Barrier Report

Report on

Barrier Insertion Loss Measurements

Undertaken at

Leeds Metropolitan University, Portland Crescent,

Leeds, West Yorkshire,

LS1 3HB

Wednesday18thDecember 2013

Student Number: 77144104

IOA Diploma 2013-14 Student Number: 77144104

Summary This report describes the processes involved when undertaking insertion loss measurements

using a white noise source for three sizes of acoustic barriers (100mm, 200mm and 300mm

height). Various configurations were tested to understand if the measured insertion loss

values were comparable with the insertion loss prediction models of (Maekawa, 1968) and

(Kurze and Anderson, 1971). It was found that correlation in octave bands was poor whilst

there was good agreement in broadband insertion loss. The measurements confirmed the

theories of (Maekawa, 1968) and (Kurze and Anderson, 1971) in that when one considers

designing an acoustical barrier the height and diffraction paths are of vital importance as is

the distance from the source and/or receiver to the barrier. Measurements also confirmed that

acoustical barriers are not effective at low frequencies (<250Hz) due to the wavelength of the

sound being greater than the dimensions of the barrier and that at higher frequencies

(>4000Hz) the sound diffracts over the barrier.


i

Contents List of Figures ............................................................................................................................ ii List of Tables ........................................................................................................................... iii Nomenclature ............................................................................................................................ iv 1. Introduction ........................................................................................................................ 1 2. Instrumentation& equipment .............................................................................................. 2

2.1. Sound level meter ........................................................................................................ 2 2.2. Calibrator ..................................................................................................................... 2 2.3. Microphone ................................................................................................................. 2 2.4. Equipment ................................................................................................................... 2 2.5. Materials ...................................................................................................................... 3

3. Measurements ..................................................................................................................... 4 3.1. Measurement layout .................................................................................................... 4 3.2. Measurement procedure .............................................................................................. 5

4. Measurement Results .......................................................................................................... 6 4.1. Insertion Loss results ................................................................................................... 7

5. Analysis .............................................................................................................................. 8 5.1. Comparison models ..................................................................................................... 8 5.1.1. Maekawa model ....................................................................................................... 8 5.1.2. Kurze and Anderson model ................................................................................... 11 5.2. Prediction model comparison .................................................................................... 11 5.3. Scaled up version of Maekawa and Kurze and Anderson models ............................ 12

6. Conclusions ...................................................................................................................... 13 6.1. Observations from measurements ............................................................................. 13 6.2. Prediction model conclusions .................................................................................... 15 6.3. Measurement inaccuracies ........................................................................................ 16 6.4. Possible designs ......................................................................................................... 17 6.5. Further Work ............................................................................................................. 18

References ................................................................................................................................ 19 Appendices ............................................................................................................................. A-1 Appendix A:Measurement results .......................................................................................... A-1 Sound Pressure Levels measurements, dB ............................................................................. A-1 Insertion Loss measurements,dB ........................................................................................... A-2 Appendix B:Matlab Scripts for Maekawa and Kurze and Anderson Methods .................. B-1 Appendix C:Calculation examples ........................................................................................ C-1 Maekawa Model ..................................................................................................................... C-1


ii

Kurze and Anderson Model ................................................................................................... C-4


ii

List of Figures

Figure 3-1– Side View of measurement .................................................................................... 4

Figure 3-2 –Photograph of measurement layout ........................................................................ 4

Figure 4-1 – Insertion loss results, dB ....................................................................................... 7

Figure 5-1-Path difference ......................................................................................................... 9

Figure 5-2-I.L predictions (Maekawa, 1968) and (Kurze and Anderson, 1971) ..................... 11

Figure 5-3- Scaled up prediction .............................................................................................. 12

Figure 6-1- Noise paths of a barrier ......................................................................................... 15

Figure 6-2 – Broadband overall Insertion Loss, dB ................................................................. 16

Figure 6-3 – Possible barrier design to increase I.L ................................................................ 17

