Assessment of directivity of real noise sources - Application ...746412/FULLTEXT01.pdfacoustic centre for each object was situated. Thereafter, the room correction factor was Thereafter,

Assessment of directivity of real noise sources - Application to vehicles

Kandidatarbete i Fordonsteknisk projektuppgift, SA108X

Kristina Larsson

Våren 2014

Traction motor and gearbox

A4

A8

A6

A10

A5 A11

A9

A7

A2

A1

A3

Diesel Engine

Cab HVAC Engine cooling fan Exhaust

Brake resistor

Transformer

Converters Brake compressor

HVAC

Abstract

The aim of this project is to evaluate a new method for noise directivity measurements; whether a room correction factor can be used to compensate for the effect of a light reverberation field. Another aim is to find if there is any suitable standard to use.

No standard to use fully was found, but SS-EN ISO 3744:2010 has a method to compensate for reverberation upon which the present method is based.

Measurements were performed for three objects in a semi anechoic room and two ordinary rooms. Sound pressure was measured for all multiples of 30° in the horizontal plane where the acoustic centre for each object was situated. Thereafter, the room correction factor was calculated and from that compensated values could be found.

The room correction factor did not fully make the wanted difference. The results only showed subtle connections, but tendencies show that the method might be valid for 250 and 500 Hz. To get a stronger correlation, the method must be refined. The distance to the microphone is for example one factor that depends on the environment.

Sammanfattning

Målet med projektet är att utvärdera en ny metod för ljuddirektivitetsmätningar; om en rumskorrektionsfaktor kan användas för att kompensera för ett svagt efterklangsfält. Utöver detta görs en litteraturstudie för att finna relevanta standarder.

Någon standard att använda helt fanns inte, men SS-EN ISO 3744:2010 har en metod för att kompensera för efterklangsfält som metoden i detta arbete är baserad på.

Mätningar utfördes för tre objekt i ett halvekofritt rum och två mer vanligt förekommande omgivningar i en industriell miljö. Där mättes ljudtryck i alla vinklar som är en multipel av 30° i samma horisontella plan där den akustiska mitten i mätobjektet befann sig. Utifrån dessa mätningar kunde rumskorrektionsfaktorn beräknas och från den kunde kompenserade värden hittas.

Resultaten visade att rumskorrektionsfaktorn inte fungerade helt önskvärt. De visade bara svaga kopplingar med vissa tendenser till att metoden fungerade bättre för 250 och 500 Hz. Nya mätningar måste därför utföras där metoden förbättrats. Exempelvis är avståndet till mikrofonen, som beror av omgivningen, viktigt.

Preface

This work is a part of a bachelor thesis work within vehicle engineering at Kungliga Tekniska Högskolan.

The aim of this project is to investigate a new method for measuring noise source directivity in industrial environments. The method is based on the standard ISO3744.

The work has been supervised by Ulf Orrenius, Bombardier and Mats Berg, Kungliga Tekniska Högskolan. Leping Feng, Kungliga Tekniska Högskolan, has developed the measurement method and has helped with the realisation of it.

23 May 2014

Kristina Larsson

[email protected]

910709-1986

Table of contents

1. Introduction ............................................................................................................................ 1

1.1 Background ....................................................................................................................... 1

1.2 Aim ................................................................................................................................... 2

1.3 Method .............................................................................................................................. 2

2. Literature study ...................................................................................................................... 3

3. Room acoustics ...................................................................................................................... 4

4. Method ................................................................................................................................... 5

4.1 Measurements ................................................................................................................... 5

Semianechoic room ............................................................................................................ 6

Basement ............................................................................................................................ 7

Classroom ........................................................................................................................... 9

4.2 Calculations ...................................................................................................................... 9

5. Results .................................................................................................................................. 11

Classroom ......................................................................................................................... 11

Basement .......................................................................................................................... 15

6. Discussion ............................................................................................................................ 19

7. Conclusions .......................................................................................................................... 21

References ................................................................................................................................ 22

Appendix 1. Matlab code with measurement data ................................................................... 23

Appendix 2. Matlab code basement ......................................................................................... 84

Appendix 3. Matlab code classroom ........................................................................................ 92

Appendix 4. Matlab function dirplot ........................................................................................ 99

1

1. Introduction

1.1 Background

Today when measuring exterior noise of a rail vehicle for certification purposes, you have to do a real test drive on standardised track. Even if test data are available for a reference vehicle and the changes from the reference vehicle is small, for example a fan has changed. The picture on the cover shows several sources of a train that might be of interest to measure. However, carrying out full certification measurement is a costly process and much could be earned if it was possible to calculate the effects of the changes on the vehicle with simulations. To build an accurate acoustic model, tests must be carried out on the different sources on the vehicle. This process is addressed within the Acoutrain project [http://www.acoutrain.eu/]

Real sources do not necessarily radiate the same amount of acoustic energy in different directions. For this reason one needs to measure the acoustic sound power radiated as a function of angles, also known as directivity.

Figure 1 Outdoor measurement setup and vertical directivity measured of an air conditioning unit for rail vehicles.

Acoustic standards for measuring directivity and source power do however require echo free conditions, see the outdoor setup illustrated in Figure 1. This can be reached by bringing the source outdoors or to an acoustic facility with absorbing walls. It may be hard to achieve with a real vehicle source though, due to its size, electricity needs etc. See for example Figure 2. For this reason, methods to determine the directivity of a source also in a room with some reflections are of interest. It is also useful to understand the errors associated with such measurements when made in a more regular industrial setting.

2

Figure 2 Setup for measurement of noise radiation of a transformer in an industrial hall

In regular rooms the walls reflect the sound, creating a field of reverbing waves called a reverberant field. The theory is that, if measurements are performed close to the source, the room will always influence the measured directivity in the same way. If so, a room correction factor should be applicable to the result in the specific room. Ideally, this factor can be used to calculate the same directivity as if the source was measured in a semi anechoic room.

1.2 Aim

The purpose of the present work is to evaluate a new method of measuring directivity, and to investigate if there is any other method used in any other fields of industry. That industry could be for example loudspeaker manufacturers who are interested in the directivity of their products.

The new method is to investigate how and when a room correction factor, 𝐸, can be applied to compensate for (light) reverberation when measuring directivity of a noise source in a reverberant room. If this room effect is constant for any source the method might have real applications.

1.3 Method

The literature study will be carried out by searching on the internet for standards, for example on SIS (Swedish Standards Institute) website [http://www.sis.se/].

The method for the measurement is gone through in a specific chapter, 4. Method.

3

2. Literature study

The most preferred way to perform measurements would be if there was a standard stating how it should be done. Finding one of those did however not turn out simple.

The first standard looked in to was SS-EN ISO 3744:2010 (Swedish standard, 2010). The full standard cannot be used because in this standard the microphone positions are spread over a hemisphere as they each cover the same area of sound emission. Conversely, the directivity is obtained by measuring in a horizontal (or vertical) plane. It does however contain a way to calculate environmental correction, demonstrating that the theory of room correction works here.

For loudspeakers there is a standard but the contents of it just states that you have to check sound quality, noise level and amount of distortion. There is not even a requirement to report them, nothing about how the measurements should be done either. ( International standard , 2007)

So what does the industry do today, as there is no standard? Common Loudspeaker Format is an industrial agreement of how the files for data supply should look like. It is an open, standardized format that is controlled by the CLF group with the purpose to make it easier to share and open directivity data for loudspeakers. As it has grown in popularity, more software programs are supporting it. (The CLF Group, 2014)

It does not seem like there is any standard or agreement of how to do directivity measurements. Therefore, measurements will be performed as stated in chapter 4.

4

3. Room acoustics

When a noise source is placed inside a room a reverberant field that mainly consists of reflected waves from the walls, floor and ceiling will arise. Close to the source, however, the direct field from the source is dominating. According to room acoustic theory a critical radius can be defined where the direct sound from the source is contributing equally to the sound level as that of the reflected waves from the walls etcetera. If measurements are performed within this distance, the influence from the reverberant field is small. (Wallin, Carlsson, Åbom, Bodén, & Glav, 2013)

The critical radius can be calculated by

𝑟! = 𝑟∗ = !!∙!!"!

!/! (1)

where 𝛤 is the directivity index and 𝐴′ is the room constant, which in practical use can be taken as 𝐴, the equivalent absorption area. The sound level within the critical radius decreases fast with increasing distance from the origin, see Figure 3.

Figure 3 Critical distance. SPL stands for Sound Pressure Level.

Källa:http://www.ssc.education.ed.ac.uk/courses/pictures/dmay0137.gif

5

4. Method

4.1 Measurements

The new idea of this method is that directivity is measured in rooms where a reverberant field is present and must be taken into account. Equipment used for measuring is a microphone, BSWA MP201, a preamplifier, BSWA MA201, and a current source, MWL_Uno. The software used is Spectra Plus for measurements, and Matlab for calculations. The Matlab codes can be found in Appendices 1-4.

The data of interest are sound pressure levels as a function of directions from the source. Measurements were performed in one third octave bands in the horizontal plane for three different objects in three different rooms. The objects were two real sources; a fan and a dipole, and an artificial source; a monopole. The dipole, see Figure 4, consists of two speaker membranes without casing mounted with the back side right next to each other, made to vibrate 180 degrees out of phase in respect to each other. The acoustic centre is right between the membranes, in the middle. The diameter of the dipole is about 0.15 m.

Figure 5 shows the fan. The fan has an exhaust pipe for air meaning that the wind could influence the results. Therefore, a wind shield is used for all measurements involving the fan. The fan has its acoustic centre in the midpoint of the rotating blades. The height is about 0.30 m.

The last object is shown in Figure 6. The monopole has a small outlet compared to the acoustic wave length which makes it a monopole below 5 kHz. A monopole is omnidirectional meaning that the sound level should be equal in all directions around it. The acoustic centre of the monopole is the centre of the open end of the pipe. The pipe is about 0.60 m long.

Figure 4 The dipole Figure 5 The fan

6

Figure 6 The monopole

Measurements were performed at all angles that are multiples of 30° in the horizontal plane. At each point the sound pressure in third octave bands between 100 and 5000 Hz were measured for five seconds. The microphone was always placed at the same fixed distance from the acoustic centre for each room, and the horizontal plane where the acoustic centre is was also the measurement plane. The microphone was always pointing straight towards the source. In the different rooms the approach was slightly different.

Semianechoic room The first test environment was a semi anechoic room. This kind of room simulates conditions outside with a reflecting surface underneath and no boundaries in any other direction. Figure 7 shows the dipole in place in the semianechoic room. Since this room is equally absorbing in all horizontal directions, a turntable can be used for the measurements. The microphone is placed 1.61 m from the acoustic centre of the source, which was the biggest practical distance that could be used. It could be this big because less than 1 percent of the incidental sound power to the walls will return to the room. (Wallin, Carlsson, Åbom, Bodén, & Glav, 2013) The reverberant field in a semianechoic room is consequently rather insignificant meaning that the distance can be big without getting outside of the critical radius.

7

Figure 7 The dipole on the turn table in the semi anechoic room

In the semianechoic room the dipole and the fan respectively was placed in the middle of the room on the top of a turn table. The turn table has a diameter of 0.40 m and a height of 0.20 m. The acoustic centre ended up 0.33 m above the floor for the dipole and 0.415 m for the fan. 0° was facing one of the membranes, and the air outlet. The turntable was then operated and stopped at all angles that were a multitude of 30°, where a measurement was performed.

Basement One test environment was a room in the basement of MWL. This should illustrate a worst case industrial scenario; a small space and lots of stuff everywhere. The unoccupied area was approximately a cube with the side 3.6 m long, the ceiling about 3 m up. This was a worst case scenario in many ways and the purpose is to see if any results here are useable. 0° is where the microphone is standing in Figure 8. In one direction, 90°, there is a painted concrete wall. Painted concrete has a low absorption factor (Wallin, Carlsson, Åbom, Bodén, & Glav, 2013) meaning that most of the sound bounce back into the room. The measuring distance here was chosen as 0.90 m, mostly because that was the biggest distance that could be achieved for practical reason in this small area.

8

Figure 8 The fan in the basement

In the basement measurements were done without turn table. Instead, the microphone was moved around to all multiples of 30°. The dipole and monopole were adjusted to be placed at the same height and position when measuring each, the acoustic centre were about 0.60 m up. Measurements were also performed with the fan placed in the middle of the open space with acoustic centre 0.175 m up. First with the fan on and then the side-by-side method; an artificial monopole at five specific locations with the fan off. See Figure 9. Positions 1-4 are in the same plane as the centre of the fan, 5 is on the top.

Figure 9 Monopole positions around the fan

The angle is 0° if pointed to the exhaust pipe for air. The distance was 0.90 m from the acoustic centre.

