3. Experimental set-up
3.3. Sweep signal
The signal that is analyzed is a linear sweep sound from 50 to 5000 Hz made with a Matlab script.
The script is listed in appendix 2. The used sweep sound lasts four seconds, but this is easily altered in the script. In the script of the sweep sound there is also a timer. This timer has multiple variables that can be altered by the user; the interval between the sweeps, the start time and the end time.
For this experiment a begin time of 22:00 and end time of 7:00 was taken with an interval of half an hour. By playing the sweep sound after working hours the inconvenience for the people in Flux and Cascade is brought to a minimum.
4. Results and Discussion
4.1. Prediction
The paper of T. Van Renterghem and D. Botteldooren (van Renterghem & Botteldooren, 2014), gives an idea of what to expect from the experiment. There are some differences, such as the shielding that is present in the experiment of van Renterghem, but not in this experiment. A model is used to predict the propagation of sound over layered porous media with extended reaction by a point source from the paper by Kai Ming Li, Tim Waters-Fuller, and Keith Attenborough (1998, United Kingdom). The input of this model is the number of layers, the depth, the impedance of the layers and the propagation constant.
The Slit Pore model is used to calculate the impedance- and the propagation constant of the vegetation. The necessary input for this model (porosity and flow resistance at various water content levels) was taken from (Beekman, 2012). The parameters are listed in table 1.
In the paper of Beekman (2012) the parameter βpercentage of saturationβ is used. This parameter can be converted to VWC (for this soil) by setting 22,4% VWC, which is the measured saturation during the calibration, to 100% saturation. The rest of the values can then be altered with the equation below.
πππΆ (%) = % ππ π ππ‘π’πππ‘πππ β 0.224 (19) In the same paper, the impedance of a green substrate is measured in an impedance tube. The depth of the substrate (7.56 cm), is close to that of the substrate on the roof of Cascade. By implementing these values in a Slit Pore model, the impedance and propagation constant are calculated for different Volumetric Water Content. The impedance and propagation constant are used to give a prediction of the sound pressure level difference between the two microphones for different Volumetric Water Content.
Table 1, flow resistivity and porosity for different values of volumetric water content, converted from saturation percentage as found in the paper of Beekman, 2012.
VWC (%) Porosity Flow resistivity (pa*s/m2)
0 0.43 25000
11.5 0.44 25000
17.0 0.43 23000
17.9 0.31 22000
22.4 0.23 24000
Figure 7, prediction of the sound level difference in decibel between the two microphones for different percentage of volumetric water content for one layer. The two microphones are placed 5.1 meter apart with a thickness of 4 cm. The source is located at a height of 2.5 cm and 60 cm from the first microphone. The depth of the substrate is 7.65 cm.
The model predicts a decreasing SPL difference for increasing Volumetric Water Content, as expected. The bigger the difference, the more sound absorption there is between the two
microphones. The decrease is steeper for the frequencies above 1 kHz. This is in accordance with the paper of Gent which shows no dependence between absorption and VWC from 0 to 250 Hz and little dependency up to 400 Hz. However, the graphs for 11.5% and 17.0% are very similar. This can be explained by looking at the values for the flow resistivity and porosity. For all the VWC above, these values are very close to each other and therefore the Matlab model gives more or less the same result. More accurate values of the impedance and propagation constant as function of the VWC may give better results.
4.2. Test measurements
The prediction is in good agreement with the SPL difference calculated from the test measurements.
Although the peak is shifted approximately 1000 Hz to the right when compared to figure 7.
Figure 8, sound pressure level difference in decibel calculated from the test measurement with the microphone positions 5.1 meter apart.
The result looks as if interference is going on. But at first it seems the ground effect canβt be the explanation, because the speaker and the microphones are placed close to the ground resulting in a very small path length difference for the direct and indirect sound (ΞπΏ β 4.4 β 10β4 π). But as stated in chapter 4 a phase shift of almost 180 degrees occurs in the low frequency range when the sound interacts with the vegetation, resulting in destructive interference (C. Howorth, 1991). Another way to represent the absorption of sound is to normalize the SPL of the second microphone by the SPL of the first microphone, this is shown in figure 9 for the same data as used for figure 8..
Figure 9, fraction of the magnitude that is recorded by the second microphone by normalizing the second microphone with the first microphone, calculated from the test measurements. With the same set up as inserted in the model prediction.
Figure 9 shows that between the 30% and 60% of the decibels arrived at the second microphone.
Interference is now more visibly in the higher frequency range which is not caused by the phase change, but due to the geometry of the set-up.