Figure C-1-Dimensions of measured barrier ......................................................................... C-1


iii

List of Tables

Table A-1 – SPL (No Barrier) ............................................................................................... A-1

Table A-2 – SPL (100mm barrier, 1m from Mic/Loudspeaker) ............................................ A-1



Table A-5 – SPL (100mm Barrier, 100mm from Loudspeaker Only) .................................. A-1





Table A-10 – Insertion Loss (100mm barrier, 1m from Mic/Loudspeaker) .......................... A-2



Table A-13 – Insertion Loss (100mm Barrier, 100mm from Loudspeaker Only) ................. A-3





Table C-1- Insertion Loss (Maekawa Model) ........................................................................ C-3

Table C-2-Insertion Loss (Kurze and Anderson Model) ....................................................... C-4


iv

Nomenclature I.L Insertion Loss, dB Mic Microphone SLM Sound Level Meter


1

1. Introduction Sound pressure level measurements of a plywood acoustic noise barrier were undertaken

within the anechoic chamber at Leeds Metropolitan University, Portland Crescent, Leeds,

West Yorkshire, LS1 3HB. The supplied noise signal was that of white noise. This was

amplified via a power amplifier and relayed through a loudspeaker. Various configurations

were tested. First of all sound pressure levels were measured without a barrier in place .This

measurement was then repeated but for barriers of heights 100mm, 200mm and 300mm of

which all had source to barrier and receiver to barrier distances of 1m and heights of 0.3m

from floor to receiver and source. To understand the effects of having the noise source

closer/further away from the barrier a series of measurements were then undertaken using the

100mm barrier. These involved moving the loudspeaker to as close as 100mm and as far as

500mm away from the barrier (in 100mm stages). In hindsight the 100mm barrier should not

have been chosen given that there was a direct line of sight between the source and receiver.

However the general observations of acoustical barrier theory were observed i.e. Height,

source to receiver and diffraction effects. Given this the 300mm barrier was chosen for

subsequent analysis. This was chosen due to there being no line of sight between the source

and receiver. The I.L measurements of the 300mm barrier (derived from the sound pressure

level measurements) were compared with the insertion loss prediction models of (Maekawa,

1968) and (Kurze and Anderson, 1971). It was found that in octave bands correlation was

poor whilst broadband insertion loss gave good agreement.


2

2. Instrumentation & equipment

2.1. Sound level meter Manufacturer Norsonic

Model 118

Class type 1

Serial Number 31310

Calibration due Not specified

2.2. Calibrator Manufacturer Norsonic

Model 4231

Serial Number 2389088


2.3. Microphone Manufacturer Norsonic

Model Unknown

Serial Number Unknown


2.4. Equipment Manufacturer Wharfedale Speaker (White Noise Source Speaker)

Model 30D 6


Calibration due Not specified Manufacturer NTI Minarator (Signal Generator)

Model MR Pro

Serial Number Not specified



3

Manufacturer Bruel & Kjaer Power Amplifier

Model Unknown



2.5. Materials Material 1 10mm thick, 100m plywood board Material 2 10mm thick, 200m plywood board Material 3 10mm thick, 300m plywood board


4

3. Measurements

3.1. Measurement layout

Figure 3-1– Side View of measurement

Figure 3-2 –Photograph of measurement layout

Microphone Sound Source

Barrier


5

3.2. Measurement procedure

All measurements sound pressure level measurements were undertaken within the anechoic

chamber at Leeds Metropolitan University, Portland Crescent, Leeds, West Yorkshire, LS1

3HB.

The supplied noise signal was that of white noise. This was amplified via a power amplifier

and relayed through a loudspeaker.

All equipment was inspected prior to and after measurements.

Measurements were made at various distances from the barrier. The first measurements

involved measuring the sound pressure level with no barrier present. This was to allow for

Insertion Losses (I.L) to be computed. Each barrier size was then tested at a distance of 1m

from both the loudspeaker (source) and the Sound Level Meter (SLM), (receiver). To

understand the effects of having the noise source closer/further away from the barrier a series

of measurements were then undertaken using the 100mm barrier. These involved moving the

loudspeaker to as close as 100mm and as far as 500mm away from the barrier (in 100mm

stages).

