A BSORPTION PROPERTIES OF G REEN S OUND B ARRIERS
Sherif Fouda
Stockholm, Sverige 2018
Master's degree project (30 hp) TRITA-SCI-GRU 2018:166
ISSN 1651-7660
Abstract
This thesis was conducted on behalf of Butong AB, who wanted to test and develop an environmental friendly, so called green sound barrier, which combines both art and science.
Different configurations of the product were proposed by the company with various filling materials, as it was predicted that the filling materials would be the main sound absorbent among all parts of the structure.
The thesis work started by selecting the best of the proposed fillings which could be of interest - that is those which were expected to have high sound absorption coefficients. The selection process was based on experience, reading and advice. The main idea behind the selection process was saving cost for the company as well as effort.
Impedance tube method was used for performing the measurements on samples of the green sound barriers, in order to calculate the acoustical properties of each material and every construction, as it was considerably reliable, cheap and fast to use.
The measurements were done according to a combination between standards described in ISO 10534-2:1998 and ASTM E2611-09, for performing test measurements using the impedance tube.
This master thesis gives an explanation of the predicted absorption characteristics of the green sound barriers including the usage of different fillings, as well as the advantages and disadvantages of using it in real life applications.
Key words: Impedance tube, Sound absorption measurement, transfer function, three microphones, Sound barrier, ISO 10534-2, ASTM E2611-09.
Table of contents
1. Introduction ... 1
2. Sound generation and traffic noise ... 2
2.1. Sound waves ... 2
2.2. Sound characteristics ... 3
2.2. Frequency domain... 4
2.4. Sound fields ... 5
2.5. The logarithmic scale ... 5
2.6. Sound levels ... 6
2.7. Sound attenuation... 7
2.8. Sound absorption ... 7
2.10. Noise and human health... 8
3. Green Sound barriers ... 10
3.1. Construction... 10
3.2. Fillings ... 10
4.Measurements ... 12
4.1. Methodology... 12
4.3. The impedance tube ... 13
4.4.The sample... 16
5. Results ... 21
5.1. Empty test rig ... 22
5.2. The outer pipe ... 23
5.3. Butong's concrete panel ... 24
5.4. Configuration 1*... 25
5.6. Configuration 3*... 28
5.7. Configuration 4*... 30
6.1. Conclusion... 35
6.2. Discussion ... 36
Appendix ... 37
References ... 38
Symbols
𝑷̂ Peak Amplitude (pa)
𝑷̃ Root means square of sound pressure (R.M.S)
λ Wave length (m)
T Period (sec)
f Frequency (hz)
C Speed of Sound (m/s)
ω Angular frequency
𝝋 Phase angle at each point of observation.
𝒋 = √−𝟏 Imaginary part of y-axis.
𝒔̅ Signal time average measured in Pa.
𝑻𝒎 Measurement time in seconds
𝒙𝒂,𝒃,𝒄,𝒅,𝒆,𝒇 Distances between the sample and the observation points a, b, c, d, e and f respectively.
𝑷𝒍 Instantaneous sound pressure for each point of observation, where the subscript "l" refers to microphones a,b,c,d, e and f.
𝒑̂ 𝒍 Measured pressure amplitudes (gains) by the microphones a, b, c, d, e and f respectively, where the subscript "l" refers to microphones a,b,c,d, e and f.
𝒓 Reflection coefficient.
𝑯𝒄𝒃 Complex acoustical transfer function between microphones b and c 𝑯𝒄𝒂 Complex acoustical transfer function between microphones a and c 𝑯𝒅𝒆 Complex acoustical transfer function between microphones e and d 𝑯𝒅𝒇 Complex acoustical transfer function between microphones f and d 𝑷𝒂, 𝑷𝒃, 𝑷𝒄,
𝑷𝒅, 𝑷𝒆, 𝑷𝒇
Sound pressures at the observation points a, b, c, d, e and f respectively.
𝒌𝟎 Wave number.
𝑺𝒉, 𝑺𝒍 Distances between the two microphone positions, for high and low frequency ranges respectively.
𝑯𝟐𝟏 Transfer functions between the two microphones 2 and 1.
𝒙𝟏= 𝑫𝟎+𝑺𝒉 Distance between the sample and the further microphone.
𝑯𝑹 Real part of 𝐻
𝑯𝑰 Imaginary and real part of 𝐻
𝒓𝒂 Reflection coefficient for waves towards the sample at point xa=0.
𝒓𝒃 Reflection coefficient for waves towards the sample at point xb=0.
𝒕𝒂𝒃 Transmission coefficient from downstream to upstream.
𝒕𝒃𝒂 Transmission coefficient from upstream to downstream.
1
1. Introduction
Some of our everyday problems are street air pollution and noise pollution, especially noise from cars on highways or in densely populated areas with heavy traffic and many traffic lights, which results in recurring braking and acceleration done by moving vehicles.
Companies are nowadays competing in developing new types of sound barriers, known as green sound barriers, with plants planted in the filling between two panels. Such barriers could have the dual effect of both absorbing noise, as well as decreasing air pollution, by increasing the planted area close to the road. In addition, plants also bring aesthetical quality to the otherwise hard and grey surroundings of the road, as well as promoting biodiversity[1].
The challenge is to reach the most effective design. One of the most interesting designs was produced by Butong AB which recently grabbed the interest of many construction companies working in the field of sound barriers, since it combines art and science together.
Figure 1: An example of a green sound barrier (Source: Butong AB) [2]
ABB has developed according to ISO and ASTM standards a special pipe for KTH which is used for measuring the absorption coefficient, reflection coefficient and the transmission loss of samples with fixed diameter and different thicknesses. This pipe is known as "The impedance tube". The impedance tube is a very common method nowadays, since one can collect a lot of information about the samples acoustical properties even before performing lab measurements.
The tests were done through measurements on the components of several configurations and designs. Thereafter a program code using MATLAB was used to combine the obtained results and build up a theoretical model of optimal designs and thicknesses.