9

Classroom The last room was a classroom. This was a relatively open space with several metres in each direction. 0° is where the microphone is standing in Figure 10. The closest wall, the one in 90° in the picture, is a screen wall with an outer layer of some kind of fabric. This means that the absorption factor is at least slightly bigger compared to the concrete which implies that less sound is bouncing back to the microphone (Wallin, Carlsson, Åbom, Bodén, & Glav, 2013). The distance to the microphone here was chosen as 1.10 m.

Figure 10 The fan in the classroom

In the classroom three measurements were performed; in the horizontal plane around fan, dipole and monopole in the same acoustic centre, 0.175 m up. The wind pipe of the fan and one of the dipole membranes are pointed towards 0°.

4.2 Calculations

The directivity of the source in a semi anechoic room is denoted 𝐷0 and in the real situations 𝐷𝑅. 𝐷𝑅 − 𝐷0 can then be interpreted as the environmental influence to the directivity. Two approaches are tested; replacement method and side-by-side method. The replacement method means that the directivity is first measured for the real source and then with the source removed and with a monopole placed in the same acoustic centre. The environmental correction vector, 𝐸, is expressed as

𝐸 = 𝐷𝑅!"#$% − 𝐷0!"#$% ≈ 𝐷𝑅!"#$% − 𝐷 (2)

where 𝐷 is the average of 𝐷𝑅!"#$% and all units are dB. The directivity of the real source can be obtained from the measured directivity with the correction vector subtracted

10

𝐷!"#$ = 𝐷𝑅!"#$ − 𝐸 (3)

Comparing the normalized values of 𝐷!"#$ with the normalized value of 𝐷0!"#$ gives the accuracy of the method. If the compensation is successful these two normalized directivities should be the same. meaning that the environmental influence is fully removed.

When the equipment cannot be moved the side-by-side method is applied. Like before, the directivity is first measured nfor the equipment. Second the directivity is measured for a point source at five locations around the machine and the results are averaged according to .

𝐷𝑅!"#$% = 10 ∗ log (!!

10!"!"#$%,!/!"!!!! ) (4)

where 𝑁 is equal to the number of points used. Thereafter it is the same calculation as for the replacement method, just that 𝐷𝑅!"#$% is inserted instead of 𝐷𝑅!"#$% in (2), and 𝐷 is the average of 𝐷𝑅!"#$%. Figure 9 in chapter 4.1 shows the applied locations on a test object.

11

5. Results In the following sections the correction factors calculated in the class-room and the basement. The measured results in the semi anechoic room are used as a reference.

Classroom

Table 1-5 shows the calculated room correction factor, according to (2) for five chosen third octave frequency bands. When the correction factor varies much between the different angles, it might be a sign of many isolated reflectors causing unreliable results. Therefore 125, 1000 and 2000 Hz might not give desirable results.

Table 1 Correction replacement method 125 Hz Table 2 Correction replacement method 250 Hz

-5

-5

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Correction factor 125 Hertz classroom

replacement

-5

-5

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o


replacement

12

Table 3 Correction replacement method 500 Hz Table 4 Correction replacement method 1000 Hz

Table 5 Correction replacement method 2000 Hz

These factors are then subtracted from measured values, according to (3) to get compensated values. They were then compared to the semi anechoic results to see how big and correct the corrections are. As a reference, the measured values without compensation is also compared. Since the different measurements were not in the same dB-range they were all normalized by subtracting the average of their frequency band, in the same measurement, before the comparison.

-5

-5

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o


replacement

-5

-5

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o


replacement

-5

-5

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o


replacement

13

In order for the correction factor to be useful the compensated value should give a smaller average difference than the measured. In Table 6 below the average difference in absolute values are calculated. Generally, where there is improvement to the difference it is less than 1 dB.

Table 6 Average difference compared to results in echo free room. dB

Diff. Compensated value Diff. Measured value 125 Hz dipole 1.9 2.1 250 Hz dipole 2.3 2.8 500 Hz dipole 2.1 2.2 1000 Hz dipole 1.7 1.5 2000 Hz dipole 3.1 2.2 125 Hz fan 4.4 4.0 250 Hz fan 0.7 0.8 500 Hz fan 2.0 1.9 1000 Hz fan 2.7 3.0 2000 Hz fan 1.8 1.4

In Table 7-16 the difference for each angle are plotted. Since the correction factor in the classroom is the same for both sources, comparisons can be made to see which angles the factor seems to work for both. For example in 250 Hz there is improvement in the angles -60°, 30°, 60°,90°,120°, 150° and 180° for both sources. Most noticeable is though that the measured and compensated curves are accompanying each other significtantly more than the compensated and the reference.

Table 7 Difference dipole in classroom 125 Hz Table 8 Difference fan in classroom, 125 Hz. Observe scale

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Effect of compensation, 125 Hz classroom dipole

compensatedmeasuredreference

-30

-30

-25

-25

-20

-20

-15

-15

-10

-10

-5

-5

0

0

5

5

10

10

15 dB

15 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Effect of compensation, 125 Hz classroom fan


14

Table 9 Difference dipole in classroom 250 Hz Table 10 Difference fan in classroom 250 Hz



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



15


Basement

Table 17-21 shows the calculated room correction factor, according to (2) and (4) for five chosen third octave frequency bands. To be able to compare between the replacement method and the side-by-side method, the room correction factor should be approximately the same. For 500 Hz the curves seem almost the same and can be useable. 250, 1000 and 2000 Hz might also be close enough, they do partly differ by a few dB though. 125 Hz does not look similar at all though and results are probably not useable. Additionally, it varies a lot between angles which implies there is a lot of surfaces where reflections can occur.

Table 17 Correction factor 125 Hz Table 18 Correction factor 250 Hz

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Correction factor 125 Hertz basement

replacementside-by-side

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



16

Table 19 Correction factor500 Hz Table 20 Correction factor 1000 Hz

Table 21 Correction factor 2000 Hz

These factors are then subtracted from measured values, according to (3) to get compensated values. They were then compared to the semianechoic results to see how big and correct the corrections are. As a reference, the measured values without compensation is also compared. Since the different measurements were not in the same dB-range they were all normalized by subtracting the average of data in all directions (???), in the same measurement, before the comparison.

In order for the correction factor to be useful the compensated value should give a smaller average difference than those measured. In Table 22 below the average difference in absolute values are calculated. There are only two cases though where the average difference is smaller for the compensated value, and then by 0.3 dB or lower.

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



17

Table 22 Average difference per angle between reference and compensated/measured value

Diff. Compensated value Diff. Measured value 125 Hz dipole 3.1 2.9 250 Hz dipole 1.9 1.9 500 Hz dipole 1.6 1.4 1000 Hz dipole 2.3 2.2 2000 Hz dipole 1.1 1.0 125 Hz fan 4.1 3.8 250 Hz fan 1.0 1.3 500 Hz fan 1.3 1.3 1000 Hz fan 4.0 3.0 2000 Hz fan 5.4 5.4

In Table 23-32 the difference for each angle is plotted. There it can be stated that the compensated values are more accurate for a few angles. Since the correction factor is calculated differently for the two sources in the basement, no comparison can be done between them.

Table 23 Diff. dipole in basement 125 Hz. Obs. scaling Table 24 Diff. fan in basement 125 Hz. Obs. scaling

-30

-30

-25

-25

-20

-20

-15

-15

-10

-10

-5

-5

0

0

5

5

10

10

15 dB

15 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Effect of compensation, 125 Hz basement dipole


-30

-30

-25

-25

-20

-20

-15

-15

-10

-10

-5

-5

0

0

5

5

10

10

15 dB

15 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o

Effect of compensation, 125 Hz basement fan


18

Table 25 Difference dipole in basement 250 Hz Table 26 Difference fan in basement 250 Hz

Table 27 Difference dipole in basement 500 Hz Table 28 Difference fan in basement 500 Hz

Table 29 Difference dipole in basement 1000 Hz Table 30 Difference fan in basement 1000 Hz. Obs. scaling

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6

6

8

8

10 dB

10 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



19

Table 31 Difference dipole in basement 2000 Hz Table 32 Difference fan in basement 2000 Hz. Obs. scaling

6. Discussion

When looking into Table 6 and 22 some tendencies can be seen. As expected from the correction factor, 125, 1000 and 2000 Hz give the biggest average deviation in actual dB value. 250 Hz in the basement was also expected to differ a lot, which it does when looking into table 25-26, it is just that there is a few angles deviating a lot while the rest seem pretty spot on. Generally, the correction factor mainly made the difference bigger, but some effect can be noticed. For 250 and 500 Hz the actual dB values varied a lot less, with just amply 1 dB from the wanted value while the other differences were several times bigger. Most noticeable is though that the measured and compensated curves are accompanying each other significtantly more than the compensated and the reference. The correction factor gives a too small difference to get any usable results.

One explanation might be that the measurements in the semianechoic room were not performed with entirely the same conditions. The height above the floor to the acoustic centre differs to all other rooms, and the turn table is possibly big enough to cause interference to the sound. Actually, the only room where all sources were placed in the same acoustic centre was in the classroom. The only way to do that for the monopole is to lean the pipe against something, having the opening pointing more in one direction. The sound did indeed become louder there, meaning it is not a perfect monopole when not standing up. The difference was up to about 2 dB in the different directions when leaning.

It was not that easy to know exactly how good the items were placed either. The measurements were hard to get precise. Mainly since the tools of disposal just were a one metre steel ruler and a large tape measure. On the floor they were all right, but as soon as the attempts to measure distance to a microphone in the air begun it became difficult to get a desired accuracy. Approximately, some measurements could differ a few centimetres. The microphone stand was not completely stiff either with the several joints for adjustments. When moving the microphone around it might have readjusted.

-8

-8

-6

-6

-4

-4

-2

-2

0

0

2

2

4

4

6 dB

6 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9 dB

9 dB

90o

60o

30o0o

-30o

-60o

-90o

-120o

-150o

180o150o

120o



20

Even though measurements were done at each spot there might still be an error. A few centimetres cannot be all to blame though so more must be wrong.

All measurements were performed for about 5 s. Just one measurement for each point were executed because the results did not seem to fluctuate much after the first second, and the background noise stayed the same. Therefore, more measurements will probably get approximately the same result. The fan did though have periods where it made more noise than before and after. These did however seem to occur randomly and could go on for several minutes, without a clear transition. To wait for it to sound the same – which was really hard to determine – would have taken too much time. Doing more measurements would probably not have helped either because of the unpredictability. This could be solved with more than one microphone measuring simultaneously, ensuring that the source and background emit the same sound power for several measurements.

Another thing to note is that the fan in both rooms get a lower difference than the dipole for the two most reliable frequencies (250 and 500 Hz). Firstly, it shows that the side-by-side method seems to be comparable to the replacement method. Secondly, the correction factor appears to work better on the fan for these frequencies. For the rest of the frequencies looked into, the fan differs more than the dipole.

Last but not least – one of the most important factors is the distance to the microphone. In this study, a practical and rough estimate of the distance needed was done. For practical reasons, the critical distance was not calculable in the two ordinary rooms. Each area must be taken into account and get an approximate absorption factor which is not doable with the many areas and objects in these environments. What could be done though is to find the critical radius by for example measuring the sound pressure at different distances to find where the total dB decreases slower, according to Figure 3.

Taking this into account, the result may show a small connection. Still, the room correction factor does not improve nearly close enough to be useful in these measurements.

21

7. Conclusions

The purpose of this report was to evaluate a new method proposal and search for possible existing standards for …. No standard to be used fully was found but parts of one, (Swedish standard, 2010), could be used.

From the new evaluation of the proposed method some conclusions could be drawn.. The correlation between the use of the room correction factor and more accurate results seems tenuous in this case. The difference in dB between the result in echo free conditions and the measured/compensated result is always bigger than the difference between measured and compensated value. If looking at very small tendencies anyways it seems at frequencies around 250 Hz up to 500 Hz the theory could have some potential.

Therefore, new tests have to be put through to show if it really has any potential. For starters the acoustic centre should be kept the same distance from all surfaces in all situations. If for example a turn table is to be used, it could preferably be used as a stand in all non-anechoic rooms as well, in order to also keep the same reflective surfaces. Optimally it should not be used though for this reason. Moreover, the correct distance to the microphone should be calculated. Preferablyseveral microphones measuring simultaneously too.

So, the method has not been tested rigorously enough to draw any firm conclusions and might have some potential, but more comprehensive tests have to be fulfilled.

22

References

Acoutrain. (2014, May 24). Acoutrain. Retrieved from http://www.acoutrain.eu/

International standard . (2007, July). ICE 60268-5 . Sound system equipment – Part 5: Loudspeakers. Geneva, Switzerland.