Throughout the measurement process both the SLM and loudspeaker were mounted on a

tripod and were not moved. The measurement duration was 10 seconds.

Prior to the commencing measurements, the calibration of the SLM described in Section 2.1

was undertaken using the calibrator (referred to in Section 2.2). The calibrator level was

measured correctly at 114 dB(A).

The calibration of the SLM was re-checked successfully on completion of the measurements.


6

4. Measurement Results From the measured sound pressure levels (with and without the barrier present) I.L values

were computed. These are illustrated within Figure 4-1. For all measurement results the

reader is referred to Appendix A:


7

4.1. Insertion Loss results

Figure 4-1– Insertion loss results, dB


8

5. Analysis

5.1. Comparison models To understand if empirical insertion loss prediction models such as (Maekawa, 1968) and

(Kurze and Anderson, 1971) are comparable with the computed insertion loss values of

Figure 4-1 a series of simple calculations were undertaken. For ease of calculation all models

were computed within a simple Matlab script1 and only one configuration (300m barrier at

1m from loudspeaker and mic) was chosen for analysis. The computed frequency range was

63Hz to 8000Hz.

5.1.1. Maekawa model (Maekawa, 1968) proposed two formulas for predicting insertion loss, dependent on receiver

position. The first formula (Equation (5.1)) was dependent on the receiver being located

within the ‘illuminated zone’ (hence there being a direct line of sight between source and

receiver) with the second (Equation (5.2)) being dependant on the receiver being within the

‘shadow zone’ (no direct line of sight). An illustration of these zones is given within Figure

5-1.

( )10I.L=10log 3-20 dBN (5.1) ( )10I.L=10log 3+20 dBN (5.2) Maekawa presented his results through the way of a curve representing I.L (in dB) as a

function of the Fresnel’s number N. The Fresnel’s number being a ratio of the path difference

(the difference in distance between the diffracted path and the direct path of sound to the half

wavelength).

1 For the complete Matlab script the reader is referred to Appendix B:


9

Figure 5-1-Path difference

The Fresnel’s number Nis computed from Equation (5.3)

2N δλ

⎛ ⎞= ⎜ ⎟⎝ ⎠

(5.3)

Where δ is the path difference which is given by Equation (5.4)

( )a b cδ = + − (5.4)

a

c

b

Source

Receiver

Shadow zone

Illuminated zone

Barrier

dr ds

Hs Hr

Hb


10

From Figure 5-1 the path difference δ may be calculated by using Pythagoras theorem for

three right angled triangles with a, b and c as the hypotenuse (Smith et al., 2011, p.47).

( ) ( )0.52 2

b s sa H H d⎡ ⎤= − +⎣ ⎦ (5.5)

( ) ( )0.52 2

b r rb H H d⎡ ⎤= − +⎣ ⎦ (5.6)

( ) ( )0.52 2

r s s rc H H d d⎡ ⎤= − + +⎣ ⎦ (5.7)

The Wavelength λ in metres is easily calculated from:

cf

λ⎛ ⎞

= ⎜ ⎟⎝ ⎠

(5.8)

Where c is the speed of sound in metres per second and f is the frequency of interest, Hz

Maekawa assumed the barrier was semi-infinite, thin and rigid and that all predictions are

free field (Everaert et al., 2010). Due to this Equations (5.1) and (5.2) only include reflections

on the barrier and diffraction on the top of the barrier. He further assumed that the noise

barrier was of finite length and of a sufficient thickness and hence ground or wall

transparency is not accounted for.


11

5.1.2. Kurze and Anderson model As with (Maekawa, 1968) the prediction model of (Kurze and Anderson, 1971) uses the

Fresnel number to calculate I.L, however it is slightly different in that it introduces a tanh

function and a 5dB constant .

