௜ଶ

(12)

Let the integral in Equation 12 can be written as,ܳௌଶ ȁ  ߠȁ݀ܵௌ Ͷߨ‫ݎ‬௜‫ܨ‬௜ ൌ න(13)The, ‫ܨ‬௜ , can be approximated numerically under the conditions that the ݀ܵ elements are neither
very large, nor very close to the sound source position and ܳௌ is smooth in the direction of interest.
This integral is obtained by assuming that ܳௌ ǡ ‫ݎ‬௜ and ߠ do not vary significantly along ܵௌ . In thisway, ܳௌ ǡ ‫ ߠ  ݎ‬can be taken out of the integral and we get‫ܨ‬௜ ൎܵௌ ή ܳௌǡ௜ȁ  ߠ௜ ȁͶߨ ή ܴ௜ଶ

(14)

Where, ܴ௜ is the length of vector that goes from the source to the centre of secondary source ݅and ߠ௜ , is the angle of incidence of vector, ܴ௜ . The ܳௌǡ௜ denotes the mean directivity value forparticular value of ߠ௜ . We calculate the integral ‫ܨ‬௜ numerically by the well-known adaptive
Simpson’s method. Thus the incident power on the each secondary source of an element can becalculated byܲ௔ ή ‫ܨ‬௜
(15)ͶߨUsing Equation 15 and the definition of the transmission coefficient, the sound power transmitted
from source to receiver room by one secondary source is given byܹௌǡ௜ ൌ‫ܨ‬௜ܹௌௌ ൌ ܲ௔ ή ߬ௌ ሺߠሻ ή ൬ ൰
Ͷߨ

(16)

Using Equation 9 and Equation 5, we get ߬ௌ ሺߠሻ and hence, ܹௌௌ . And finally the contribution ofthe ‫ ݀ܦ‬path for the finite size patch to the mean squared pressure in the receiving room is derived asfollows by using the expression given by Equation 17 with ܳ௝ , as directivity of secondary source and‫ܣ‬ோ , as the equivalent absorption area of the room.
ଶ‫݌‬ௌǡோൌ ߩ଴ ܿ ή ܹௌௌ ቆܳ௝Ͷଶ൅‫ ܣ‬ቇͶߨ‫ݎ‬௝
ோ

(17)

1725

The time domain representation of the sound pressure for single ‘ܵܵ’ is given by Equation 18,
where ܵ௜ is the area of the walls and ‫ݎ‬௝ is the distance of receiver from secondary source.
ଶ‫݌‬ௌǡோ
ൌߩܿ ή ܲ௔ ή ߬ௌ ሺߠሻ ή ܵௌ ܳ௝ ή ‫ܨ‬௜
‫ܨ‬௜
ቆ
൅
ቇ
ଶ
ଶ
ܵ௜
ߨ‫ܣ‬ோ
ͳ͸ߨ ‫ݎ‬௝

(18)

For an input time signal, ‫ݏ‬ሺ‫ݐ‬ሻ and transfer function ߬ௌ ሺߠሻ, the final sound pressure in temporal
domain from source to receiver for one secondary source as radiating element is given by,ܳ௝ ή ‫ܨ‬௜‫ݎ‬௜ ൅ ‫ݎ‬௝‫ݎ‬௝ܲ௔ ή ߬ௌ ሺߠሻ ή ܵௌ‫ܨ‬௜‫݌‬ோǡௌௌ ሺ‫ݐ‬ሻ ൌ ඨή ‫ݏ‬ሺ‫ݐ‬ሻ ‫ כ‬൮ඨ൰൅ඨή ݄ோ ቀ‫ ݐ‬െ ቁ൲ଶ ή ߜ ൬‫ ݐ‬െ
ଶ
ܵ௜
ܿ
ߨ‫ܣ‬ோ
ܿ
ͳ͸ߨ ‫ݎ‬௝

(19)