Swedish standard. (2010, November). SS-EN ISO 3744:2010. Acoustics- Determination of sound power level and sound energy levels of noise sources using sound pressure - Engineering methods for an essentially free field over a reflecting plane. Stockholm, Sweden.

The CLF Group. (2014, April 27). Common Loudspeaker Format. Retrieved from http://www.clfgroup.org/index.htm

Wallin, H. P., Carlsson, U., Åbom, M., Bodén, H., & Glav, R. (2013). Ljud och Vibrationer. Stockholm: Universitetsservice US-AB.

23

Appendix 1. Matlab code with measurement data clear all close all clc global LP HZ125fb HZ250fb HZ500fb HZ1000fb HZ2000fb HZ125ft HZ250ft HZ500ft HZ1000ft HZ2000ft HZ125fc HZ250fc HZ500fc HZ1000fc HZ2000fc HZ125mc HZ250mc HZ500mc HZ1000mc HZ2000mc HZ125mb HZ250mb HZ500mb HZ1000mb HZ2000mb HZ125dt HZ250dt HZ500dt HZ1000dt HZ2000dt HZ125db HZ250db HZ500db HZ1000db HZ2000db HZ125dc HZ250dc HZ500dc HZ1000dc HZ2000dc HZ1251 HZ2501 HZ5001 HZ10001 HZ20001 HZ1252 HZ2502 HZ5002 HZ10002 HZ20002 HZ1253 HZ2503 HZ5003 HZ10003 HZ20003 HZ1254 HZ2504 HZ5004 HZ10004 HZ20004 HZ1255 HZ2505 HZ5005 HZ10005 HZ20005 %dipole classroom Lp0=[41.273453 43.935837 45.094608 42.343925 41.191692 40.337456 44.79081 48.250614 48.585213 52.298965 54.048969 59.739063 63.769466 53.916569 54.57774 52.433331 52.934475 41.069061 ]; Lp30=[43.122711 43.248871 46.291027 42.50964 41.566254 40.033001 43.931824 47.857849 47.972313 51.614582 53.5042 57.612263 61.545631 51.642929 53.418987 48.051517 46.079655 40.490993 ]; Lp60=[42.160671

24

45.587051 44.329533 42.191467 41.518917 39.547031 41.603184 44.78577 42.970833 47.655346 48.650597 53.627281 56.212322 50.665882 49.877083 47.430431 46.909576 40.088322 ]; Lp90=[43.705444 46.361008 42.407558 42.928688 42.444839 40.776432 39.946327 40.648869 41.23093 42.54504 45.98811 50.986462 53.697643 49.126358 49.081459 45.847088 41.316292 32.836025 ]; Lp120=[44.033875 44.225388 44.398647 44.115608 42.3438 41.48505 41.546982 40.477253 45.540394 44.328014 48.243401 52.258854 54.851021 49.724243 50.120506 48.040764 48.03743 41.125744 ];

25

Lp150=[43.51226 43.927174 44.210751 43.309925 43.010071 43.723412 44.817532 44.124813 49.279724 48.767365 52.272488 57.524597 60.9277 53.010277 52.951752 47.7192 45.494202 40.234764 ]; Lp180=[42.802231 43.432468 42.929279 43.628372 43.121815 44.621185 45.261768 45.571613 50.412403 49.932728 53.8232 59.110294 63.860722 55.870892 54.660301 50.218929 51.490726 39.035397 ]; Lp210=[43.878876 44.880512 44.831944 42.872128 43.109253 43.86467 44.142654 44.902534 49.081215 48.626316 51.545315 56.741272 60.944912 53.025352 50.105545

26

45.442482 46.221535 39.93298 ]; Lp240=[46.262348 44.060089 44.124569 42.348293 42.380188 41.964298 41.957783 41.208576 45.854084 43.750851 47.379311 50.171982 53.664665 49.714096 49.846622 46.802525 48.486809 38.987572 ]; Lp270=[46.807133 43.757912 41.251396 43.155861 40.945156 39.568615 41.123924 39.783066 42.186657 41.738953 45.42078 49.071995 52.830048 49.974747 49.161163 44.482166 40.951412 32.680321 ]; Lp300=[46.629253 44.968651 43.571793 41.782684 39.657337 38.637981 42.205986 43.452736 42.009964 46.956108

27

48.182285 51.909519 56.39259 50.253902 49.706566 47.102207 48.695408 40.2458 ]; Lp330=[42.290756 44.666725 44.773682 43.321449 41.373619 40.074173 44.078636 47.172428 46.63895 50.852829 52.606697 57.626926 61.400387 51.08736 50.902969 47.831985 45.973743 38.823814 ]; HZ125dc=[]; HZ250dc=[]; HZ500dc=[]; HZ1000dc=[]; HZ2000dc=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125dc=[HZ125dc hz125]; HZ250dc=[HZ250dc hz250]; HZ500dc=[HZ500dc hz500]; HZ1000dc=[HZ1000dc hz1000]; HZ2000dc=[HZ2000dc hz2000]; end %dipol källare

28

Lp0=[35.474232 34.611485 36.361629 32.737518 37.698254 35.731522 39.935246 41.372608 46.029797 44.065529 52.416538 57.281921 61.870338 57.004761 58.465729 55.434303 49.878571 35.831837 ]; Lp30=[36.562984 31.80685 36.512085 35.630287 37.022038 37.40477 38.874924 41.327763 44.279648 44.665577 51.723591 55.188206 59.651993 53.950947 54.627888 50.645638 44.991493 37.488396 ]; Lp60=[35.305923 28.608932 34.04837 34.172146 37.358829 35.834671 36.794216 37.03838 39.926487 41.193062 46.624756 50.956043 51.761066 47.690796 50.407673 49.588421 44.713398 37.677601

29

]; Lp90=[35.687389 40.642933 32.418381 31.143375 35.672073 33.065193 32.601692 33.259853 33.961113 38.22731 41.325054 45.671871 51.102283 47.106113 47.959904 44.352093 39.787621 32.290337 ]; Lp120=[34.330425 31.143795 35.152985 36.949543 34.181595 40.893177 30.557552 36.909195 37.866081 35.67794 45.112995 49.036598 52.140553 46.169178 50.574463 47.745602 43.853813 35.481037 ]; Lp150=[33.72406 34.274529 33.156376 34.996059 34.915386 34.128124 33.410133 40.559341 42.190338 39.113838 50.045815 53.903198 58.247982

30

53.330353 54.135712 48.203728 43.021976 36.844116 ]; Lp180=[34.788177 37.049995 35.63382 34.097149 34.815865 32.28709 36.02129 41.787762 43.549419 41.332161 52.324028 56.096649 61.756603 57.864861 59.341072 53.671421 46.942543 36.334618 ]; Lp210=[36.104233 37.479065 38.43697 32.895702 34.682446 32.952747 34.479088 41.908112 42.713303 37.977612 51.542843 54.648884 59.684559 54.888363 55.661335 49.058151 43.510242 35.813293 ]; Lp240=[36.734344 36.206688 33.682785 31.797985 35.433807 30.865601 32.791195 38.073105 38.325172

31

34.810684 45.403721 49.936153 53.748249 48.126789 50.709549 47.472229 45.085445 36.560467 ]; Lp270=[35.849411 31.389034 31.682175 31.731747 33.92292 34.761555 31.923794 34.096439 34.802597 37.368149 40.711296 48.549126 50.719719 47.826611 47.735497 43.64344 40.304203 30.871853 ]; Lp300=[35.571972 31.979221 32.131905 33.440868 34.228085 35.613453 36.922989 36.687672 41.524738 40.568947 47.535706 50.933289 54.641212 45.912552 50.478268 48.574173 46.896618 36.692104 ]; Lp330=[35.601135 34.157528 33.456245 33.918709 36.987156 37.145863 38.735489

32

40.413612 44.822376 44.16061 51.046154 55.86607 60.510906 54.477726 55.109001 48.91473 43.999126 35.355816 ]; HZ125db=[]; HZ250db=[]; HZ500db=[]; HZ1000db=[]; HZ2000db=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 500 Hz hz2000=N(14); %bara 2000 Hz HZ125db=[HZ125db hz125]; HZ250db=[HZ250db hz250]; HZ500db=[HZ500db hz500]; HZ1000db=[HZ1000db hz1000]; HZ2000db=[HZ2000db hz2000]; end %dipol turntable (semi anechoic room) Lp0=[36.560284 36.105312 37.835606 41.915031 43.458382 41.424561 46.830177 45.071396 47.825699 48.750565 48.308083 50.181221 53.885117 56.286617 59.581429 54.805111 49.710262 41.363472 ]; Lp30=[35.726208 35.19297

33

37.429142 41.287663 42.939503 40.907711 46.164608 44.168224 46.80442 47.99551 47.683697 49.036873 52.034676 52.969471 54.663136 50.147175 47.984192 41.448448 ]; Lp60=[32.583046 32.732151 34.778385 37.334675 37.970047 37.438904 42.080624 40.301159 42.520382 44.125343 44.717239 46.239807 47.909237 47.076111 49.823235 49.771755 47.243649 39.855515 ]; Lp90=[31.697491 32.450024 33.613239 35.188793 36.880177 37.899734 39.52869 40.677334 41.400589 42.193802 43.308384 45.144001 46.826912 45.806389 46.796894 46.355892 45.426697 38.544746 ];

34

Lp120=[32.13345 34.226936 33.990898 34.342827 37.426514 39.815639 38.360855 42.841591 43.236954 44.318886 44.490894 45.918427 47.967964 46.475262 49.040607 50.035156 47.350609 39.542759 ]; Lp150=[32.154667 35.589844 34.85363 34.093754 38.183598 41.231678 38.238934 44.492207 44.912487 46.763439 46.373486 47.823883 52.048824 52.505272 54.874832 49.147263 47.215279 39.458344 ]; Lp180=[31.40802 35.614891 34.006721 33.125103 38.139942 41.094685 37.722218 44.719975 45.573086 47.548882 47.203087 48.228931 54.123814 56.453999 59.979649 54.637222 48.658707

35

38.370258]; Lp210=[31.414173 35.146034 33.814152 33.107822 37.720299 40.804947 37.472885 44.326607 45.03289 46.710785 46.67627 46.410381 52.178268 53.32478 55.395195 49.745892 45.402214 37.683033]; Lp240=[31.165058 33.173775 32.612473 32.982292 36.523979 38.92828 36.504139 42.098232 42.355335 43.747791 44.433292 43.818115 47.914402 45.829987 49.21217 48.78331 45.69635 37.314461 ]; Lp270=[30.936348 31.128204 32.770035 34.123158 35.661785 36.904251 38.12957 39.585575 40.194103 41.121029 42.539745 43.646088 46.442402 44.925396

36

45.888367 44.744705 43.833271 36.41256 ]; Lp300=[33.647682 33.736961 35.785709 38.275444 39.27282 38.537483 42.919735 41.437943 43.652851 44.902554 45.38483 47.131725 48.755081 47.977577 50.497246 50.188194 48.270859 41.245949 ]; Lp330=[28.305298 29.157471 32.746525 35.172112 34.571926 34.212162 40.648262 39.27832 42.139091 44.332104 43.365707 46.421757 49.470516 50.530926 53.039486 48.322205 45.047054 38.083138 ]; HZ125dt=[]; HZ250dt=[]; HZ500dt=[]; HZ1000dt=[]; HZ2000dt=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz

37

hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125dt=[HZ125dt hz125]; HZ250dt=[HZ250dt hz250]; HZ500dt=[HZ500dt hz500]; HZ1000dt=[HZ1000dt hz1000]; HZ2000dt=[HZ2000dt hz2000]; end %basement fan Lp0=[80.707771 74.857193 70.529083 67.226768 71.074883 79.155151 70.855637 78.463493 76.720955 78.937073 78.397781 73.879799 75.635712 74.283012 72.279312 68.994507 61.708328 51.693096]; Lp30=[55.311905 58.996418 62.314434 62.614296 67.696701 77.1745 69.245575 79.704773 76.200638 77.607178 78.850792 75.239487 74.198883 73.943375 73.151077 69.116325 61.487862 50.478035]; Lp60=[52.634232 54.715862 59.640289 62.475616 67.652069 76.838379 69.285049

38

78.888954 75.627686 74.559776 75.763626 71.242653 73.992767 66.844986 67.665688 59.388775 54.920486 44.722794]; Lp90=[48.680851 51.216557 54.644009 60.870296 69.966408 80.038063 66.517281 78.917892 74.19783 72.166771 73.272888 70.072418 71.349617 65.94117 64.777428 63.713272 56.728336 44.989235]; Lp120=[45.450027 50.709064 53.301937 62.26086 68.895744 77.17099 69.566536 69.550613 71.973984 73.90847 73.7342 69.877876 68.287651 65.702332 63.898788 61.717056 57.738873 44.543797]; Lp150=[48.321007 53.135479 56.296543 58.480915 63.635998 82.238945 68.851227 72.365532