102

I.L 5 20logtanh 2

NN

ππ⋅

= +⋅

(5.9)

Where N is the Fresnel’s number computed from Equation (5.3)

5.2. Prediction model comparison

Figure 5-2 is a plot of the computed values of the (Maekawa, 1968) and (Kurze and

Anderson, 1971) prediction models. These values are plotted against the measured values

from the anechoic chamber. For an in-depth explanation/example of how these values were

computed the reader is referred to Appendices C1 and C2.

Figure 5-2-I.L predictions (Maekawa, 1968) and (Kurze and Anderson, 1971)


12

5.3. Scaled up version of Maekawa and Kurze and Anderson models

To recreate a real barrier situation the values used for the computations given within

Appendices C1 and C2 were multiplied by a factor of 10 i.e. the results computed for

10000Hz describe the real life situation at 1000Hz. The values of this computation are

illustrated within Figure 5-3.

Figure 5-3- Scaled up prediction


13

6. Conclusions

6.1. Observations from measurements

The observations that maybe drawn from the measurements are as follows:

• Insertion Loss increases with height of barrier.

• Insertion Loss increases when the barrier is closer to the sound source/receiver.

• At frequencies below 250Hz the sound is able to diffract around the barrier. This is due

the dimensions of the barrier being small compared to its wavelength i.e. at 250Hz the

wavelength is approximately 1.36m which is larger than any dimension of the barrier.

• At higher frequencies (>4000Hz) the sound appears to diffract over the barrier. This

causes the I.L performance to decrease.

• Previous experiments have indicated that the anechoic chamber is not completely free-

field i.e. 6dB per doubling of distance does not occur. This is likely to have an effect on

the measured I.L values.

• It was noted that there was a reflective surface under the barrier i.e. anechoic chamber is

semi-anechoic. This may have increased the measured levels by up to 3dB.

• It was unclear what the sound reduction index of the barrier material was. From (Watson

and Downey, 2008, p.85) the level of sound transmitting through the barrier should be at

least 10dB lower than the level of sound passing around the barrier i.e. the mass per unit

area of the barrier material should be large enough to block the required amount of

broadband noise. Again this is likely to have an effect on the measured I.L values. The

minimum mass maybe calculated from a formula given by (Watson and Downey, 2008,

p.85):

( )( )( )broadbandattenution+10 14minmass =3 10− (6.1)


14

For example if one wished for 20dB of broadband attenuation the minimum mass per unit

area required would be as follows:

( )( )( )

( )( )( )( )( )

-20+10 14

-10 14

0.71

2

minmass =3 10

=3 10

=3 10

15.4kg m

−

−

− −

=

• Whilst undertaking the measurements it was noted that there was potential paths at both

the sides and underneath the barrier.


15

• Further to the above there are several paths that the sound can take which will decrease

the amount of I.L afforded by the barrier. Some of these paths are illustrated within

Figure 6-1 which was extracted from (pcfarina.eng.unipr.it, n.d)

Diffraction at upper of the screen: i.e. the barrier is very long and the effective heights not too high

Diffraction at sides of the screen: when the distance between the source and the screen edge is less than 5 times the effective height

Passing through the screen

Reflection over other surfaces present in proximity: when the location allows it

Figure 6-1- Noise paths of a barrier

6.2. Prediction model conclusions With respect to the I.L models outlined within section 5 there was not a good octave band

correlation achieved between the measured and predictive models (Maekawa, 1968) and

(Kurze and Anderson, 1971). This maybe in part due to the inaccuracies outlined above.

However as we can see from Figure 6-2 the agreement between the measured broadband I.L

and the models of (Maekawa, 1968) and (Kurze and Anderson, 1971) is excellent. The

measured broadband I.L was 23.4dB where as the model of (Kurze and Anderson, 1971) was

computed at 24.7dB with the (Maekawa, 1968) model being 25.1dB. For the worst case

(Maekawa model) this is an increase of 7.3% from the measured I.L.