2
2. Sound generation and traffic noise
This part is a brief and basic background explaining the generation of sound waves and its characteristics.
2.1. Sound waves
Sound waves are mechanical elastic waves which require a medium that posses mass and elasticity to be transmitted and are studied under the field of applied mechanics.[8]
Sound disturbances can only be tracked as a function of time and often studied and analyzed as function of frequency. Sound disturbances in the medium are normally very small and can be detected as small variations in the ambient pressure.
In general there are many types of sound waves, however the medium where sound waves propagate decides the type of the wave propagating, for example some mediums support the propagation of transverse and bending waves (ex: solid mediums),while others doesn't support it (ex: air). Since the medium where the sound barrier exist will be air then our focus will be on longitudinal waves, which is the only type of waves that exists and propagates in air.
Longitudinal sound waves
This type of waves have a particle motion parallel to the direction of wave propagation. It normally appears as a sequence of contractions and rarefactions in the medium as shown in figure 2 .
Figure 2: An example of a longitudinal sound wave moving through a structure. (Source: Sound and vibration)[8]
3 2.2. Sound characteristics
Sound waves is characterized by several concepts, based on the idea of periodicity, which is defined as the repetition of the wave after a fixed period of time. Using the following curve a brief summary of these concepts and their definitions could be easily described and understood.
Figure 3: A graph illustrating sound characteristics (Source: Fundamentals of Noise and Vibration Analysis for Engineers)[10]
Amplitude (𝑷̂): is the maximum pressure displacement measured from the equilibrium position, expressed in Pa.
Root means square of sound pressure (R.M.S) (𝑷̃): is simply the square root of the average of the squared instantaneous sound pressure. It is commonly used to describe the strength of the signal over a period of time.
Wave length (λ): is defined as the distance between two peaks, also can be defined as the distance between two rarefactions, wave length is measured in meters.
Period (T): is the time taken for a sound wave to repeat itself, it can be also defined as time taken by a wave to complete one cycle. The period is measured in seconds.
Frequency (f): is the number of oscillations per second measured in Hertz (Hz). The following formula represents the relation between the period and frequency:
𝑇 =1 𝑓
Frequency is related to speed of sound propagation using this formula:
𝐶 = 𝜆𝑓
Where, C is the speed of sound propagation measured in m/s.
4 Sound waves can be generated by different methods. One way of generating sound waves is by using sound speakers, which transforms electrical signals into sound. Such method has an advantage during measurements, since one can choose to generate the sound with different types of signals. Following are the three types of signals which can be generated.
Periodic sound signal: It is a signal that repeats itself after a regular period of time (T).
A periodic signal satisfies the following mathematical expression, 𝑓(𝑥 + 𝑇) = 𝑓(𝑥)
Where, T is the period.
Sine and cosine functions are examples of periodic functions which are commonly used for describing sound waves, following is an example for a periodic sinusoidal pressure signal describing the instantaneous sound pressure of a sound wave:
𝑷(𝒕) = 𝑷̂. 𝒔𝒊𝒏 (𝝎𝒕 + 𝝋) (1)
Where,
P(t) is the instantaneous, time dependent sound pressure.
ω is the angular frequency, where ω = 2πf ϕ is the phase angle.
Random sound signal: It's a signal which is caused by the chance mechanism and does not repeat over the time.
Transient sound signal: It's a signal with a short duration which starts and ends at zero.[8]
2.2. Frequency domain
Frequency domain is the representation of the signal with respect to frequency, since analyzing the signal in the frequency domain gives a lot of useful information, which might help in understanding a certain behavior.
The frequency domain helps mainly in finding out the decomposition of the signal which the output signal is composed of and eliminate the undesired signals to get better results.
In figure 4, the output signal is composed of three components., however such information won't be noticed by only looking on the time domain graph, instead one can notice such decomposition by looking on the frequency domain, which shows that such sound wave is decomposed of three sound waves which are buildup at three different frequencies and by adding these wave together the final wave shown in the time domain will be the result.
5
Figure 4: Frequency domain and time domain for a output signal. (Source: National instruments)
2.4. Sound fields
Free Field (Direct field): It is a field where sound propagates without any form of obstruction.
Near field: The near field of a source is the region close to a source where the sound pressure and acoustic particle velocity are not in phase. In this region the sound field does not decrease by 6 dB each time the distance from the source is increased (as it does in the far field). The near field is limited to a distance from the source equal to about a wavelength of sound or equal to three times the largest dimension of the sound source (whichever is the larger).[4]
Far field: The far field of a source begins where the near field ends and extends to infinity.
Note that the transition from near to far field is gradual in the transition region. In the far field, the direct field radiated by most machinery sources will decay at the rate of 6 dB each time the distance from the source is doubled. For line sources such as traffic noise, the decay rate varies between 3 and 4 dB.
Diffuse field (Reverberant field): The reverberant field of a source is defined as that part of the sound field radiated by a source which has experienced at least one reflection from a boundary of the room or enclosure containing the source.[4]
2.5. The logarithmic scale
The logarithmic scale was introduced due to the broad sensation of a human sound, as the lowest sound pressure a normal person can hear is 20 μPa, and the highest a normal person can hear is about 100 Pa, which makes it a ratio of about million to one, furthermore; it was found that the ear does not respond linearly, but logarithmically to stimulus. For these reasons a logarithmic scale was introduced.
The logarithmic scale is basically a ratio between a measured value and a reference value.
6
Figure 5: The output sound of several sources and the effect of logarithmic scale. (Source: Acoustics and acoustical measurements)
2.6. Sound levels
In order to describe the strength of the acoustical signal, one needs to quantify it. For such purposes the following concepts are used.
Sound pressure level (SPL): is the most common expression used when talking about measuring the loudness of sound. It is the logarithmic ratio between the absolute sound pressure and a reference value of sound pressure (2.10-5), which corresponds to the lowest sound pressure a young person with normal hearing can perceive at 1 kHz (also known as the threshold of hearing). [8]
Sound pressure level defined mathematically as follows:
𝐿𝑝 = 10. log 𝑃̃2 𝑃𝑟𝑒𝑓2 Where,
𝐿𝑝 the sound pressure level.