4.3.Artificial Watering
Because the waterproof microphones couldnβt be used, experiments were done with the same microphone as the test measurements. To change the moisture content of the roof, water is poured over the roof that was divided into square meters. Each time, 900 ml was distributed as uniformly as possible over the square meter and after twenty minutes, a measurement is done. In order to determine the VWC, four measurements were made at different points in the vegetation (between the two receiver positions) and the average was taken.
Figure 10, sound pressure at the second microphone, normalized by dividing it by the sound pressure at the first microphone, for different VWC (in %) after artificial watering of the green roof. The uncertainty in the VWC is approximately 7% for values around 30%. Both microphones are 5.1 meters apart at a height of 4 cm.
The normalized magnitude in figure 9 is significantly larger than during the test measurements, which means less sound is absorbed. This is especially the case at the low frequencies where only 20% is absorbed. An explanation may be the high VWC during the artificially watered measurements (the vegetation was visibly less dank during the test measurements), additionally the SPL at the first microphone was higher during the watered experiment, which may have led to some reflections.
The black line represents the first measurement. This is strange because it should have the lowest VWC. Another thing that stands out is the little difference between the measurements. The
vegetation was already very dank at the beginning of the experiment, probably close to saturation.
When the vegetation is saturated, all the extra water will be collected in the black cups under the filter layer. When the cups are filled, the water wonβt be retained anymore and will flow towards the sewer. The differences between the VWC is not significant, because the uncertainty in the VWC is 21 β ππππ‘πππ which is around 7% for 30% VWC. The derivation of this uncertainty is listed in appendix 1. The VWC percentage is above the measured saturation value during the calibration measurements. An explanation for this can be the fact that the calibration piece had less moss and was perhaps already sear and could therefore absorb less moisture.
The big uncertainty in the VWC can be caused by the inhomogeneity of the vegetation on the roof . Furthermore the compactness of the soil, which also influences the voltage of the moisture meter, differs over the roof. Lastly the moisture meter needs to be inserted under an angle, because the vegetation isnβt deep enough to insert the meter vertically. According to the manufacturer, it was no problem, but the manual said it would influence the uncertainty.
The high VWC measured (higher than the calibrated saturation value) has effect on the conversion of
% of saturation to VWC(%) that was used for the prediction of figure 7. The VWC listed in table 1 will be lower for a higher saturation value.
5. Conclusion
The green roof on the building of Cascade at Eindhoven University of Technology is suitable for a long term experiment with the two microphones from Gent and the EC-5 moisture meter. The optimal position is with the microphone 4.7 meters from the edge of the roof on the east side. The two microphones should be 5.1 meters apart in order to obtain a good signal for a SPL around 70 dB at the first microphone. The best way to represent the absorption is by normalizing the SPL of the second microphone by that of the first.
The model predicts a decreasing absorption with increasing water content, which is confirmed by comparing the test measurement to the artificially watered measurement. The absorption increases with the frequency, although there is an interference pattern visible due to the phase change of almost 180 degrees when the sound waves interact with the vegetation.
6. Further Research
If the microphone from Gent is repaired, the experiment can be conducted for a long time with natural rainfall. The moisture meter should be held in one place, that way the effect of
increasing/decreasing VWC will be visible. The question is whether to invest in an extra moisture meter, to account for the inhomogeneous water content in the vegetation. The uncertainty of the calibration remains constant, but for high VWC the inhomogeneity increases which also influences the uncertainty. An extra moisture meter would therefore be especially beneficial for higher VWC.
Another thing that could be interesting to investigate is the drainage layer. This layer can be filled with water or not resulting in an air layer or approximately a hard backing layer of water. The script that is used for the predictions can be further altered for two layers to investigate the effect of this.
Another thing that could be included is a normalized prediction for different VWC.
7. Bibliography
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.
8. Appendix
8.1 Derivation of the 68% interval for VWC
ππππΆ = ββ (ππππΆ
fs = 48000; % sample frequency (how many samples per second) sl = 1; % signal length
N = 4*sl.*fs;
dt = linspace(0,1/fs,N); % time sample (how many second per sample)
% vector from flow to fup logaritmical of 4*48000 parts omega = 2.*pi.*fc;
%the function soundsc automaticaly scales in range 0 to 1.