16

Figure 6-2 – Broadband overall Insertion Loss, dB

The scaled up model predicted a broadband I.L of 35.2dB. For a thin rigid barrier this is not

realistic given that (Smith et al., 2011, p.47) places a limit on barrier I.L at 15-20dB.

6.3. Measurement inaccuracies As the comparison is between two measurements taken at the same location at relatively the

same time the effect of the position and reading on the SLM is minimal. The SLM does

however have an inherent inaccuracy of approximately ±1.1dB, hence no measurement can

be taken to be better than this. Furthermore the fact that only one measurement at one

position was carried out constrains the conclusions that can be drawn. To improve

measurement inaccuracies it would be beneficial to measure at varying positions.

Directionality effects were also not considered. Further to this whilst undertaking the

measurements there were three adults within the anechoic chamber. Therefore it is likely that

the absorption properties of these adults will have had an effect on the measurements. Effects

of temperature, humidity, air pressure were assumed to be negligible.


17

6.4. Possible designs Important design parameters can be drawn from this experiment these being:

• The more the height of the barrier the greater the I.L. Although there is a limit to

this.(Munjal, 2013, p.145) puts this limit at 5m.

• For greater I.L the barrier should be placed close to the sound source or receiver i.e.

located within the shadow zone.

• The mass per unit area of barrier should be of a sufficient mass.

• All flanking/diffraction paths shall be minimised.

Typical designs extracted from (Munjal, 2013, p.147) that will increase I.L are:

a. Thicker barrier

b. Double barrier

c. Barrier with flat cap

d. Barrier with forked end

Figure 6-3 – Possible barrier design to increase I.L

(a) (b) (c) (d)


18

6.5. Further Work

To verify the conclusions and design guidance given above one may wish to undertake

further testing. This could include testing different barrier materials and configurations i.e.

adding absorption to barrier surfaces. Other prediction models maybe analysed to see if they

are more accurate than those of (Maekawa, 1968) and (Kurze and Anderson, 1971). For this

one may wish to consult (Li and Wong, 2005) who have reviewed several I.L prediction

models and compared these to actual measurements.


19

References

Everaert, V. , Progneaux, A. and Bouillard, Ph. (2010). Simulation of Sound Wave Propagation in Presence ofNoise Barrier by using the Partition of the Unity FiniteElements Method : a comparison with analytical methodsin 2D cases. [Online]. Available from: https://www.isma-isaac.be/past/conf/isma2010/proceedings/papers/isma2010_0182.pdf. [Accessed 5th January 2014] Kurze, U.J. and Anderson, G.S. (1971). Sound attenuation by barriers. Applied Acoustics. [Online]. 4(1), pp.35-53. Available from: http://www.sciencedirect.com/science/article/pii/0003682X71900247.

Li, K.M. and Wong, H.Y. (2005). A review of commonly used analytical and empirical formulae for predicting sound diffracted by a thin screen. Applied Acoustics. [Online]. 66(1), pp.45-76. Available from: http://www.sciencedirect.com/science/article/pii/S0003682X04000842.

Maekawa, Z. (1968). Noise reduction by screens. Applied Acoustics. [Online]. 1(3), pp.157-173. Available from: http://www.sciencedirect.com/science/article/pii/0003682X68900200.

Munjal, L.M. (2013). Acoustics of Rooms, Partitions, Enclosures and Barriers. In: Munjal, L.M. ed. Noise and Vibration Control. London: World Scientific Publishing, pp.132-167.

pcfarina.eng.unipr.it. (n.d). Noise Barriers. [Online]. Available from: http://pcfarina.eng.unipr.it/Public/Acoustics-Course/.../08_ghiacci_222030.doc. [Accessed 12th January 2014]

Smith, J.B. , Peters, J.R. and Hollins, M. (2011). Acoustics and Noise Control. 3rd ed. Harlow: Pearson Education Limited.

Watson, R. and Downey, O. (2008). Little Red Book of Acoustics 2nd ed. Great Britain: Blue Tree Acoustics.