𝑃̃ the root means square (r.m.s.) of the measured sound pressure.
𝑃̃ the reference value of the sound pressure and is said to be 2*10𝑟𝑒𝑓 -5 Pa.
Sound power level: is the logarithmic ratio between the time averaged sound power and a reference value of sound power.
It is expressed as follows:
𝐿𝑊 = 10. log 𝑊̅ 𝑊𝑟𝑒𝑓
7 Where,
𝐿𝑊 is the sound power level.
𝑊̅ is the time averaged sound power.
𝑊𝑟𝑒𝑓 is the international reference value of sound power and is said to be 10-12 W.
Sound intensity level:
𝐿𝐼= 10. log 𝐼̅
𝐼𝑟𝑒𝑓 Where,
LI is the sound intensity level.
W̅ is the time averaged sound intensity.
Wref is the international reference value of sound intensity and is said to be 10-12 W/m2.
2.7. Sound attenuation
Attenuation is a word used to describe the decrease or loss of sound energy. Sound attenuation could happen due to several reasons as absorption and scattering.[7]
2.8. Sound absorption
Sound absorption is defined as the amount of acoustic energy dissipated in a material as sound waves pass through it. Sound absorption coefficient is dimensionless property and normally is referred to by the symbol (α). The amount of sound absorption normally lies between 0:1, where zero refers to an ideal reflective material, while one refers to a perfect sound absorbent.
Figure 6 shows a scheme of sound wave behavior when meeting an obstacle.
Figure 6: Behavior of sound waves when meeting an obstacle (Source: Development of A Low Cost Impedance Tube).
The rest of the sound waves that are not absorbed by the material are either reflected or transmitted through the material.
8 2.9. Traffic noise
Noise is a difficult word to define and the definition could be very subjective at some points, however according to the Swedish public health authority "Folkhälsomyndigheten"
noise is defined as the unwanted sound or in other words the sound that disturbs humans and one wishes not to hear. [1]
According to the Swedish board of transportation "Transportstyrelsen", noise is defined as an unpleasant sound.[6]
2.10. Noise and human health
Noise is not only considered to be disturbing, but in many cases noise could be very harmful and have many bad effects on human health, as it could cause hearing impairment, hypertension, ischemic heart disease and blood pressure problems.
The traffic noise is another example of daily problems. It disturbs the neighborhood during their sleeping hours which results in a lack of sleep and accordingly tiredness and exhaustion will appear as a result. In many cases this is considered to be a serious problem as such results could lead to traffic, job or even home accidents.
For such reasons noise barriers were developed for protecting inhabited areas close to highways or dense traffic roads inside big cities from being exposed to disturbing sound levels.
Figure 7: Map showing measured sound level registered on "Borkyrka" municipality according to the Swedish board of transportation. (Source: Trafikverket) [16]
Figure (7) shows a map for the measured sound pressure levels in heavy traffic roads, in
"Botkyrka" municipality, Sweden, where a total of 3 million cars are using these roads every year.
9 The measurements were done using the European Standards, measuring the so called Lden (i.e."den" stands for: day, evening and night), which means the measurement is independent of the measuring time over the day (i.e. day time, evening or night).[17]
The Sound pressure level was measured 4 meters away from the ground. In the map yellow color indicates areas with acceptable measured sound pressure levels of values Lden ≥ 55db, while red color indicates areas with Lden ≥65 db. The values mentioned previously were decided by the Swedish parliament (i.e. Riksdag) as a guidance values for traffic noise.[18]
10
3. Green Sound barriers
This chapter is focusing on the structure of Green Sound barriers and type of fillings used in it.
3.1. Construction
Butong’s green barriers have a unique construction, which is not commonly found among sound barriers, since it combines both art and science.
The green barriers are created by pressing a cast substance between two form-matrices with extruded cells – thus creating panels consisting of two mesh structures. [15]. Two of those panels are thereafter used to enclose a filling, which results in a sandwich profile (see figure 8). The filling will act as earth for plants, but it also acts as the main absorbent of the green barrier.
Figure 8: A drawing showing the formation of Butong’s green barrier (Source: Butong AB) [2]
3.2. Fillings
The filling can be divided into two parts. The main part is the soil used for planting and the second part is the vegetation, since the vegetation itself will act as a sound absorbent while analyzing the structure.
The soil filling is one of the most important and challengeable components in the green barrier construction, as it must act both as a good earth substrate for the plants and as an effective sound absorbent. On top of that, it should also be easily handled at a maintenance process. It is quite hard to find a material with all these properties at the same time.
In addition to the previously described parts, comes the water content inside the soil, since plants needs to be watered to live and keep the good look of the design, as well as such sound barriers will be mounted outdoors, which means it will be subjected to different weather conditions, including rainy times and very low temperatures, which will cause icing problems and will obviously dramatically decrease the absorption coefficient of the whole structure.
One of the main efforts in this thesis was to reach and recommend a list of materials that might fulfill the previous requirements, either by itself or by mixing two or more of them with different proportions.
11 Listed underneath are the materials:
- Leca balls.
- Coconut fiber.
- Crushed leca.
- Pumice stones.
Figure 9: Pictures showing types of filling used.
From left to right Leca balls (Azmi Rahmani, Hydroponics and plant care pte ltd), Coconut fiber (Indiamart.com), Crushed leca (Bonsai tree) and Pumice stones (Americos industries).
12
4.Measurements
The measurement process was done with the impedance tube method, which gives pre- information about the amount of noise that can be absorbed by different configurations of materials at different thicknesses, as shown in figure 10.
Figure 10: The impedance tube used for the measurements.
4.1. Methodology
The idea behind the duct measurements is mainly to save time and money, while the lab is used for performing a full scale test to get more realistic and reliable results.
Since many samples and configurations needed to be tested, a combination between measuring and simulation methods using the impedance tube chose to be used, which was found to be more time efficient and still giving almost the same results as the ones obtained from the measurement done in the reverberation room.