39

74.087959 72.502945 71.971306 71.17334 67.980339 64.162369 63.848984 56.829849 57.388405 42.657673]; Lp180=[50.555374 54.686913 56.550503 57.498459 70.207687 79.921707 69.306778 76.355659 74.893509 71.571236 70.650719 71.035553 69.561424 66.302849 64.141769 57.056755 60.095249 44.487492]; Lp210=[51.884544 55.778275 57.951839 59.375053 69.885559 79.874092 71.391701 78.144035 72.645157 72.531006 71.325386 71.482681 68.653488 65.256226 63.558399 57.21207 60.136318 46.098061]; Lp240=[53.003635 56.25489 57.498451 61.507759 68.332497 85.886681 71.614021 76.903618 75.494019

40

74.591789 75.324188 74.391083 69.922691 66.749245 63.000267 60.643913 64.795219 50.693001]; Lp270=[51.606552 55.077206 56.896904 61.823364 70.252197 85.174301 73.410927 77.729652 75.121254 72.783257 75.008728 70.222313 69.614372 67.835388 66.628372 61.677464 59.89344 48.72924]; Lp300=[50.852596 53.749657 56.593067 62.148098 71.963661 84.03553 73.400696 75.116592 72.65522 73.418182 73.908997 75.40728 73.41021 69.352859 67.352501 64.73954 62.112396 52.123039]; Lp330=[53.949329 55.88332 57.61301 62.96291 70.334785 81.479439 73.239456 79.186813 77.568802 78.694809

41

78.396355 75.33844 74.393204 73.5634 73.032036 63.853207 61.645779 50.819912]; HZ125fb=[]; HZ250fb=[]; HZ500fb=[]; HZ1000fb=[]; HZ2000fb=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125fb=[HZ125fb hz125]; HZ250fb=[HZ250fb hz250]; HZ500fb=[HZ500fb hz500]; HZ1000fb=[HZ1000fb hz1000]; HZ2000fb=[HZ2000fb hz2000]; end %fan turntable la till 180 grader jmf excel så utblås 0 grader Lp210=[43.812752 49.009487 49.418259 52.549255 59.835552 75.659233 61.504589 68.28907 64.12838 63.586102 59.869473 58.626724 62.664185 62.442513 58.550766 48.783367 49.650887 36.973915 ]; Lp240=[44.1479 49.033463

42

49.56699 52.908772 61.996025 77.155357 63.854065 68.502922 65.55854 65.439735 56.425766 59.268452 64.095543 62.480545 58.253036 52.475971 55.221115 43.062111 ]; Lp270=[42.766964 48.024712 49.887276 53.409683 62.82214 79.86882 64.892143 69.009033 64.80069 62.958328 61.272202 60.364399 64.143753 64.887947 61.789043 54.981064 53.747253 42.225014 ]; Lp300=[41.736713 46.073097 49.622688 53.712227 63.513317 79.929222 64.433235 64.382668 61.797478 57.021458 51.152157 59.561733 65.203857 64.452332 63.520149 57.405956 54.411224 45.663506 ];

43

Lp330=[43.914791 47.292095 51.065281 54.477245 62.384808 78.0326 63.08675 68.30648 66.582039 65.139397 59.836536 59.055267 65.234947 66.612953 68.037788 55.427132 53.933868 49.98914 ]; Lp0=[55.945873 53.126839 52.858662 55.046345 61.452057 75.846619 60.671398 67.085907 65.868523 65.660294 60.275284 57.669666 65.101532 65.473656 66.870445 54.444382 52.555977 46.169743 ]; Lp30=[46.893867 50.385677 52.4198 55.112568 60.02121 73.334816 60.138371 68.293579 64.28495 65.686829 61.79958 57.928047 63.936977 66.639946 68.796066 56.709938

44

55.431271 51.303894 ]; Lp60=[45.459572 49.776096 51.648643 54.896507 59.872551 73.222183 60.186047 68.85022 65.345505 60.40028 60.275085 53.792732 59.71962 60.974468 63.414803 54.26368 49.076847 44.151993 ]; Lp90=[42.184074 46.580631 48.842304 53.311306 59.717777 73.470032 59.865585 67.724884 66.342453 65.121651 58.656113 55.618912 56.303825 58.75098 57.633739 50.186344 43.947453 39.184639 ]; Lp120=[39.252575 43.075027 46.882195 51.862091 59.690044 74.03569 59.187454 64.526344 62.457485 64.078247 60.388226

45

54.089123 54.714699 56.060402 55.514168 47.204243 43.485134 35.241974 ]; Lp150=[40.19788 45.042503 46.364101 50.363911 58.151901 73.56459 58.940865 63.30611 61.595657 64.014961 60.765152 56.276054 55.359756 56.215317 53.406902 45.270958 44.443855 32.62999 ]; Lp180=[42.333633 47.3475 48.035427 51.21384 58.915035 74.747459 59.71122 65.833328 61.904221 61.522816 60.812778 57.22496 60.135502 59.145412 57.804573 48.222504 47.670425 35.032768]; HZ125ft=[]; HZ250ft=[]; HZ500ft=[]; HZ1000ft=[]; HZ2000ft=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz

46

hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125ft=[HZ125ft hz125]; HZ250ft=[HZ250ft hz250]; HZ500ft=[HZ500ft hz500]; HZ1000ft=[HZ1000ft hz1000]; HZ2000ft=[HZ2000ft hz2000]; end %fan classroom Lp0=[79.23304 75.620056 70.90435 68.779877 70.839264 80.37384 70.28772 80.162262 76.438187 77.030678 75.897758 73.079903 75.550224 73.264763 70.84436 62.93404 61.526989 52.1772 ]; Lp30=[53.663055 56.215858 60.071877 62.781475 68.660202 76.849632 69.529991 80.828789 75.539963 76.750397 77.504051 73.386391 74.95726 74.026756 72.7388 64.144249 63.562004 51.407124 ]; Lp60=[52.465031 54.889164 56.67944 62.774303 69.30648 76.915543 70.041748

47

79.726669 75.1884 72.296478 75.418541 71.63913 73.151588 67.279678 67.721214 58.719402 57.824055 44.35857 ]; Lp90=[49.997826 54.451801 54.403305 62.210346 70.302017 77.797661 68.193642 75.097687 74.295898 71.941269 73.303574 69.778259 70.52298 66.710854 64.604431 56.195976 54.870762 42.810993 ]; Lp120=[48.868889 50.17313 53.257839 61.557892 69.80098 78.081749 68.43132 73.360672 71.412773 70.472923 70.438652 68.261833 68.494629 65.333397 62.812576 55.973492 53.756828 42.612736 ]; Lp150=[49.776203 51.594444 54.012169 59.170467 68.873497

48

78.13279 67.155418 74.092163 73.485443 70.600861 71.136566 69.889053 68.064606 65.492088 63.129986 54.782578 53.317375 41.993641 ]; Lp180=[51.83765 53.788132 55.424603 59.983196 68.498039 77.410492 68.478539 74.989616 74.322258 72.001747 68.750519 69.352486 70.808205 67.253151 62.722961 55.477318 53.356846 43.400822 ]; Lp210=[52.184963 55.848255 57.537937 61.110737 68.754753 80.093933 70.052475 76.265816 72.960724 72.661728 70.395638 69.724739 70.881165 68.137962 63.158642 55.288216 55.61998 45.44928 ];

49

Lp240=[52.770782 56.462173 57.125008 60.595089 70.547707 81.986931 72.508301 78.609612 75.700912 74.712029 73.948387 73.455826 72.081215 67.676483 63.027988 58.739536 58.783714 49.132149 ]; Lp270=[51.124889 55.212662 57.222042 62.098824 71.755386 82.277214 73.390465 76.499901 75.048019 72.582542 73.114288 70.213646 71.730263 69.14595 64.087112 60.977432 57.013634 47.691029 ]; Lp300=[49.398445 54.054901 57.223793 62.326115 70.100883 82.045975 72.944611 73.804802 73.381447 72.733322 73.872169 73.191895 74.506683 69.167839 65.742973 62.156597

50

59.857063 50.024212 ]; Lp330=[51.68206 55.556896 57.243 63.439926 70.518005 80.991386 72.166199 74.147934 77.256721 78.112358 75.424805 73.142075 75.374359 74.092087 71.292435 64.577202 61.462132 52.862774]; HZ125fc=[]; HZ250fc=[]; HZ500fc=[]; HZ1000fc=[]; HZ2000fc=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125fc=[HZ125fc hz125]; HZ250fc=[HZ250fc hz250]; HZ500fc=[HZ500fc hz500]; HZ1000fc=[HZ1000fc hz1000]; HZ2000fc=[HZ2000fc hz2000]; end %monopole classroom Lp0=[42.460133 43.369583 44.360878 41.483761 40.73037 48.657467 48.081059 49.190067 55.295616 55.227646

51

57.497173 58.284054 59.976025 57.061119 54.291771 55.511402 60.158611 50.559414 ]; Lp30=[43.524956 42.49065 46.012093 41.130096 41.057606 48.838867 47.566307 48.091457 54.157593 56.136978 57.315239 57.831879 60.265007 56.984333 54.839321 55.4151 59.546078 50.121235 ]; Lp60=[42.674728 45.571548 43.518639 41.845142 41.846161 47.697124 47.938354 49.099342 53.128342 53.398384 55.121258 56.034435 58.643581 55.987225 53.766121 55.031567 57.167999 47.545452 ]; Lp90=[43.079132 46.446972 42.153915 42.74123 42.154713 47.573338 47.123955 49.659313

52

54.897083 55.035294 55.264973 53.904648 55.702103 53.802353 55.622765 56.766788 59.22588 45.694637 ]; Lp120=[43.93079 44.865128 44.941158 43.339279 42.187859 47.286808 47.761906 48.783257 53.509026 53.267471 53.631889 55.776241 57.996456 54.763519 54.561405 54.426903 56.631126 46.407772 ]; Lp150=[44.052853 43.492004 43.528198 42.179535 41.682438 48.745014 46.546741 48.541847 53.614815 54.182632 56.849098 57.706944 61.282093 58.014534 55.120529 55.509914 59.166145 51.163528 ]; Lp180=[43.188587 47.450798 43.911919 43.690384 42.450932

53

48.479504 47.641922 48.424721 54.648212 54.709442 55.84676 57.380119 60.035519 58.731831 55.20779 54.052876 58.712639 49.024796 ]; Lp210=[41.897156 44.270924 44.178734 41.901279 42.562504 48.762867 47.91383 48.963173 53.064285 54.516815 57.230396 58.682503 60.200073 57.808224 54.146347 54.288334 59.874409 50.974743 ]; Lp240=[43.567715 42.323578 43.490795 41.1819 41.928638 49.163151 47.622601 47.435608 52.604427 56.829323 58.551521 56.736462 62.07069 56.660233 55.935783 52.949944 62.025223 52.249191 ];

54

Lp270=[47.270485 44.636501 41.098125 42.831055 41.186882 48.488335 48.243507 48.493889 52.951759 57.471066 58.121868 55.873775 61.78249 56.46595 55.742016 57.160069 61.456379 54.013836 ]; Lp300=[46.164055 44.762039 42.600231 40.90226 40.12727 48.877136 48.110023 47.794163 52.501385 56.377972 58.20504 56.298698 60.78162 58.1922 55.185341 55.287464 61.612038 53.213402 ]; Lp330=[42.362614 44.734009 44.722633 42.388554 40.928684 49.372818 48.273415 48.880108 53.116825 54.817368 57.577881 57.925224 60.032486 58.530937 54.634392 56.735523 60.798584

55

53.308128 ]; HZ125mc=[]; HZ250mc=[]; HZ500mc=[]; HZ1000mc=[]; HZ2000mc=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125mc=[HZ125mc hz125]; HZ250mc=[HZ250mc hz250]; HZ500mc=[HZ500mc hz500]; HZ1000mc=[HZ1000mc hz1000]; HZ2000mc=[HZ2000mc hz2000]; end %monopol källare Lp0=[37.109642 34.345383 32.3507 32.265167 36.529053 40.946865 44.659496 47.069664 50.367706 51.738026 57.509373 54.483646 58.998859 59.477898 59.667469 59.062622 59.761345 51.042633]; Lp30=[37.7701 31.525898 34.003963 31.868473 35.954086 43.929935 43.389465 46.946392 50.445847 52.340752 57.070145 54.914642 59.457928 59.401817