A-1

Appendices

Appendix A: Measurement results

Sound Pressure Levels measurements, dB

Table A-1 – SPL (No Barrier)

Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

No Barrier,dB 40.4 37.6 51.2 55 63.6 70.7 81.2 72.9

Table A-2 – SPL (100mm barrier, 1m from Mic/Loudspeaker)

Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 37.5 37.4 52.5 54.9 61.6 66.2 68.8 61.2


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

200mm Barrier, dB 35.7 36.8 52.4 53.1 57.8 58.2 64.1 64.2


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

300mm Barrier, dB 35.7 36.8 52.4 53.1 57.8 58.2 64.1 64.2

Table A-5 – SPL (100mm Barrier, 100mm from Loudspeaker Only)

Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 40.9 40.7 47 40.9 41.5 48.5 53.2 49.4


A-2


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 40.4 34.3 48 44.5 44.3 49.2 57.1 52


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 34.9 34 49.3 46.1 47 50.9 56.6 53.3


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 38.5 35.9 50.2 47.8 47.7 51.6 54 53.5


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 33.6 35.4 50.9 49 50.3 50.1 56.1 53.5

Insertion Loss measurements,dB

Table A-10 – Insertion Loss (100mm barrier, 1m from Mic/Loudspeaker)

Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 2.9 0.2 -1.3 0.1 2 4.5 12.4 11.7


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

200mm Barrier, dB 4.7 0.8 -1.2 1.9 5.8 12.5 17.1 8.7


A-3


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

300mm Barrier, dB 4 0.8 -0.2 4.1 11.3 20 18.9 13.4

Table A-13 – Insertion Loss (100mm Barrier, 100mm from Loudspeaker Only)

Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB -0.5 -3.1 4.2 14.1 22.1 22.2 28 23.5


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 0 3.3 3.2 10.5 19.3 21.5 24.1 20.9


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 5.5 3.6 1.9 8.9 16.6 19.8 24.6 19.6


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 1.9 1.7 1 7.2 15.9 19.1 27.2 19.4


Octave Band, Hz 63 125 250 500 1000 2000 4000 8000

100mm Barrier, dB 6.8 2.2 0.3 6 13.3 20.6 25.1 19.4


B-1

Appendix B: Matlab Scripts for Maekawa and Kurze and Anderson Methods

Octave Band Frequency's , Hz f=[63 125 250 500 1000 2000 4000 8000]; Prompts for required inputs prompt = 'Enter height of source from ground in m '; Hs = input(prompt); prompt = 'Enter height of receiver from ground in m '; Hr = input(prompt); prompt = 'Enter height of barrier from ground in m '; Hb = input(prompt); prompt = 'Enter distance of source from the barrier in m '; ds = input(prompt); prompt = 'Enter distance of receiver from the barrier in m '; dr = input(prompt); Speed of Sound C=340; %Default 340 m/s% Computations %Wavelength, m% lamda=(C./f); %Pythrogoras% a=((Hb-Hs)^2+(ds)^2)^0.5; b=((Hb-Hs)^2+(dr)^2)^0.5; c=((Hr-Hs)^2+(ds+dr)^2)^0.5; %Path Difference, m% PD=(a+b)-c; %Fresnel Number% N=(2.*PD./lamda); Computed Insertion Loss (Maekawa Method) IL_Maekawa=10.*log10(3+(20*N));