The measurements were done in accordance to standards ISO 10534-2:1998 Acoustic- Determination of sound absorption coefficient and impedance in impedance tube- part 2:
transfer method and ASTM E2611-09 Standard test method for measurement normal incidence sound transmission of acoustical materials based on the transfer matrix method.
13 4.2. Arrangement
The measurements are done on samples of the barrier’s main components. The main components of the barrier are described as following:
1- Different Butong panels with reasonable diameters.
2- Several types of fillings that can be used and thought to have effective absorbing characteristics.
3- Different thicknesses of the barrier (i.e. the whole structure).
Each component will be measured by itself (i.e. without being a part of the full structure), moreover some measurements were done on a full model sample (i.e. two panels enclosing fillings), in order to compare the results obtained from the measured samples with the results obtained from the simulation program.
The measurements start by measuring each of the barrier’s components by themselves in the duct. The obtained results are saved in an excel sheet, thereafter measurements of a prototype of a full model samples with different configurations and thicknesses were performed. In parallel a Matlab program is used to help predicting the absorption of different combinations of the measured components. Using the results obtained from the full model samples, a comparison can be done between the measured data and the theoretical data obtained from the simulation program.
The method used is the transfer function method. A random signal is activated, using a loudspeaker driven by a computer program producing plane sound waves. Microphones then measure the signal at three positions before and after the sample, and then the transfer functions between a sequence of points are in a Matlab based program for calculating the acoustical parameters of the material under test.
4.3. The impedance tube
The impedance tube is the name of the tube used in performing the measurements, the tube is designed such that only plane waves are generated inside the tube, such condition is satisfied using the following criteria: [5]
1- The distance between the loudspeaker and the closest microphone should be larger than three time the diameter of the tube in order to allow enough space for the plane waves to fully develop.
2- The diameter and the working frequency range should fulfill the following condition[5]: 𝑑 <𝐾𝑐
𝑓𝑢 or 𝑓𝑢 <𝐾𝑐
𝑑
Where,
d if the diameter of the tube.
c is the speed of sound.
𝒇𝒖 is the upper frequency limit.
K= 0.586
14 3- The spacing between the microphones, since the lower frequency limit should be greater than one percent of the wavelength corresponding to the lower frequency of interest.
𝑆𝑙 > 0.01. 𝜆𝑙 Where,
𝑺𝒍 is the distance between the two microphones (see figure 11).
𝝀𝒍 is the wave length of the low frequency of interest.
The test rig is constructed of several parts, following is a list of these parts and its purpose:
1- The loudspeaker: is used for generating plane waves of a broadband noise in the frequency range of interest.
2- Low density absorbent: is located right after the sound speaker, the purpose of using such material is to avoid the resonance generated due to the low mechanical impedance of the load speaker membrane (diaphragm).
3- The upstream tube: is the part of the tube close to the loud speaker, it has a seamless circular steel cross section pipe with 3 mm thickness in order to avoid sound transmission through the tube. The inner side of the tube should be clean, smooth and perfectly circular in order to maintain low sound attenuation.
4- Sample holder: is a detachable holder made of the same material as the upstream tube, the main advantage of such type is the easiness of dismantling the tube for storing and is easier to reach the sample while performing the measurements.
5- Downstream tube: is the part of the tube that lies after the sample, it has the same structure properties as the upstream tube.
6- Anechoic termination: it is the last part of the tube and is attached to the downstream tube, it is made of low density absorbent, the main purpose it to minimize the reflected sound waves, which might generate standing waves in the tube.
7- Mounting structure: is the part where the tube is mounted over, the main purpose of it is to keep the tube aligned and prevent any external vibrations while doing the measurements.
15
Figure 11 :The upper figure shows different parts of the impedance tube.
The lower figure shows the place of the sample inside the pipe as well as the direction of sound propagation.
8- A built in ruler: used to place the sample in a symmetric position, (see figure 12).
Figure 12: The Duct has a built-in ruler to help putting the sample in a symmetric position.
9-Microphones:
As seen in figure 13, six microphones were used in the measurement process, in order to allow covering a broad frequency range, since covering the high frequency range can be done by calculating the transfer functions between the two microphones "b" and "c" and the low frequency range can be covered using the transfer function between the two microphones "a" and "c" in the upstream part.
Similarly "d" and "e " microphones are used for high frequency range in the downstream, as well as "d" and "f" microphones for the low frequency range in the downstream part.
16 The main reason for using six microphones is the frequency range, as it provides the absorption coefficient of the structure over a broad frequency range.
Since a combination between the ASTM E2611-09 and ISO 10534-2 were used, so using an extended impedance tube was needed for calculating the transmission loss, therefore the use of three microphones won't be convenient .
Figure 13
A sketch showing the microphone positions and the dimensions needed.
A and B represent the incident and reflected waves in the upstream part respectively.
C and D represent the transmitted and reflected waves in the downstream part respectively.
4.4.The sample
The sample constructed of three different parts, first a 15 cm cardboard pipe which acts as the outer frame of the sample, filling which acts as a soil for the plants and is considered to be the main absorber and a holed concrete cover (Butong) manufactured in order to allow growing of the plants.
Figure (14) shows a picture of one of the sample configurations used during the measurements.
Figure 14: Left picture shows sample of the concrete panel of the construction and the right picture shows the complete assembly of the measured sample.
17 4.4. Calculations
Using the measured quantities from the previous prescribed measurement process, the instantaneous sound pressure for the incident and reflected waves respectively at all six points of observations will be calculated using the following formula:
𝑃𝑙= 𝑝𝑖[𝑒(𝑗𝑘𝑥𝑙)+(r. 𝑒(−𝑗𝑘𝑥𝑙))] (3)
Where,
𝑷𝒍 is the instantaneous sound pressure for each point of observation, where the subscript
"l" refers to microphones a,b,c,d, e and f respectively.
J is the imaginary number
𝒙𝒍 are the distances between the sample and the observation points, where the subscript "l"
refers to the observation points a,b,c,d, e and f on the respectively.
r is the reflection coefficient.