%% Timer for playing the sound during the night
while toc < 2000 % can be while 1 to let it play infinitely long
current_time_hours = toc/3600 + c(4)+ c(3)/60;
current_time_minutes = toc/60 + c(5)+ c(6)/60;
if current_time_hours > 24
current_time_hours = toc/3600 + c(4)+ c(3)/60 - 24;
if current_time_hours >= begintijd || current_time_hours <= eindtijd disp(toc/60 + c(5)+ c(6)/60)
The Matlab script for analyzing the data of the microphones from Gent and the EC-5 moisture meter.
close all
A1 = newdata_410(:,5) == 30;
length_sweeps1 = find(diff(K1)>10);% index of the beginning of every new sweep
length_sweeps2 = find(diff(K2)>10);% index of the beginning of every new sweep
%% sommeren over de lengte van de opnamens
Averages410 = zeros(length(length_sweeps1)-1,31);% 31 = number of frequencybands Averages411 = zeros(length(length_sweeps2)-1,31);
for i = 1:length(length_sweeps1)-1;
Averages410(1,:) = sum(Sweeps1(1:length_sweeps1(1),8:end),1)/length_sweeps1(1);
Averages410(i+1,:) =
Averages411(1,:) = sum(Sweeps2(1:length_sweeps2(1),8:end),1)/length_sweeps2(1);
Averages411(i+1,:) =
sum(Sweeps2(length_sweeps2(i)+1:length_sweeps2(i+1),8:end),1)/(length_sweeps2(i+1)-length_sweeps2(i));
end
% The matrix Averages has the spectrum of a sweep on every row
Difference = Averages411 - Averages410(1:23,:);%can be changed to Averages410(:,:) time of first sweep have to be filled in here
inedx_starttijd = find(cellfun(@(x) isequal(x,'20:17:16'),tijd_vector));
index_start = find(index_startdatum == inedx_starttijd);
%% Taking the rigth data from moisture data
interval = 10; % time between measurepoints of the moisture meter in minutes interval_sweeps = 30; %time between sweeps in minutes
Voltage = zeros((length(newdata.data)-index_start)/(interval_sweeps/interval)+1,1);
for i = 0:(length(newdata.data)-index_start)/(interval_sweeps/interval)
Voltage(i+1,1) = newdata.data(index_start+i*interval_sweeps/interval,2);%
Getting data from indexstart end
VWC = 222.1.*Voltage-57.5;%calibration line of the moisture meter
%% Plotting attenuation versus VWC for every frequency band
plot(VWC(1:length(Difference)), Difference)% can be changed to VWC(:,Difference)
Matlab script used for the predictions
close all
% speed of sound during measurement [m/s]
lamda = c1./fc; % wave length
rho1 = 1.2; % density of air [kg/m^3]
omega = 2*pi*fc;
k1 = omega/c1; %wavevector
fcenter = [200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000]; % 1/3 octave bands
flower = round(2^(-1/6).*fcenter); % lowest frequency clear T
hhs = [0.025 0.025];%hoogte van de bron
hhr = [0.04 0.04];% hoogte van de 1ste en 2de microfoon rr = [0.6 5.7]; %afstand source - mic1 en source - mic2
sigma = [25000 0.43 0.0756]; %flow resistivity/porosity/thickness
%% impedance model (Slit-pore) K = 1.42e5; % adiabatic bulk modulus Pr = 0.713; % Prandtl number
r = rr(mmm);
n2_1 = kc./k1;
s2_1 = 1./(Zc.*n2_1);
% density ratio
costh = sqrt(1-1./(n2_1.^2)+cos(theta).^2./(n2_1.^2));
Zmodel_p = 1i.*Zc./(sigma(2)*costh).*cot(kc.*sigma(3).*costh);
V_1 =
(1i.*Zc(mn).*u_1.*cot(costh2_1.*kc(mn).*sigma(3))./k1(mn)-(sigma(2).*costh2_1))./((1i.*Zc(mn).*u_1.*cot(costh2_1.*kc(mn).*sigma(3)))./k1(mn)+
costh2_2=sqrt(kc(mn).^2-k1(mn).^2+u_2.^2)./kc(mn);
V_2=((1i.*Zc(mn).*u_2.*cot(costh2_2.*kc(mn).*sigma(3)))./k1(mn)-(sigma(2).*costh2_2))./((1i.*Zc(mn).*u_2.*cot(costh2_2.*kc(mn)*sigma(3)))./k1(mn)+(
sigma(2).*costh2_2));
pe_2(:,mn)=-1i.*sum(V_2.*besselj(0,sqrt(k1(mn).^2-u_2.^2).*r).*exp(1i.*u_2.*(hs+hr)).*du_2.*i);
pe(:,mn)=pe_1(:,mn)+pe_2(:,mn)+exp(1i.*k1(mn).*Rdirect)./Rdirect;