56

59.83675 59.379105 60.424816 50.765205]; Lp60=[36.62899 29.602448 31.780041 34.827202 37.114986 40.810997 44.824993 46.498322 50.67054 54.031506 56.930195 54.208027 59.548096 58.095299 60.230587 59.510178 60.54118 50.084583]; Lp90=[36.695881 29.540405 35.281326 31.585712 37.31992 41.963852 44.644047 47.212074 49.232082 53.920162 58.767063 55.585888 59.524612 61.394432 59.085594 59.751949 60.259705 49.67535]; Lp120=[35.227512 28.393684 33.116699 34.699371 35.966896 46.714935 44.385277 46.831059 50.129929 53.746799 57.769314 56.201618 58.974075 58.62471 59.815731

57

58.648228 60.259201 48.856228]; Lp150=[37.763103 38.021168 30.670506 34.27132 36.795006 45.458004 40.764408 48.336967 49.966087 52.161331 57.392494 55.568588 59.453297 59.850365 60.653469 59.49939 60.734158 50.763298]; Lp180=[36.794819 32.672333 33.105759 31.129074 37.31797 43.20034 44.647289 46.736355 51.204395 52.391056 58.052776 55.828262 59.71228 59.468193 61.039879 60.224419 60.585934 50.847649]; Lp210=[37.216763 34.738102 34.516273 31.744614 37.046692 44.627964 44.17231 46.464489 51.455547 51.658855 57.614208 54.935108 59.03418 60.39843 59.780384 60.888771

58

60.853756 49.627682]; Lp240=[38.308426 35.726025 30.703327 33.365257 35.884129 43.975479 44.294952 47.774616 49.706127 51.891155 57.652225 54.910919 59.380329 59.345497 61.146446 59.944443 61.256741 50.039871]; Lp270=[37.897945 32.865295 28.8908 33.548946 33.561314 42.620857 43.398701 46.795067 50.185204 51.152576 57.518936 56.217583 60.197403 58.632477 58.958904 58.903107 60.514622 51.221447]; Lp300=[40.03878 35.692127 33.13884 33.012562 35.464676 44.734646 43.723454 46.651939 51.272148 51.729198 57.184227 54.166054 58.400723 58.841393 58.493866 58.793777 60.146538

59

50.922543]; Lp330=[37.933437 32.795292 29.779221 32.474438 38.233978 45.890278 42.249001 46.877892 51.861633 50.287201 57.226044 55.208538 58.302509 60.61861 59.886951 59.315472 59.365845 51.675877]; HZ125mb=[]; HZ250mb=[]; HZ500mb=[]; HZ1000mb=[]; HZ2000mb=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ125mb=[HZ125mb hz125]; HZ250mb=[HZ250mb hz250]; HZ500mb=[HZ500mb hz500]; HZ1000mb=[HZ1000mb hz1000]; HZ2000mb=[HZ2000mb hz2000]; end %punktkällor %punkt 1 Lp0=[42.138821 37.416325 36.89846 34.421238 42.039017 51.217102 41.514309 46.307411 52.956841 58.69949 57.045151

60

64.647522 58.035988 58.207638 56.366405 61.847107 64.481392 54.23999]; Lp30=[42.11557 36.059902 38.127274 35.031563 39.547047 50.541599 41.812801 44.844715 47.669102 55.347424 57.624706 63.273647 58.757851 57.525761 56.341488 58.74041 61.279411 48.802467]; Lp60=[40.587372 34.847118 39.706478 36.037239 40.482964 49.498993 41.336266 46.387638 49.804794 53.428143 52.988037 57.678509 54.537117 57.341831 51.032196 54.308041 58.70908 44.741402]; Lp90=[38.236603 34.255646 36.568024 35.432369 42.413181 52.042561 37.984032 46.721989 50.675518 54.203506 56.457153 58.678699

61

55.338955 56.50695 57.184917 55.729607 57.641483 43.532734]; Lp120=[36.372158 34.30117 31.819645 36.277828 42.906467 46.430218 40.751537 41.229019 51.507923 51.953278 54.407272 58.031498 53.611401 58.298306 55.973064 55.574375 55.484589 44.684223]; Lp150=[37.985676 35.282906 39.215515 34.58429 38.369156 51.502434 37.840786 44.36417 50.393276 52.006393 52.498039 58.256912 56.001621 56.292133 55.990917 56.166168 56.956646 43.080429]; Lp180=[40.092838 38.415424 38.866817 33.943375 43.41721 48.209099 40.804329 48.714832 52.222889 54.649086 53.972843 57.225689 55.469414

62

55.436798 56.83886 59.089142 60.480282 44.175709]; Lp210=[40.800007 38.862728 38.280834 35.280041 41.893261 49.496109 42.941463 51.25536 53.992523 55.611259 58.987839 59.174324 53.333195 53.90284 55.362034 61.479702 66.394272 43.878143]; Lp240=[40.620785 39.548122 36.206322 36.76897 42.183998 54.924793 44.344494 51.136681 56.078785 56.508156 62.808598 64.860703 55.738899 57.327286 58.947426 62.637669 70.555107 53.294357]; Lp270=[40.765156 38.562202 33.860405 36.153233 43.410675 54.936626 43.978291 51.864307 58.047562 57.699715 60.813869 60.757706 56.535439 58.427433

63

62.536777 68.452148 75.106987 64.785355]; Lp300=[41.752594 38.30542 37.662292 35.622253 43.683403 54.870716 42.002083 50.254627 56.249325 57.390472 62.355583 63.980907 58.019608 60.174381 55.791008 66.040741 66.306282 58.037979]; Lp330=[41.69593 38.137184 37.919907 33.737347 43.422062 52.069481 39.852848 49.863308 54.595272 58.714722 62.994244 58.521194 59.434357 60.478031 58.101128 64.461189 64.215004 57.762527]; HZ1251=[]; HZ2501=[]; HZ5001=[]; HZ10001=[]; HZ20001=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ1251=[HZ1251 hz125]; HZ2501=[HZ2501 hz250];

64

HZ5001=[HZ5001 hz500]; HZ10001=[HZ10001 hz1000]; HZ20001=[HZ20001 hz2000]; end %punkt 2 Lp0=[41.333542 36.289536 36.417469 34.239243 38.405624 46.254745 45.421825 46.974274 53.850761 52.847019 57.557289 57.287777 57.667686 56.294872 55.482235 53.999435 55.267452 45.616005]; Lp30=[41.229633 34.989666 38.984932 34.877895 36.195705 44.89061 47.069912 48.926739 51.815891 53.107979 57.018391 59.245438 56.671543 57.180855 54.057583 56.491375 57.833767 49.229027]; Lp60=[40.68848 38.458775 39.636513 36.378204 39.470062 48.58918 50.455654

65

49.821915 56.835033 60.226723 63.476917 57.399216 64.562393 62.797081 58.852024 63.497051 69.177849 59.039219]; Lp90=[38.236603 34.255646 36.568024 35.432369 42.413181 52.042561 37.984032 46.721989 50.675518 54.203506 56.457153 58.678699 55.338955 56.50695 57.184917 55.729607 57.641483 43.532734]; Lp120=[36.875587 35.687981 32.984867 35.860775 38.444336 49.370682 52.596657 49.84713 56.463078 58.428085 57.485546 56.154205 56.962452 57.382851 60.032032 62.045425 64.202522 50.875801]; Lp150=[40.01577

66

37.498829 38.814674 34.211166 37.838539 52.899044 51.852707 51.5228 56.081715 57.399117 59.615307 59.496925 63.546608 61.118523 57.106655 65.495766 65.494637 55.048447]; Lp180=[39.400337 47.239353 38.733551 33.40773 38.083015 46.091709 45.491844 48.36021 54.539677 55.872673 57.963863 58.219048 59.059814 59.051224 57.837921 56.515862 55.626713 47.213867]; Lp210=[40.996956 40.131157 38.215328 33.899628 39.97821 53.59251 51.375523 52.09906 55.355717 57.242203 63.485474 63.73159 57.733349 61.09264 62.500111 65.762093 66.820923

67

55.748253]; Lp240=[40.553467 39.076092 35.483181 35.265121 37.304245 50.47509 49.541447 49.358208 55.659512 59.573814 60.045521 61.156322 61.188599 56.55666 60.303894 65.851395 70.342773 58.424603]; Lp270=[39.080498 37.363499 34.09753 34.602352 36.895382 48.921154 46.991096 47.622219 54.727573 57.736427 60.957954 58.359436 61.891979 59.152821 57.365887 58.911644 64.100983 56.410744]; Lp300=[39.935276 37.191353 36.189503 35.437759 37.773647 46.07518 45.747108 45.789093 52.912712 54.242397 54.660587

68

58.010715 57.029331 60.017277 55.329681 56.138123 62.945015 55.240433]; Lp330=[40.149387 37.312645 37.885334 33.260544 40.423634 44.020908 47.053696 45.53405 50.486752 54.185059 55.933201 56.580307 56.517109 56.921558 54.833076 53.319183 57.381332 48.514896]; HZ1252=[]; HZ2502=[]; HZ5002=[]; HZ10002=[]; HZ20002=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ1252=[HZ1252 hz125]; HZ2502=[HZ2502 hz250]; HZ5002=[HZ5002 hz500]; HZ10002=[HZ10002 hz1000]; HZ20002=[HZ20002 hz2000]; end %punkt 3 Lp0=[41.14925 36.270367 36.242027 33.881714 38.262852

69

47.864056 47.8978 49.204945 55.530048 58.69313 63.82621 49.114407 54.542194 56.25346 55.342854 55.876648 61.021118 44.582005]; Lp30=[40.967556 36.088642 38.707661 35.210064 37.893494 51.584541 51.615704 52.800552 55.943619 58.376606 64.030197 48.956913 55.23262 53.622383 60.517071 58.755646 63.531773 46.617245]; Lp60=[41.599979 36.572342 40.237797 36.68153 40.763729 50.49762 52.060444 49.962044 51.92654 62.074993 65.017754 49.016579 59.754196 57.426723 61.89616 63.892082 68.106873 54.774502];

70

Lp90=[39.311493 36.540527 37.595116 35.794949 41.65316 52.73402 48.9077 50.582314 54.228214 62.256989 69.845444 56.766373 61.047165 60.230587 64.873734 68.897057 67.046593 57.526459]; Lp120=[38.569523 36.968369 33.608761 36.137558 41.44928 50.314114 52.96138 49.157005 53.007751 63.681221 67.432228 52.101139 59.373219 56.122025 62.591656 66.163078 71.288025 54.054161]; Lp150=[38.756088 35.738625 38.50465 34.963936 38.538586 53.883427 53.560635 50.540409 54.558434 62.30658 67.675873 48.992847 56.078785 58.920895

71

61.015305 63.380177 68.361961 56.074478]; Lp180=[41.241261 38.140934 38.012829 35.479866 39.586472 51.717789 47.241154 50.023975 55.624607 61.639019 66.4711 52.058346 58.313595 57.467659 59.131989 60.139339 62.457733 57.438461]; Lp210=[39.366852 38.215382 37.917942 34.813984 39.732201 44.239365 48.460232 46.313572 52.648891 60.380833 65.748154 52.157455 58.147552 58.906353 55.100361 55.439526 60.869198 49.741505]; Lp240=[39.058559 37.901405 36.210007 33.441956 39.049618 43.838718 47.272148 44.26292 51.454987

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58.287315 61.134285 48.742077 57.301464 57.260632 55.163532 56.779335 57.201298 46.450771]; Lp270=[39.146378 37.210854 33.8909 32.634811 36.737213 46.108463 46.641174 46.596462 52.996696 57.79908 63.717182 51.283604 56.464115 55.606529 58.801212 57.029099 57.468098 42.371613]; Lp300=[39.415951 37.094887 36.335133 34.255142 38.970589 43.646832 47.36451 46.522354 51.083412 56.057625 57.785469 47.952469 56.961071 55.072735 56.816803 56.159676 58.892441 46.793629]; Lp330=[39.542427 36.611359 37.790359

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32.40612 39.720032 44.813053 46.693989 45.697571 52.394226 56.25531 61.498505 50.937519 55.570339 55.78466 56.888103 52.885418 58.815533 50.718067]; HZ1253=[]; HZ2503=[]; HZ5003=[]; HZ10003=[]; HZ20003=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ1253=[HZ1253 hz125]; HZ2503=[HZ2503 hz250]; HZ5003=[HZ5003 hz500]; HZ10003=[HZ10003 hz1000]; HZ20003=[HZ20003 hz2000]; end %punkt 4 Lp0=[43.095322 38.614979 36.716999 33.365795 39.36425 50.154587 50.154873 52.959255 56.558071 56.074371 59.764126 63.149307 60.704849 56.651642 62.719498 65.00856 63.132736 54.544514];