Transfer functions between the microphones and the reference signals (input signal to the loudspeaker) are measured.
According to equation (4), those transfer functions are of the form:
𝐻𝑐𝑏=𝑃𝑃𝑐
𝑏= 𝑒(𝑗𝑘𝑥𝑐)+(r.𝑒(−𝑗𝑘𝑥𝑐))
𝑒(𝑗𝑘𝑥𝑏)+(r.𝑒(−𝑗𝑘𝑥𝑏)) , 𝐻𝑐𝑎=𝑃𝑃𝑐
𝑎 = 𝑒𝑒(𝑗𝑘𝑥𝑎)(𝑗𝑘𝑥𝑐)+(r.𝑒+(r.𝑒(−𝑗𝑘𝑥𝑐)(−𝑗𝑘𝑥𝑎)))
(4) 𝐻𝑑𝑒 =𝑃𝑃𝑑
𝑒 = 𝑒𝑒(𝑗𝑘𝑥𝑑)(𝑗𝑘𝑥𝑒)+(r.𝑒+(r.𝑒(−𝑗𝑘𝑥𝑑)(−𝑗𝑘𝑥𝑒))) , Hdf=PPd
f = e(jkxd)+(r.e(-jkxd))
e(jkxf)+(r.e(-jkxf))
Where,
𝑯𝒄𝒃 is the complex acoustical transfer function between microphones b and c 𝑯𝒄𝒂 is the complex acoustical transfer function between microphones a and c 𝑯𝒅𝒆 is the complex acoustical transfer function between microphones e and d 𝑯𝒅𝒇 is the complex acoustical transfer function between microphones f and d 𝑷𝒂, 𝑷𝒃, 𝑷𝒄, 𝑷𝒅, 𝑷𝒆, 𝑷𝒇 are sound pressures at the observation points a, b, c, d, e and f respectively.
The reflection coefficient can simply be calculated by inserting the results from the previous equations in this equation:
𝑟 = 𝐻21− 𝐻𝐼
𝐻𝑅− 𝐻21exp(2𝑗𝑘0𝑥1) (5) 𝒋 The imaginary part of y-axis.
𝒌𝟎 The wave number.
𝑺𝒉, 𝑺𝒍 The distance between the two microphone positions, for high and low frequency ranges respectively.
𝑯𝟐𝟏 The transfer functions between the two microphones 2 and 1.
𝒙𝟏= 𝑫𝟎+𝑺𝒉 The distance between the sample and the further microphone.
𝑯𝑹 and 𝑯𝑰 The imaginary and real part of 𝐻21.
According to ISO 10534, the absorption coefficient of the material, when backed by a rigid plate can be calculated from the following equation:
18
∝= 1 − |𝑟|2 (6)
However a sound barrier is often in practice placed alongside the road (i.e. closer to the case when backed by a free space than by a rigid wall), for this reason, we have to estimate the sound power dissipated inside the material when it is standing in a "free" space.
Standard ASTM E2611-09 describes how to measure the reflection and transmission coefficients of a specimen backed by a "free" space in an extended impedance tube [5]:
𝑃𝑏= 𝐴−𝑒𝑗𝑘𝑥𝑎+ 𝐴+𝑒−𝑗𝑘𝑥𝑎 (7.1)
𝑃𝑐= 𝐴−𝑒𝑗𝑘𝑥𝑐+ 𝐴+𝑒−𝑗𝑘𝑥𝑐 (7.2)
𝑃𝑑= 𝐵−𝑒𝑗𝑘𝑥𝑑+ 𝐵+𝑒−𝑗𝑘𝑥𝑑 (7.3)
𝑃𝑒= 𝐵−𝑒𝑗𝑘𝑥𝑒+ 𝐵+𝑒−𝑗𝑘𝑥𝑒 (7.4)
The complex components are then,
𝐴− =𝑃𝑏𝑒𝑗𝑘𝑠−𝑃𝑐
2𝑗 sin (𝑘𝑠). 𝑒−𝑗𝑘𝑑 (8.1)
𝐴+ =𝑃𝑐−𝑃𝑏𝑒−𝑗𝑘𝑠
2𝑗 sin (𝑘𝑠) . 𝑒𝑗𝑘𝑑 (8.2)
𝐵− =𝑃2𝑗 sin (𝑘𝑠)𝑑𝑒𝑗𝑘𝑠−𝑃𝑒. 𝑒−𝑗𝑘𝑑 (8.3) 𝐵+ =𝑃2𝑗 sin (𝑘𝑠)𝑒−𝑃𝑑𝑒−𝑗𝑘𝑠. 𝑒𝑗𝑘𝑑 (8.4) Where,
"+" and "-" signs refers to the direction of the wave propagation relative to the coordinate.
S=Sh=Sl is the distance between the two microphones.
d is the distance between the surface of the sample and the further microphone (i.e.
D0+Sh).
As seen in figure (14) , the test sample is not symmetric about the thickness, which means the reflection coefficient from one side (ab) is not the same as the other side (ba), in order to overcome this problem an additional measurement is needed. ASTM E2611-09 Standards suggests to use either two sources or two loads method. In our second measurement we inversed the sample as suggested by reference [9], which in principle same as the two source method.
The matrices can be then formulated as following:
[𝐴+1 𝐵+2
𝐵+1 𝐴+2]=[𝑟𝑎 𝑡𝑏𝑎 𝑡𝑎𝑏 𝑟𝑏] [
𝐴−1 𝐵−2
𝐵−1 𝐴−2] (9)
The equation is then reformulated to be,
[𝑟𝑎 𝑡𝑏𝑎
𝑡𝑎𝑏 𝑟𝑏]=[𝐴+1 𝐵+2 𝐵+1 𝐴+2] [
𝐴−1 𝐵−2 𝐵−1 𝐴−2]
−1
(10) Where,
19 𝒓𝒂is the reflection coefficient for waves towards the sample at point xa=0.
𝒓𝒃 is the reflection coefficient for waves towards the sample at point xb=0.