B-2

Computed Insertion Loss (Kurze and Anderson Method) x=sqrt(2.*pi.*N); y=tanh(x); IL_Kurze_Anderson=5+20*log10(x./y); 300mm Barrier, 1m from Mic/Loudspeaker (Measured Values) Test_3_IL =[4 0.8 -0.2 4.1 11.3 20 18.9 13.4]; Plot of measured Insertion Vs Maekawa and Kurze and Anderson Methods figure(1) clf semilogx(f,Test_3_IL ,'mo','LineWidth',2.5'), grid hold on semilogx(f,IL_Maekawa,'r--','LineWidth',2.5') semilogx(f,IL_Kurze_Anderson,'b','LineWidth',2.5') hold off xlabel(['\fontsize{14}','Octave Band Hz']); ylabel(['\fontsize{14}','Measured Insertion Loss (dB)']); set(gca,'XTick',[63,125,250,500,1000,2000,4000,8000]) set(gca,'YTick',[-1,0,5,10,15,20,25]) xlim([63 8000]); ylim([-1 25]); legend('Measured Insertion Loss for 300mm Barrier, 1m from Mic/Loudspeaker',... 'Calculated Insertion Loss,(Maekawa Method)','Calculated Insertion Loss (Kurze and Anderson Method)'... ,'Location','NorthWest'); Displaying Data disp(['Insertion Loss (Maekawa) = ', num2str(RoundOff(IL_Maekawa,0.1)), ' dB']); disp(' '); disp(['Insertion Loss (Kurze and Anderson) = ', num2str(RoundOff(IL_Kurze_Anderson,0.1)), ' dB']); disp(' ');


C-1

Appendix C: Calculation examples

Maekawa Model

FigureC-1-Dimensions of measured barrier

One can use Equations (5.5)(5.6) and (5.7) to calculate the path difference, δ

( ) ( )

( ) ( )

0.52 2

0.52 20.3 0.1 1

1.02m

b s sa H H d⎡ ⎤= − +⎣ ⎦

⎡ ⎤= − +⎣ ⎦

=

( ) ( )

( ) ( )

0.52 2

0.52 20.3 0.1 1

1.02m

b r rb H H d⎡ ⎤= − +⎣ ⎦

⎡ ⎤= − +⎣ ⎦

=

a

c

b

Source

Receiver

Shadow zone

Illuminated zone

Barrier

1m 1m

0.1m 0.1m

0.3m


C-2

( ) ( )

( ) ( )

0.52 2

0.52 20.1 0.1 1 1

4m

r s s rc H H d d⎡ ⎤= − + +⎣ ⎦

⎡ ⎤= − + +⎣ ⎦

=

Now using Equation (5.4) we calculate the path difference δ

( )

( )1.02 1.02 4

0.04m

a b cδ = + −

= + −

=

If we assume the speed of sound in air to be 340 m/s then the wavelength, λ maybe

calculated from Equation (5.8). For this example the frequency of interest, f is 1000 Hz

340 0.34m1000

cf

λ⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠

One can then compute the Fresnel Number, N from Equation (5.3)

2 2 0.04 0.2350.34

N δλ

×⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


C-3

As there is no line of sight the insertion loss at 1000 Hz is computed using Equation (5.2)

( )

( )( )

10

10

I.L=10log 3+20

10log 3+ 20 0.235

8.8dB

N

= ×

≈

The values at all other frequencies are given within TableC-1

TableC-1- Insertion Loss (Maekawa Model)

Octave Band, Hz

63 125 250 500 1000 2000 4000 8000 Calculated Insertion Loss, dB 5.2 5.5 6.2 7.3 8.8 10.9 13.4 16


C-4

Kurze and Anderson Model If we use the value of N from above the insertion loss (at 1000 Hz) for the Kurze and

Anderson model maybe calculated from Equation (5.9)

( )

10

10

10

10

2I.L 5 20log

tanh 2

2 0.2355 20log

tanh 2 235

1.215 20logtanh 1.21

1.215 20log0.838

5 3.2

8.2dB

NN

ππ

ππ

⋅= +

⋅

⋅= +

⋅

= +

⎛ ⎞= + ⎜ ⎟⎝ ⎠

= +

=

The values at all other frequencies are given within Table C-2

Table C-2-Insertion Loss (Kurze and Anderson Model)

Octave Band, Hz

63 125 250 500 1000 2000 4000 8000 Calculated Insertion Loss, dB 5.3 5.5 6.0 6.8 8.2 10.2 12.8 15.7

Documents

Barrier Report