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Lp30=[42.048679 37.196873 39.152279 37.001774 39.370068 51.38422 51.273842 51.823956 55.355213 56.728596 60.919624 55.921562 61.335442 57.867447 61.37569 65.95639 67.201378 52.130863]; Lp60=[40.383972 33.577225 39.052036 34.875767 38.458912 43.659454 46.610378 46.984379 55.286488 53.30006 54.835361 56.694794 59.212147 60.588718 54.16032 55.110924 55.787148 46.370346]; Lp90=[37.787933 36.250023 36.389095 34.496841 37.969864 46.149883 46.036362 48.83704 53.897411 58.518993 61.410465 57.409969 61.728859

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60.605762 61.136021 63.532597 66.932343 58.1576]; Lp120=[35.809212 33.548908 31.462318 35.061481 38.939373 41.989742 47.287056 46.679333 55.988094 58.854477 59.824913 59.525566 61.333405 62.258244 58.35162 60.156704 63.610149 53.159637]; Lp150=[38.195782 34.128963 38.452099 34.406288 36.73645 46.722595 47.928318 47.873825 52.682774 55.390469 58.91782 57.922348 58.163597 60.049969 60.718071 62.186489 61.094387 49.043446]; Lp180=[39.500874 37.359848 37.725571 33.275902 38.552559 48.020962 45.859482

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47.697098 52.076481 52.413849 56.545815 52.956116 60.893326 62.899296 62.959385 57.088486 62.292 53.565559]; Lp210=[39.019505 38.313305 38.058495 34.494469 39.689526 44.930931 47.123272 47.448067 53.148045 54.18948 56.104301 57.934925 60.522701 58.627609 59.741592 56.601437 60.271435 50.457733]; Lp240=[39.433029 38.153908 35.078873 33.971596 39.679295 47.428051 44.410767 47.213699 52.739845 54.547825 56.128429 57.201824 60.612808 59.32959 58.359997 57.305012 58.014122 51.622429]; Lp270=[39.833858

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38.752693 36.005169 35.48172 39.782822 47.780144 45.086033 48.587948 52.836132 56.244034 54.879299 56.265594 57.836704 58.886337 57.702774 60.125214 60.281872 46.738388]; Lp300=[40.660801 37.628902 36.470524 36.256042 38.359253 48.260277 49.371853 51.376339 54.404503 56.908146 56.516014 60.095638 57.571709 58.827885 58.972603 64.721924 64.884972 50.180786]; Lp330=[41.811005 37.199928 36.350529 30.702728 39.167412 48.189903 51.188732 51.246231 55.389942 56.287006 61.565571 63.011116 62.712513 61.670876 57.924095 66.105225 66.874771

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53.559395]; HZ1254=[]; HZ2504=[]; HZ5004=[]; HZ10004=[]; HZ20004=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ1254=[HZ1254 hz125]; HZ2504=[HZ2504 hz250]; HZ5004=[HZ5004 hz500]; HZ10004=[HZ10004 hz1000]; HZ20004=[HZ20004 hz2000]; end %punkt 5 Lp0=[41.761936 35.656055 37.256062 33.459618 40.520107 46.381584 44.481182 47.180649 50.908924 51.435596 57.458069 55.23975 57.039574 62.222145 62.006203 59.48859 59.510662 54.889244]; Lp30=[41.225109 35.263359 38.874645 35.515606 36.440563 46.935097 46.73761 46.546955 50.921654 51.133518 54.547108

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55.843018 55.056179 61.730389 63.22551 59.523026 61.481457 54.270889]; Lp60=[40.523369 33.60133 39.358131 34.845188 36.911888 44.505642 46.649872 45.046917 52.71389 53.668728 53.801857 54.430153 58.031841 62.926998 63.979698 61.347294 60.621792 50.782288]; Lp90=[38.159302 33.977211 36.492062 34.659328 38.485863 46.768372 44.334976 49.050182 51.257198 53.694355 57.268692 56.422134 56.298164 61.723038 64.18792 57.46431 62.155209 52.091209]; Lp120=[38.159302 33.977211 36.492062 34.659328 38.485863

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46.768372 44.334976 49.050182 51.257198 53.694355 57.268692 56.422134 56.298164 61.723038 64.18792 57.46431 62.155209 52.091209]; Lp150=[37.844349 34.429649 37.404781 34.46336 36.320236 48.106148 48.173042 47.412415 50.231056 53.523708 57.056152 53.319462 57.404594 61.674656 59.996891 59.250248 61.351513 50.37999]; Lp180=[39.500874 37.359848 37.725571 33.275902 38.552559 48.020962 45.859482 47.697098 52.076481 52.413849 56.545815 52.956116 60.893326 62.899296 62.959385 57.088486 62.292 53.565559];

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Lp210=[40.066334 38.382561 37.779861 35.010315 40.174503 48.151344 47.677601 47.791252 52.216194 53.479382 54.758614 53.376431 56.020653 61.471951 63.728363 57.779633 58.717266 53.145596]; Lp240=[39.820961 38.835567 34.565353 33.174828 38.539471 48.903885 45.458889 48.213299 50.46656 52.091564 55.114948 55.169506 58.38916 62.539169 63.988506 58.803314 59.903141 54.660782]; Lp270=[41.00098 38.031822 33.041138 34.049957 39.905293 48.096424 43.755043 48.159702 51.742344 52.605114 53.804119 54.978085 56.667912 62.554409

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63.244274 60.280926 56.951172 49.891232]; Lp300=[42.262238 39.363708 39.440269 35.255253 36.770851 46.819447 46.25531 47.138302 51.63467 51.765942 53.956905 53.061546 58.418591 62.008564 63.937664 59.810959 58.054653 54.117081]; Lp330=[40.819649 37.050041 36.665878 32.138382 39.51173 43.750099 47.297268 46.697575 52.790409 52.495777 55.432262 52.661934 56.392685 61.107277 64.818352 61.576698 57.463932 52.051231]; HZ1255=[]; HZ2505=[]; HZ5005=[]; HZ10005=[]; HZ20005=[]; for N=[Lp0, Lp30, Lp60, Lp90, Lp120, Lp150, Lp180, Lp210, Lp240, Lp270, Lp300, Lp330, Lp0] %för alla punkter hz125=N(2); %bara 125 Hz hz250=N(5); %bara 250 Hz

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hz500=N(8); %bara 500 Hz hz1000=N(11); %bara 1000 Hz hz2000=N(14); %bara 2000 Hz HZ1255=[HZ1255 hz125]; HZ2505=[HZ2505 hz250]; HZ5005=[HZ5005 hz500]; HZ10005=[HZ10005 hz1000]; HZ20005=[HZ20005 hz2000]; end LP=[0,30,60,90,120,150,180,-150,-120,-90,-60,-30,0];

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Appendix 2. Matlab code basement close all global LP HZ125fb HZ250fb HZ500fb HZ1000fb HZ2000fb HZ125ft HZ250ft HZ500ft HZ1000ft HZ2000ft HZ125fc HZ250fc HZ500fc HZ1000fc HZ2000fc HZ125mc HZ250mc HZ500mc HZ1000mc HZ2000mc HZ125mb HZ250mb HZ500mb HZ1000mb HZ2000mb HZ125dt HZ250dt HZ500dt HZ1000dt HZ2000dt HZ125db HZ250db HZ500db HZ1000db HZ2000db HZ125dc HZ250dc HZ500dc HZ1000dc HZ2000dc HZ1251 HZ2501 HZ5001 HZ10001 HZ20001 HZ1252 HZ2502 HZ5002 HZ10002 HZ20002 HZ1253 HZ2503 HZ5003 HZ10003 HZ20003 HZ1254 HZ2504 HZ5004 HZ10004 HZ20004 HZ1255 HZ2505 HZ5005 HZ10005 HZ20005 %Basement % beräkning E=DRpunkt-average(DRpunkt) för frekvenser. %125 Hz dipole DRpunkt=HZ125mb; avDRpunkt=sum(HZ125mb)/13; E=DRpunkt-avDRpunkt; DDreal=HZ125db; Dreal=DDreal-E; DOreal=HZ125dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal125d=Dreal-avDreal; %normalization norm_DOreal125d=DOreal-avDOreal; norm_DDreal125d=DDreal-avDDreal; difference125Hzdipolebasement=norm_Dreal125d-norm_DOreal125d; difference125Hzdbutan=norm_DDreal125d-norm_DOreal125d; diffav125bd=sum(abs(difference125Hzdipolebasement))/13 %calculate average difference from reference diffav125bdu=sum(abs(difference125Hzdbutan))/13 %calculate average difference from reference %125 Hz plot figure (1) dirplot(LP,E,'r',[6 -10 8]) hold on %125 Hz fan DRpunkt1=HZ1251; DRpunkt2=HZ1252; DRpunkt3=HZ1253; DRpunkt4=HZ1254; DRpunkt5=HZ1255; N=5; DRpunkt=10*log10(1/N*(10.^(DRpunkt1./10)+10.^(DRpunkt2./10)+10.^(DRpunkt3./10)+10.^(DRpunkt4./10)+10.^(DRpunkt5./10))); avDRpunkt=sum(DRpunkt)/13; E=DRpunkt-avDRpunkt; DDreal=HZ125fb; Dreal=DDreal-E; DOreal=HZ125ft;

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avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal125f=Dreal-avDreal; %normalization norm_DOreal125f=DOreal-avDOreal; norm_DDreal125f=DDreal-avDDreal; difference125Hzbasementfan=norm_Dreal125f-norm_DOreal125f; difference125Hzbfutan=norm_DDreal125f-norm_DOreal125f; diffav125bf=sum(abs(difference125Hzbasementfan))/13 %calculate average difference from reference diffav125bfu=sum(abs(difference125Hzbfutan))/13 %calculate average difference from reference %125 Hz plot dirplot(LP,E,'b') title('Correction factor 125 Hertz basement') legend('replacement','side-by-side') %250 Hz dipole DRpunkt=HZ250mb; avDRpunkt=sum(HZ250mb)/13; E=DRpunkt-avDRpunkt; DDreal=HZ250db; Dreal=DDreal-E; DOreal=HZ250dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal250d=Dreal-avDreal; %normalization norm_DOreal250d=DOreal-avDOreal; norm_DDreal250d=DDreal-avDDreal; difference250Hzdipolebasement=norm_Dreal250d-norm_DOreal250d; difference250Hzdbutan=norm_DDreal250d-norm_DOreal250d; diffav250bd=sum(abs(difference250Hzdipolebasement))/13 %calculate average difference from reference diffav250bdu=sum(abs(difference250Hzdbutan))/13 %calculate average difference from reference %250 Hz plot figure (2) dirplot(LP,E,'r',[6 -10 8]) hold on %250 Hz fan DRpunkt1=HZ2501; DRpunkt2=HZ2502; DRpunkt3=HZ2503; DRpunkt4=HZ2504; DRpunkt5=HZ2505; N=5; DRpunkt=10*log10(1/N*(10.^(DRpunkt1./10)+10.^(DRpunkt2./10)+10.^(DRpunkt3./10)+10.^(DRpunkt4./10)+10.^(DRpunkt5./10))); avDRpunkt=sum(DRpunkt)/13;

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E=DRpunkt-avDRpunkt; DDreal=HZ250fb; Dreal=DDreal-E; DOreal=HZ250ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal250f=Dreal-avDreal; %normalization norm_DOreal250f=DOreal-avDOreal; norm_DDreal250f=DDreal-avDDreal; difference250Hzbasementfan=norm_Dreal250f-norm_DOreal250f; difference250Hzbfutan=norm_DDreal250f-norm_DOreal250f; diffav250bf=sum(abs(difference250Hzbasementfan))/13 %calculate average difference from reference diffav250bfu=sum(abs(difference250Hzbfutan))/13 %calculate average difference from reference %250 Hz plot dirplot(LP,E,'b') title('Correction factor 250 Hertz basement') legend('replacement','side-by-side') %500 Hz dipole DRpunkt=HZ500mb; avDRpunkt=sum(HZ500mb)/13; E=DRpunkt-avDRpunkt; DDreal=HZ500db; Dreal=DDreal-E; DOreal=HZ500dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal500d=Dreal-avDreal; %normalization norm_DOreal500d=DOreal-avDOreal; norm_DDreal500d=DDreal-avDDreal; difference500Hzdipolebasement=norm_Dreal500d-norm_DOreal500d; difference500Hzdbutan=norm_DDreal500d-norm_DOreal500d; diffav500bd=sum(abs(difference500Hzdipolebasement))/13 %calculate average difference from reference diffav500bdu=sum(abs(difference500Hzdbutan))/13 %calculate average difference from reference %500 Hz plot figure (3) dirplot(LP,E,'r',[6 -10 8]) hold on %500 Hz fan DRpunkt1=HZ5001; DRpunkt2=HZ5002; DRpunkt3=HZ5003; DRpunkt4=HZ5004;