𝒕𝒂𝒃is the transmission coefficient from downstream to upstream.
𝒕𝒃𝒂is the transmission coefficient from upstream to downstream.
The indices 1 and 2 refers to the normal and reversed positions of the sample respectively.
Reformulating the previous matrices in order to obtain the reflection and transmission coefficient, will lead to the following form,
[𝑟𝑎 𝑡𝑏𝑎 𝑡𝑎𝑏 𝑟𝑏]=
[𝐴1+ 𝐵+2
𝐵+1 𝐴2+][𝐴−2 −𝐵−1
−𝐵−2 𝐴−1 ] 𝐴−1
𝐴−2
−𝐵−1
𝐵2− = 1
𝐴−1 𝐴2−
−𝐵−1
𝐵−2 [𝐴+1𝐴−2−𝐵−1𝐵+2 𝐴−1𝐵+2 − 𝐴+1𝐵−2 𝐵+1𝐴−2−𝐵−1𝐴+2 𝐴−1𝐴+2−𝐵+1𝐵−2
] (11)
Solving the previous system leads to calculating both reflection and transmission coefficients.
𝑟𝑎= 𝐴+1𝐴−2−𝐵−1𝐵+2 (12.1)
𝑟𝑏= 𝐴−1𝐴+2−𝐵+1𝐵−2 (12.2)
𝑡𝑏𝑎= 𝐴−1𝐵+2 − 𝐴+1𝐵−2 (12.3)
𝑡𝑎𝑏= 𝐵+1𝐴−2−𝐵−1𝐴+2 (12.4)
The transmission loss can be calculated using the two transfer functions in the transmission loss equation.
𝑇𝐿 = −20. log (|𝑡|) (13)
Where,
𝒕 is the calculated transmission coefficient.
Since we are using the extended impedance tube and we are interested in knowing the energy dissipated inside the material, then we have to consider the energy transmitted through the material and neglect it from our calculations.
Using the previous parameters, one can calculate the energy dissipated inside the material as described in reference [9]
∝𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑= 1 −|𝑟|2−|𝑡|2 (14)
The following equation is used for obtaining results equivalent to the results obtained using equation (10) when measured in the standard condition using regular impedance tube with a rigid end as mentioned in ISO 10534-2 Standards, considering the measurement direction from a to b.
∝𝑎𝑐𝑡𝑢𝑎𝑙= 1 − |𝑟𝑎|2−| 𝑡2
1−𝑟𝑏|
2
− 2𝑅𝑒 (𝑟1−𝑟𝑎∗.𝑡2
𝑏) (15)
Summary
20 This part is summarizing the steps for performing pipe measurements mentioned
previously in this paper.
Measurement steps
1- Connect all the needed connections and devices.
2- Start up the computer program (spectra plus).
3- Create a sound signal through the program and the loudspeaker.
4- Save the measured data recorded at the microphone in an excel sheet.
5- Move the microphone to the next position and repeat steps 3 and 4.
6- Flip the sample and repeat steps 3-5 (two source method).
7- Repeat steps 3 -6 for all the needed measurements.
8- Convert all the results into Matlab format.
9- Use Matlab to calculate the transfer functions as mentioned before.
10- Calculate absorption coefficient and sound transmission loss for all the cases (See table 1).
11- Compare the measured values with the calculated results.
21
5. Results
The results obtained using the previous measurements and calculations will be discussed and illustrated in this section.
Since the tested materials and configurations were designed to be used as sound barriers, then the main concern will be focusing on the low frequency region, as sound barriers will mainly be used on high ways and regular car roads.
It's important to mention that the following configurations have been chosen for measurements, as it was expected to obtain positive results out of it:
Configuration Description Thickness (mm) Amount of added water (dl)*
Configuration 1 Pipe, Leca balls and concrete panel.
100 0
Configuration 2 Pipe, Crushed leca and concrete panel.
40-50 0
Configuration 3 Pipe, Coconut fiber and concrete panel.
50-75-100 0
Configuration 4 Pipe, Pumice and concrete panel.
50-75-100 0
Configuration 5
Pipe, mixture of (33%
Pumice, 33%
Coconut fiber,33%
Leca balls) and concrete panel.
50-75-100 0
Configuration 6
Pipe, mixture of plants and soil (33%
Pumice, 33%
Coconut fiber,33%
Leca balls) and concrete panel.
100 0
Configuration 7
Pipe, wet mixture of (33% Pumice, 33%
Coconut fiber,33%
Leca balls) and concrete panel.
100 1,2, and 3 dl
Table 1: Measurements done using impedance tube in Marcus Wallenberg laboratory (MWL) at KTH.
* The amount of water added using a 1 dl measuring spoon. The humidity is not counted in the number above.
22 For the measurements with added water, the water was added manually to different types of fillings, and a visual leakage inspection was performed after each time the water was added, so that it's sure that all the amount of water added was absorbed by the soil (i.e.
filling).
Extra measurements were done for some of the chosen configurations without the concrete panel, as it was interesting to compare the results with the original configurations and see the effect of the concrete panel on the absorption coefficient of the whole structure.
Following expressions are important in order to better understand the graphs shown in this chapter:
Dissipated energy: The energy dissipated inside the sample under test, using equation (14).
Actual absorption: The actual absorption coefficient calculated for the sample using equation (15),which is the same absorption coefficient obtained using the regular impedance tube with a rigid end as described in ISO 10534-2 Standard, while Butong's panel is facing the loudspeaker.
Butong open: Indicates Butong's concrete panel with open holes.
Butong (LF): Indicates Butong 's concrete panel with fully closed holes.
5.1. Empty test rig
The first measurement was done for the duct itself, to make sure the duct is fully sealed and has no sound leakage or any faults in the mounting process.
Of course the predicted dissipated energy for such case should be close to zero, figure (15) shows the dissipated energy for the extended impedance tube.
In the figure, "ab" stands for the direction of the sound wave that goes from point "a" to point "b" and "ba" stands for the reflected sound waves that goes from the opposite direction. (See figure 13).