2.3 Auralization
Once, the filters for sound insulation are calculated as described in the previous section,auralization makes the sound pressure in the receiving room audible at the ears of the listener by anappropriate equipment using reproduction techniques. From an input time signal ‫ݏ‬ሺ‫ݐ‬ሻ and transfer
functions (i.e. filters), the time signal at the output of any LTI system can be calculated by means ofconvolution techniques. Hence, the time signal at a receiver in a room is calculated from the source
signal and the transfer function from all secondary sources to the listener by convolution. However,the filters length is an important parameter for convolution technique. We generally consider thebuilding acoustics frequency range to be defined by one-third-octave-bands from 50 to 5000 Hz. For
signal processing, these quantities have to be turned into frequency spectra with a pract ical numberof frequency lines. In case of sound insulation filters, an input with 21 values in one -third octave
bands ranging from 50 Hz to 5000 Hz are given. To obtain a frequency spectrum with 4097 lines,
these values have to be interpolated. This is done by applying cubic spline interpolation on insulation
filters.
In the receiving room the secondary sources, located at different positions and orientation relative
to the listener’s ears, are excited by bending waves due to the sound transmission from the source,
therefore, they are required to be perceptually localized to create a spatial impression of listening theroom. Hence, it is necessary to consider an auralization with measured or indi vidualized binauralsignals by head related impulse responses (HRIR) or corresponding head related transfer function .
‫ ݅ݎ‬൅‫݆ݎ‬௥೔ ା௥ೕ
The expression ߜ ቀ‫ ݐ‬െ ௖ ቁ in Equation 19 is then replaced with ‫ܴܫܴܪ‬ሺߠ௝ ǡ ߮௝ ǡ ܿ ሻ for binauralroom impulse response. In our signal processing, the HRTFs of the ITA dummy head are used.
Furthermore, to listen the impression of the receiving room, we have simulated impulse response forthe receiving room for each secondary source to the listener position. The expression, ݄ோ ሺ‫ݐ‬ሻ , inEquation 19 is the room impulse response form a secondary source to the receiver and is statisticallyvalid for all points inside the room.

3. RESULTS
3.1 Verification of Sound Reduction Index ‘ࡾ’The method presented is tested in a scenario where the receiving room dimensions are taken asͶǤͺ ൈ Ͷ ൈ ͵ ݉ . The external wall of the room is made of concrete material and is taken as
homogeneous finite size plate with internal loss factor, ߟ௜௡௧ ൌ ͲǤͲͲͷ and critical frequency, ݂௖ ൌͳͷʹ ‫ݖܪ‬. To verify the results for the direct sound transmission it is segmented into small patches (ܵܵ)
as shown in Figure 1, and for each patch the transmission coefficients are calculated after applying
spatial windowing technique. Here it is necessary to mention that each patch is concrete with samematerial properties so that we can verify the results of model with ISO standar d. After computing
sound reduction index ܴௌ for each ܵܵ the total reduction index is obtained by using Equation 20,
from Vigran (8), and comparison with ISO standards is shown in Figure 2.
௡ோೄͳܴ௧௢௧௔௟ ൌ ͳͲ  ൤ ෍ ܵௌ Ǥ ͳͲଵ଴ ൨
ܵ௜
௜ୀଵ

1726

(20)

Figure 2 – Comparison of Sound Reduction Index ()3.2 Visualization of Sound FiledA sound source is placed at three positions in the vicinity of the building and sound pressures levelis calculated at the exterior surfaces and in the receiving room for these positions as shown.

Figure 3 – Sound pressure level at the exterior boundaries of the building. And a, b and c are thesound pressure level at ‫ ݖ‬ൌ ͳǤͷ ݉, height from floor in receiving rooms for three source positions

1727

4. CONCLUSIONSWe presented a sound insulation model for filter design in the context of outdoor sources. The
findings of this work are analogous to the results of ISO standards. From the results we can conclude
that the spatial windowing techniques is quite advantageous for segmenting the building elements into
finite size small patches as multitude secondary sources. Hence, it is possible to treat each secondary
sources as a sound radiating element for the auralization with its specific phase rather than taking thewhole wall as a single point source radiator located at its centre. Furthermore, since the authors assume
that the moving outdoor sound source can be perceptually localized within the dwellings and are oneof the major reasons for distraction and annoyance, therefore, the next step is to conduct listening
experiments to auralise a building scene where the outdoor source would be placed at any location in
the vicinity of the building to analyse the localization capabilities of the listeners.

ACKNOWLEDGEMENTS
This work was funded by HEAD-Genuit Foundation under the Project ID: <P-17/4-W>.

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