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DRpunkt5=HZ5005; N=5; DRpunkt=10*log10(1/N*(10.^(DRpunkt1./10)+10.^(DRpunkt2./10)+10.^(DRpunkt3./10)+10.^(DRpunkt4./10)+10.^(DRpunkt5./10))); avDRpunkt=sum(DRpunkt)/13; E=DRpunkt-avDRpunkt; DDreal=HZ500fb; Dreal=DDreal-E; DOreal=HZ500ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal500f=Dreal-avDreal; %normalization norm_DOreal500f=DOreal-avDOreal; norm_DDreal500f=DDreal-avDDreal; difference500Hzbasementfan=norm_Dreal500f-norm_DOreal500f; difference500Hzbfutan=norm_DDreal500f-norm_DOreal500f; diffav500bf=sum(abs(difference500Hzbasementfan))/13 %calculate average difference from reference diffav500bfu=sum(abs(difference500Hzbfutan))/13 %calculate average difference from reference %500 Hz plot dirplot(LP,E,'b') title('Correction factor 500 Hertz basement') legend('replacement','side-by-side') %1000 Hz dipole DRpunkt=HZ1000mb; avDRpunkt=sum(HZ1000mb)/13; E=DRpunkt-avDRpunkt; DDreal=HZ1000db; Dreal=DDreal-E; DOreal=HZ1000dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal1000d=Dreal-avDreal; %normalization norm_DOreal1000d=DOreal-avDOreal; norm_DDreal1000d=DDreal-avDDreal; difference1000Hzdipolebasement=norm_Dreal1000d-norm_DOreal1000d; difference1000Hzdbutan=norm_DDreal1000d-norm_DOreal1000d; diffav1000bd=sum(abs(difference1000Hzdipolebasement))/13 %calculate average difference from reference diffav1000bdu=sum(abs(difference1000Hzdbutan))/13 %calculate average difference from reference %1000 Hz plot figure (4) dirplot(LP,E,'r',[6 -10 8])

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hold on % %1000 Hz fan DRpunkt1=HZ10001; DRpunkt2=HZ10002; DRpunkt3=HZ10003; DRpunkt4=HZ10004; DRpunkt5=HZ10005; N=5; DRpunkt=10*log10(1/N*(10.^(DRpunkt1./10)+10.^(DRpunkt2./10)+10.^(DRpunkt3./10)+10.^(DRpunkt4./10)+10.^(DRpunkt5./10))); avDRpunkt=sum(DRpunkt)/13; E=DRpunkt-avDRpunkt; DDreal=HZ1000fb; Dreal=DDreal-E; DOreal=HZ1000ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal1000f=Dreal-avDreal; %normalization norm_DOreal1000f=DOreal-avDOreal; norm_DDreal1000f=DDreal-avDDreal; difference1000Hzbasementfan=norm_Dreal1000f-norm_DOreal1000f; difference1000Hzbfutan=norm_DDreal1000f-norm_DOreal1000f; diffav1000bf=sum(abs(difference1000Hzbasementfan))/13 %calculate average difference from reference diffav1000bfu=sum(abs(difference1000Hzbfutan))/13 %calculate average difference from reference %1000 Hz plot dirplot(LP,E,'b') title('Correction factor 1000 Hertz basement') legend('replacement','side-by-side') %2000 Hz dipole DRpunkt=HZ2000mb; avDRpunkt=sum(HZ2000mb)/13; E=DRpunkt-avDRpunkt; DDreal=HZ2000db; Dreal=DDreal-E; DOreal=HZ2000dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal2000d=Dreal-avDreal; %normalization norm_DOreal2000d=DOreal-avDOreal; norm_DDreal2000d=DDreal-avDDreal; difference2000Hzdipolebasement=norm_Dreal2000d-norm_DOreal2000d; difference2000Hzdbutan=norm_DDreal2000d-norm_DOreal2000d; diffav2000bd=sum(abs(difference2000Hzdipolebasement))/13 %calculate average difference from reference

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diffav2000bdu=sum(abs(difference2000Hzdbutan))/13 %calculate average difference from reference %2000 Hz plot figure (5) dirplot(LP,E,'r',[6 -10 8]) hold on %2000 Hz fan DRpunkt1=HZ20001; DRpunkt2=HZ20002; DRpunkt3=HZ20003; DRpunkt4=HZ20004; DRpunkt5=HZ20005; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; N=5; DRpunkt=10*log10(1/N*(10.^(DRpunkt1./10)+10.^(DRpunkt2./10)+10.^(DRpunkt3./10)+10.^(DRpunkt4./10)+10.^(DRpunkt5./10))); avDRpunkt=sum(DRpunkt)/13; E=DRpunkt-avDRpunkt; DDreal=HZ2000fb; Dreal=DDreal-E; DOreal=HZ2000ft; norm_Dreal2000f=Dreal-avDreal; %normalization norm_DOreal2000f=DOreal-avDOreal; norm_DDreal2000f=DDreal-avDDreal; difference2000Hzbasementfan=norm_Dreal2000f-norm_DOreal2000f difference2000Hzbfutan=norm_DDreal2000f-norm_DOreal2000f diffav2000bf=sum(abs(difference2000Hzbasementfan))/13 %calculate average difference from reference diffav2000bfu=sum(abs(difference2000Hzbfutan))/13 %calculate average difference from reference %2000 Hz plot dirplot(LP,E,'b') title('Correction factor 2000 Hertz basement') legend('replacement','side-by-side') %comparison %2000 Hz figure (16) dirplot(LP,difference125Hzdipolebasement,'b') hold on dirplot(LP,difference125Hzdbutan,'r') dirplot(LP,norm_DOreal125d-norm_DOreal125d,'g') title('Effect of compensation, 125 Hz basement dipole') legend('compensated','measured', 'reference')

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figure (17) dirplot(LP,difference125Hzbasementfan,'b') hold on dirplot(LP,difference125Hzbfutan,'r') dirplot(LP,norm_DOreal125f-norm_DOreal125f,'g') title('Effect of compensation, 125 Hz basement fan') legend('compensated','measured', 'reference') figure (18) dirplot(LP,difference250Hzdipolebasement,'b',[6 -10 8]) hold on dirplot(LP,difference250Hzdbutan,'r') dirplot(LP,norm_DOreal250d-norm_DOreal250d,'g') title('Effect of compensation, 250 Hz basement dipole') legend('compensated','measured', 'reference') figure (19) dirplot(LP,difference250Hzbasementfan,'b',[6 -10 8]) hold on dirplot(LP,difference250Hzbfutan,'r') dirplot(LP,norm_DOreal250f-norm_DOreal250f,'g') title('Effect of compensation, 250 Hz basement fan') legend('compensated','measured', 'reference') figure (20) dirplot(LP,difference500Hzdipolebasement,'b',[6 -10 8]) hold on dirplot(LP,difference500Hzdbutan,'r') dirplot(LP,norm_DOreal500d-norm_DOreal500d,'g') title('Effect of compensation, 500 Hz basement dipole') legend('compensated','measured', 'reference') figure (21) dirplot(LP,difference500Hzbasementfan,'b',[6 -10 8]) hold on dirplot(LP,difference500Hzbfutan,'r') dirplot(LP,norm_DOreal500f-norm_DOreal500f,'g') title('Effect of compensation, 500 Hz basement fan') legend('compensated','measured', 'reference') figure (22) dirplot(LP,difference1000Hzdipolebasement,'b',[6 -10 8]) hold on dirplot(LP,difference1000Hzdbutan,'r') dirplot(LP,norm_DOreal1000d-norm_DOreal1000d,'g')

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title('Effect of compensation, 1000 Hz basement dipole') legend('compensated','measured', 'reference') figure (23) dirplot(LP,difference1000Hzbasementfan,'b') hold on dirplot(LP,difference1000Hzbfutan,'r') dirplot(LP,norm_DOreal1000f-norm_DOreal1000f,'g') title('Effect of compensation, 1000 Hz basement fan') legend('compensated','measured', 'reference') figure (24) dirplot(LP,difference2000Hzdipolebasement,'b',[6 -10 8]) hold on dirplot(LP,difference2000Hzdbutan,'r') dirplot(LP,norm_DOreal2000d-norm_DOreal2000d,'g') title('Effect of compensation, 2000 Hz basement dipole') legend('compensated','measured', 'reference') figure (25) dirplot(LP,difference2000Hzbasementfan,'b') hold on dirplot(LP,difference2000Hzbfutan,'r') dirplot(LP,norm_DOreal2000d-norm_DOreal2000d,'g') title('Effect of compensation, 2000 Hz basement fan') legend('compensated','measured', 'reference')

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Appendix 3. Matlab code classroom close all global LP HZ125fb HZ250fb HZ500fb HZ1000fb HZ2000fb HZ125ft HZ250ft HZ500ft HZ1000ft HZ2000ft HZ125fc HZ250fc HZ500fc HZ1000fc HZ2000fc HZ125mc HZ250mc HZ500mc HZ1000mc HZ2000mc HZ125mb HZ250mb HZ500mb HZ1000mb HZ2000mb HZ125dt HZ250dt HZ500dt HZ1000dt HZ2000dt HZ125db HZ250db HZ500db HZ1000db HZ2000db HZ125dc HZ250dc HZ500dc HZ1000dc HZ2000dc HZ1251 HZ2501 HZ5001 HZ10001 HZ20001 HZ1252 HZ2502 HZ5002 HZ10002 HZ20002 HZ1253 HZ2503 HZ5003 HZ10003 HZ20003 HZ1254 HZ2504 HZ5004 HZ10004 HZ20004 HZ1255 HZ2505 HZ5005 HZ10005 HZ20005 %classroom % beräkning E=DRpunkt-average(DRpunkt) för frekvenser. %125 Hz dipole DRpunkt=HZ125mc; avDRpunkt=sum(HZ125mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ125dc; Dreal=DDreal-E; DOreal=HZ125dt; avDDreal=sum(DDreal)/13; %average per Hz over all angles avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal125d=Dreal-avDreal; %normalization norm_DOreal125d=DOreal-avDOreal; norm_DDreal125d=DDreal-avDDreal; difference125Hzdipoleclassroom=norm_Dreal125d-norm_DOreal125d; difference125Hzdcutan=norm_DDreal125d-norm_DOreal125d; diffav125cd=sum(abs(difference125Hzdipoleclassroom))/13 %calculate average difference from reference diffav125cdu=sum(abs(difference125Hzdcutan))/13 %calculate average difference from reference %125 Hz fan DRpunkt=HZ125mc; avDRpunkt=sum(HZ125mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ125fc; Dreal=DDreal-E; DOreal=HZ125ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal125f=Dreal-avDreal; %normalization norm_DOreal125f=DOreal-avDOreal; norm_DDreal125f=DDreal-avDDreal; difference125Hzclassroomfan=norm_Dreal125f-norm_DOreal125f; difference125Hzcfutan=norm_DDreal125f-norm_DOreal125f; diffav125cf=sum(abs(difference125Hzclassroomfan))/13 %calculate average difference from reference

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diffav125cfu=sum(abs(difference125Hzcfutan))/13 %calculate average difference from reference %125 Hz plot figure (1) dirplot(LP,E,'r',[6 -6 12]) title('Correction factor 125 Hertz classroom') legend('replacement') %250 Hz dipole DRpunkt=HZ250mc; avDRpunkt=sum(HZ250mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ250dc; Dreal=DDreal-E; DOreal=HZ250dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal250d=Dreal-avDreal; %normalization norm_DOreal250d=DOreal-avDOreal; norm_DDreal250d=DDreal-avDDreal; difference250Hzdipoleclassroom=norm_Dreal250d-norm_DOreal250d; difference250Hzdcutan=norm_DDreal250d-norm_DOreal250d; diffav250cd=sum(abs(difference250Hzdipoleclassroom))/13 %calculate average difference from reference diffav250cdu=sum(abs(difference250Hzdcutan))/13 %calculate average difference from reference %250 Hz fan DRpunkt=HZ250mc; avDRpunkt=sum(HZ250mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ250fc; Dreal=DDreal-E; DOreal=HZ250ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal250f=Dreal-avDreal; %normalization norm_DOreal250f=DOreal-avDOreal; norm_DDreal250f=DDreal-avDDreal; difference250Hzclassroomfan=norm_Dreal250f-norm_DOreal250f; difference250Hzcfutan=norm_DDreal250f-norm_DOreal250f; diffav250cf=sum(abs(difference250Hzclassroomfan))/13 %calculate average difference from reference diffav250cfu=sum(abs(difference250Hzcfutan))/13 %calculate average difference from reference %250 Hz plot figure (2) dirplot(LP,E,'r',[6 -6 12]) title('Correction factor 250 Hertz classroom')