Looking to the figure more carefully one can notice there is an amount of energy dissipated despite in the empty test tube, the reason behind that could be one of the following:
1. Misalignment in the structure of the test rig, which is the main reason, due to the existing absorption at low frequencies.
2- Leakage in the sound isolation of the test rig.
3- Leak in the sound holder section.
23
Figure 15: Dissipated energy of the empty duct is not zero, which indicates that the duct is not perfectly sealed or misaligned.
5.2. The outer pipe
As mentioned earlier in the previous chapter, the sample is constructed of three main parts, one of these parts was a cardboard pipe of 15 cm in length and has an outer diameter of the same size as the inner side of the impedance tube.
A measurement was done for the pipe in order to measure the amount of sound energy dissipated in it and eliminate it later from the actual construction to avoid any errors.
Figure (16), shows the dissipated energy of the pipe, and as expected the value of it is quite small, since the pipe is thin and hollow, so it doesn't have large surface area to dissipate the sound energy, however one can notice the increase of the amount of energy dissipated in the high frequency region, which could be due to the gap between the pipe and the impedance tube that cause energy dissipation due to friction in such narrow gap.
On the other hand, one can notice the remarkable decrease of the dissipated energy in the low frequency region compared to the empty pipe, indicating better alignment between parts of the test tube after mounting the outer pipe.
24
Figure 16: The graph shows the dissipated energy of the pipe. Compared to the empty duct, it is noticed that there is a small amount of a sound energy absorbed by the pipe.
5.3. Butong's concrete panel
This measurement was done on the concrete panel (Butong's panel), enclosing the filling inside the tube. Since the panel is made of concrete, then one can expect small values of dissipated energy, however figure (17) shows quite high amount of energy dissipated. By dividing the curve into two regions, one will have a better understanding analyzing the reasons behind such result.
In low frequency region (0-600 Hz) this could be mainly due the misalignment in the setup arrangement, since one wouldn't expect much energy dissipated in this region as the wavelength is quite large compared to the dimensions of the Butong's panel, especially in the range 0-200 Hz, however the holes in the panel could play a role in the amount of the energy dissipated in this frequency region.
Looking on the higher frequency range (800-1800 Hz) on the other hand the amount of dissipated could be due to the holes in the panel, which allow sound waves to pass through the panel and producing friction and hence the energy dissipation.
The friction between the panel and the tube itself could also be considered as a reason at high frequency region, since the area around the circumference of the panel is not sealed.
A sudden drop could be clearly noticed at 200 Hz, this could be due to errors in installing the setup.
25
Figure 17: Dissipated energy coefficient of the concrete panel.
5.4. Configuration 1*
* Pipe, Leca balls and Butong's panel.
Only one measurement was done for this type of configuration, in this configuration a thickness of 100 mm was chosen, since a thinner profile was expected to have low amount of dissipated energy.
Looking on figure (18), it is noticed that the effective region for this lies between 800 - 1100 Hz, which indicates that such configuration will be of a good efficiency within the range of interest.
The dissipated energy is quite low in the low frequency region, since the structure's size is quite small compared to the wavelength in this frequency range.
The misalignment in the tube arrangement is to be blamed for the existence of the amount of dissipated energy in the low frequency region between 0-200 Hz.
The increase of the dissipated energy in the region 800-1400 could be due to the attenuation of sound in the spaces between the leca balls, not to forget the leca balls itself since it is porous, and plays a role dissipating a considerable amount of energy in the high frequency region.
The reason of the having different energy dissipation curves by changing the direction of the sample is the asymmetric construction of the sample under the test.
26
Figure 18: Dissipated energy for configuration 1.
5.5. Configuration 2*
* Pipe, Crushed leca and Butong LF concrete panel.
Two measurements for two different thicknesses were done using this configuration.
Again the expectations were not too high for such type, since the density of the crushed leca balls is quite high, which makes it more as a reflector than absorbent material.
It is important to mention that the concrete panel used in this measurement had a different profile than the others, which was the reason of naming it as "butong LF" indicating that the holes of the panel was not hollow, instead it was closed with a thin layer of concrete.
It can be noticed from the curves that the absorption coefficient decreases, as the thickness increases, , since with a higher thickness the configuration becomes more dense which makes it difficult for sound waves to penetrate the material layers, hence sound wave is reflected instead of absorbed.
As seen in figure (19), such configuration has quite low absorption in all the frequency ranges of interest compared to the previous configuration, which makes it considered inefficient configuration for the particular a green sound barrier assigned for.
27
Figure 19: Actual absorption calculated using eq. (15) for configuration 2 with two different thicknesses (40 and 50 mm).
The dramatic effect of the concrete panel on this configuration could be seen on figure 20.
In the figure the abbreviation (WOP) stands for the structure without panel.
One can not hesitate figuring out that closed concrete panel is decreasing the absorption efficiency of the structure, which is predictable since concrete is not a good sound absorbent, but a good reflector on the other hand.
Despite the disadvantage of having Butong (LF) (i.e. Butong's panel with closed holes) on the absorption coefficient of the whole structure, however such panels will be in a good use for a certain period till the vegetations grow up and hold the fillings inside the structure.
20: Actual absorption coefficient (Eq.15) for configuration 2 without mounting the concrete panel to the structure (WOP is the abbreviation for without panel).
28 5.6. Configuration 3*
* Pipe, Coconut fiber and Butong's panel.
Three measurements were done for three different thicknesses for this configuration.
Since Coconut fiber is of a light density, so one can expect that such material could act as an effective sound absorbent.
In figure 21 it could be noticed at low frequencies, as the thickness increases the absorbent efficiency of the configuration increases, which is understandable, since the thicker it gets the higher amount of sound energy dissipated inside the material will be as the sound waves will propagate longer distance inside the structure.
Looking at the high frequency region, one can notice there wasn't a big difference in absorption by increasing the thickness, the reason could be the amount of coconut fiber used was not dense enough to form a good sound absorbent when mounting thicker samples, since by increasing the amount of coconut fibers added to the same volume, will result in much denser layer of the coconut fiber and more energy dissipated inside the sample.
Figure 21:Actual absorption for configuration 3 with three different thicknesses (50, 75 and 100 mm).
In general this configuration shows a considerably high absorption coefficient in the low frequency region compared to other configurations of similar thicknesses, as well as for the high frequency region which makes it one of the highest recommended structure for sound barriers puposes.
Figure (22) shows the amount of energy dissipated inside the structure for all different thicknesses of the configuration, the curves show very small differences between the energy dissipated for the different thicknesses, which in return enhance the earlier mentioned reason relying the small differences to the amount of the coconut fiber added in the structure of larger thicknesses.
29
Figure 22: Dissipated energy (eq.14) for configuration 3 with three different thicknesses (50, 75 and 100 mm).
Figure (23) one can see the effect of the concrete panel on the absorption efficiency of the structure, however it should be mentioned that the concrete panel used here is with hollow holes and not blocked with concrete as in the previous configuration, which makes it decrease the absorption efficiency of the structure with less amount compared to the previous configuration.
Figure 23: Actual absorption coefficient for configuration 3 with and without concrete panel, having three different thicknesses (50, 75 and 100 mm).
By comparing the two cases, one can notice by using Butong's panel, the absorption coefficient increases in the lower frequencies region, which can be a result of the following two reasons:
- Thickness increase, since by adding the concrete panel the thickness of the whole structure will increase, hence the dissipated sound energy will increase, since the distance covered by the acoustic waves inside the structure will increase.
30 - The shift of the maximum absorption could be due to a shift of the resonance frequency of the structure, which could be a result for adding Butong's panel, hence the increase in the amount of energy dissipated, resulting in an increase of the absorption coefficient in this frequency region .
5.7. Configuration 4*
* Pipe, Pumice and Butong's panel.
In this configuration Pumice stones were used as a filling. Measurements were done on three different thicknesses of the structure (50, 75 and 100 mm). Since pumice stones are famous with its low density, as well as its porous construction, then one can expect a good absorption characteristics within the frequency region of interest.
From figure (24), one can notice the 75 mm thickness configuration is considered to be the best above other thicknesses of 50 and 100 mm, the reason could be due to the size of grains used in the 100 mm thickness sample, which were smaller and made the filling more compressed, as a result the absorption coefficient decreased.
Figure 24: Actual absorption coefficient for configuration 4 with three different thicknesses (50, 75 and 100 mm).
Figure (25), shows the dissipated energy inside the structure. Looking at the dissipated energy for the 50 mm sample, it shows a quite low amount of dissipated energy compared to the absorption coefficient of the same thickness, which indicates an error in the measurement of this thickness.
31
Figure 25: Dissipated energy (eq.14) or configuration 4 with three different thicknesses (50, 75 and 100 mm).
Figure 26, Shows the effect of the Butong's panel on the absorption quality of the structure can be easily noticed, especially in the frequency region higher than 600 Hz.
It was also noticed that with Butong's panel the peak of the maximum absorption is shifted to lower frequencies which was expected due to the change in thickness and the arrangement of the structure, similar to configuration 3.
Figure 26: Actual absorption coefficient for configuration 4 with and without concrete panel, having three different thicknesses (50, 75 and 100 mm).
32 5.8. Configuration 5*
* Pipe, mixture of (33% Pumice, 33% Coconut fiber,33% Leca balls) and Butong's panel.
This configuration was a try to mix the properties of the mentioned fillings in order to see the effect on the sound absorption of the structure.
Figure 27: Actual absorption coefficient for configuration 5, having three different thicknesses (50, 75 and 100 mm).
The idea was to put the filling in layers, so that sound waves will have different incident angle for each layer and hence increase the energy dissipated inside the structure.
First layer after the concrete panel was leca balls, then pumice and last was the coconut fiber.
Figure (28) shows the energy dissipated for both sides of the structure, it could be noticed from figure (28B) that having the coconut fiber as the first layer increases the energy dissipated in the structure and hence absorption quality of it.
33
Figure 28: a-Dissipated energy for configuration 5 with three different thicknesses (50, 75 and 100 mm) where the concrete panel towards the loud speaker. b- Dissipated energy for configuration 5 with three
different thicknesses (50, 75 and 100 mm) where the filling towards the loud speaker.
5.9. Configuration 6*
* Pipe, mixture of plants and soil (33% Pumice, 33% Coconut fiber,33% Leca balls) and Butong's panel.
Since such sound barriers are meant to have plants inside, then it was important to investigate the effect of plants on the absorption coefficient of the structure.
Figure (30), shows the effect of planting inside the structure compared to the unplanted case.
It is noticed from the curves the positive effect of the plants on the absorption coefficient of the structure compared to the unplanted case with the same thickness. This increase in the absorption coefficient could be due to the increase of the amount of the material in the same volume, which more layers of different materials and hence the increase in the dissipated energy and absorption coefficient of the structure.
Figure 29: Actual absorption coefficient (eq.15) for configuration 6 with thickness 100 mm including plants compared to the same thickness in configuration 5.
34 5.10. Configuration 7*
* Pipe, wet mixture of (33% Pumice, 33% Coconut fiber,33% Leca balls) and Butong's panel.
As a matter of fact such barriers will be subjected to different seasonal conditions around the year, moreover no plants can survive without water, such reasons was the core of this configuration, since there is a new factor which could play an interesting role in changing the absorption coefficient of the structure.
Figure (30) shows the effect of different amounts of added water on the absorption coefficient of the structure. One can notice the inverse relationship between the amount of water added and the structure's absorption coefficient.
It could be seen that by adding 3dl (~ 38%) of water to the structure, the sound absorption coefficient is decreased by about 0.2 for some frequencies compared to the dry case. The reason could be that water fill in the gabs between the filling components blocking sound waves from the passage through the material and therefore the decrease in the sound absorption coefficient.
Figure 30: Actual absorption coefficient for configuration 7 with thickness 100 mm and different amount of added water.