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legend('replacement') %500 Hz dipole DRpunkt=HZ500mc; avDRpunkt=sum(HZ500mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ500dc; Dreal=DDreal-E; DOreal=HZ500dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal500d=Dreal-avDreal; %normalization norm_DOreal500d=DOreal-avDOreal; norm_DDreal500d=DDreal-avDDreal; difference500Hzdipoleclassroom=norm_Dreal500d-norm_DOreal500d; difference500Hzdcutan=norm_DDreal500d-norm_DOreal500d; diffav500cd=sum(abs(difference500Hzdipoleclassroom))/13 %calculate average difference from reference diffav500cdu=sum(abs(difference500Hzdcutan))/13 %calculate average difference from reference %500 Hz fan DRpunkt=HZ500mc; avDRpunkt=sum(HZ500mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ500fc; Dreal=DDreal-E; DOreal=HZ500ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal500f=Dreal-avDreal; %normalization norm_DOreal500f=DOreal-avDOreal; norm_DDreal500f=DDreal-avDDreal; difference500Hzclassroomfan=norm_Dreal500f-norm_DOreal500f; difference500Hzcfutan=norm_DDreal500f-norm_DOreal500f; diffav500cf=sum(abs(difference500Hzclassroomfan))/13 %calculate average difference from reference diffav500cfu=sum(abs(difference500Hzcfutan))/13 %calculate average difference from reference %500 Hz plot figure (3) dirplot(LP,E,'r',[6 -6 12]) title('Correction factor 500 Hertz classroom') legend('replacement') %1000 Hz dipole DRpunkt=HZ1000mc; avDRpunkt=sum(HZ1000mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ1000dc;

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Dreal=DDreal-E; DOreal=HZ1000dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal1000d=Dreal-avDreal; %normalization norm_DOreal1000d=DOreal-avDOreal; norm_DDreal1000d=DDreal-avDDreal; difference1000Hzdipoleclassroom=norm_Dreal1000d-norm_DOreal1000d; difference1000Hzdcutan=norm_DDreal1000d-norm_DOreal1000d; diffav1000cd=sum(abs(difference1000Hzdipoleclassroom))/13 %calculate average difference from reference diffav1000cdu=sum(abs(difference1000Hzdcutan))/13 %calculate average difference from reference %1000 Hz fan DRpunkt=HZ1000mc; avDRpunkt=sum(HZ1000mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ1000fc; Dreal=DDreal-E; DOreal=HZ1000ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal1000f=Dreal-avDreal; %normalization norm_DOreal1000f=DOreal-avDOreal; norm_DDreal1000f=DDreal-avDDreal; difference1000Hzclassroomfan=norm_Dreal1000f-norm_DOreal1000f; difference1000Hzcfutan=norm_DDreal1000f-norm_DOreal1000f; diffav1000cf=sum(abs(difference1000Hzclassroomfan))/13 %calculate average difference from reference diffav1000cfu=sum(abs(difference1000Hzcfutan))/13 %calculate average difference from reference %1000 Hz plot figure (4) dirplot(LP,E,'r',[6 -6 12]) title('Correction factor 1000 Hertz classroom') legend('replacement') %2000 Hz dipole DRpunkt=HZ2000mc; avDRpunkt=sum(HZ2000mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ2000dc; Dreal=DDreal-E; DOreal=HZ2000dt; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13;

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norm_Dreal2000d=Dreal-avDreal; %normalization norm_DOreal2000d=DOreal-avDOreal; norm_DDreal2000d=DDreal-avDDreal; difference2000Hzdipoleclassroom=norm_Dreal2000d-norm_DOreal2000d; difference2000Hzdcutan=norm_DDreal2000d-norm_DOreal2000d; diffav2000cd=sum(abs(difference2000Hzdipoleclassroom))/13 %calculate average difference from reference diffav2000cdu=sum(abs(difference2000Hzdcutan))/13 %calculate average difference from reference %2000 Hz fan DRpunkt=HZ2000mc; avDRpunkt=sum(HZ2000mc)/13; E=DRpunkt-avDRpunkt; DDreal=HZ2000fc; Dreal=DDreal-E; DOreal=HZ2000ft; avDDreal=sum(DDreal)/13; avDreal=sum(Dreal)/13; avDOreal=sum(DOreal)/13; norm_Dreal2000f=Dreal-avDreal; %normalization norm_DOreal2000f=DOreal-avDOreal; norm_DDreal2000f=DDreal-avDDreal; difference2000Hzclassroomfan=norm_Dreal2000f-norm_DOreal2000f; difference2000Hzcfutan=norm_DDreal2000f-norm_DOreal2000f; diffav2000cf=sum(abs(difference2000Hzclassroomfan))/13 %calculate average difference from reference diffav2000cfu=sum(abs(difference2000Hzcfutan))/13 %calculate average difference from reference %2000 Hz plot figure (5) dirplot(LP,E,'r',[6 -6 12]) title('Correction factor 2000 Hertz classroom') legend('replacement') %comparison effect figure (16) dirplot(LP,difference125Hzdipoleclassroom,'b',[6 -10 8]) hold on dirplot(LP,difference125Hzdcutan,'r') dirplot(LP,norm_DOreal125d-norm_DOreal125d,'g') title('Effect of compensation, 125 Hz classroom dipole') legend('compensated','measured', 'reference') figure (17) dirplot(LP,difference125Hzclassroomfan,'b') hold on dirplot(LP,difference125Hzcfutan,'r') dirplot(LP,norm_DOreal125f-norm_DOreal125f,'g') title('Effect of compensation, 125 Hz classroom fan')

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legend('compensated','measured', 'reference') figure (18) dirplot(LP,difference250Hzdipoleclassroom,'b',[6 -10 8]) hold on dirplot(LP,difference250Hzdcutan,'r') dirplot(LP,norm_DOreal250d-norm_DOreal250d,'g') title('Effect of compensation, 250 Hz classroom dipole') legend('compensated','measured', 'reference') figure (19) dirplot(LP,difference250Hzclassroomfan,'b',[6 -10 8]) hold on dirplot(LP,difference250Hzcfutan,'r') dirplot(LP,norm_DOreal250f-norm_DOreal250f,'g') title('Effect of compensation, 250 Hz classroom fan') legend('compensated','measured', 'reference') figure (20) dirplot(LP,difference500Hzdipoleclassroom,'b',[6 -10 8]) hold on dirplot(LP,difference500Hzdcutan,'r') dirplot(LP,norm_DOreal500d-norm_DOreal500d,'g') title('Effect of compensation, 500 Hz classroom dipole') legend('compensated','measured', 'reference') figure (21) dirplot(LP,difference500Hzclassroomfan,'b',[6 -10 8]) hold on dirplot(LP,difference500Hzcfutan,'r') dirplot(LP,norm_DOreal500f-norm_DOreal500f,'g') title('Effect of compensation, 500 Hz classroom fan') legend('compensated','measured', 'reference') figure (22) dirplot(LP,difference1000Hzdipoleclassroom,'b',[6 -10 8]) hold on dirplot(LP,difference1000Hzdcutan,'r') dirplot(LP,norm_DOreal1000d-norm_DOreal1000d,'g') title('Effect of compensation, 1000 Hz classroom dipole') legend('compensated','measured', 'reference') figure (23) dirplot(LP,difference1000Hzclassroomfan,'b',[6 -10 8]) hold on dirplot(LP,difference1000Hzcfutan,'r')

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dirplot(LP,norm_DOreal1000f-norm_DOreal1000f,'g') title('Effect of compensation, 1000 Hz classroom fan') legend('compensated','measured', 'reference') figure (24) dirplot(LP,difference2000Hzdipoleclassroom,'b',[6 -10 8]) hold on dirplot(LP,difference2000Hzdcutan,'r') dirplot(LP,norm_DOreal2000d-norm_DOreal2000d,'g') title('Effect of compensation, 2000 Hz classroom dipole') legend('compensated','measured', 'reference') figure (25) dirplot(LP,difference2000Hzclassroomfan,'b',[6 -10 8]) hold on dirplot(LP,difference2000Hzcfutan,'r') dirplot(LP,norm_DOreal2000d-norm_DOreal2000d,'g') title('Effect of compensation, 2000 Hz classroom fan') legend('compensated','measured', 'reference')

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Appendix 4. Matlab function dirplot function hpol = dirplot(theta,rho,line_style,params) % DIRPLOT Polar directivity plot. % A modification of The Mathworks POLAR function, DIRPLOT generates % directivity plots in the style commonly used in acoustic and RF work. % Features include: % 1. Plots -90 to +90 or -180 to +180 degrees based on range of input % THETA, with 0 degrees at top center. % 2. Produces semicircular plots when plot range is -90 to +90 degrees. % 3. RHO is assumed to be in decibels and may include negative % values. % 4. Default automatic rho-axis scaling in "scope knob" factors. % 5. Optional PARAMS argument allows manual setting of rho-axis % scaling. % % DIRPLOT(THETA, RHO) makes a plot using polar coordinates of the % angle THETA versus the radius RHO. THETA must be in degrees, and % must be within the range -180 to +180 degrees. If THETA is within % the range -90 to +90 degrees, the plot will be semicircular. RHO is % assumed to be in decibels and the values may be positive or negative or % both. By default, with no PARAMS argument, rho-axis scaling will be determined % automatically using scope knob factors of 1-2-5. By default, 10 % ticks will be plotted. Note: Like POLAR, DIRPLOT does not rescale the % axes when a new plot is added to a held graph. % % DIRPLOT(THETA, RHO, LINE_STYLE, PARAMS) makes a plot as described above % using the linestyle specified in string LINE_STYLE, and using the rho-axis % scaling specified in vector PARAMS. Either of these optional arguments may be % used alone. Vector PARAMS is a 3-element row vector defined as % [RHOMAX RHOMIN RHOTICKS]. String LINE_STYLE is the standard MATLAB linestyle % string. See PLOT for a description. % % HPOL = DIRPLOT(...) returns a handle to the LINE object generated by the PLOT % function that actually generates the plot in DIRPLOT. % % See also POLAR, PLOT, LOGLOG, SEMILOGX, SEMILOGY. % % Tested in MATLAB v. 6.0 (R12) % % Revision History % 18 January 2014: Fixed a bug that caused RHO to be plotted incorrectly if % RHOMIN was specified, and RHO was less than RHOMIN. Thanks to Wajih Elsallal. % 11 June 2012: Changed contact email address only % 18 January 2002: Original posting

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% % Adapted from The MathWorks POLAR function by % Steve Rickman % [email protected] if nargin <= 1 error('Requires 2, 3, or 4 input arguments.') elseif nargin == 2 line_style = 'auto'; elseif nargin == 3 if isnumeric(line_style) params = line_style; line_style = 'auto'; end end if exist('params') if length(params) ~= 3 error('Argument PARAMS must be a 3-element vector: [RHOMAX RHOMIN RHOTICKS].') end if params(1) <= params(2) error('Error in PARAMS argument. RHOMAX must be greater than RHOMIN.') end if params(3) <= 0 params(3) = 1; warning('Error in PARAMS argument. RTICKS set to 1.') end end if isstr(theta) | isstr(rho) error('THETA and RHO must be numeric.'); end if ~isequal(size(theta),size(rho)) error('THETA and RHO must be the same size.'); end if (max(theta) - min(theta)) < 6.3 warning('THETA must be in degrees'); end if min(theta) >= 0 warning('Plot is -90 to +90 or -180 to +180 degrees'); end if max(abs(theta)) > 180 error('Plot is -90 to +90 or -180 to +180 degrees'); end % Get range of theta and set flag for full or half plot. if (max(theta)-min(theta)) > 180 | max(theta) > 90 fullplot = 1; else fullplot = 0; end % Translate theta degrees to radians theta = theta*pi/180; cax = newplot; next = lower(get(cax,'NextPlot')); hold_state = ishold;

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if hold_state & exist('params') warning('Plot is held. New plot parameters ignored') end % get x-axis text color so grid is in same color tc = get(cax,'xcolor'); ls = get(cax,'gridlinestyle'); % Hold on to current Text defaults, reset them to the % Axes' font attributes so tick marks use them. fAngle = get(cax, 'DefaultTextFontAngle'); fName = get(cax, 'DefaultTextFontName'); fSize = get(cax, 'DefaultTextFontSize'); fWeight = get(cax, 'DefaultTextFontWeight'); fUnits = get(cax, 'DefaultTextUnits'); set(cax, 'DefaultTextFontAngle', get(cax, 'FontAngle'), ... 'DefaultTextFontName', get(cax, 'FontName'), ... 'DefaultTextFontSize', get(cax, 'FontSize'), ... 'DefaultTextFontWeight', get(cax, 'FontWeight'), ... 'DefaultTextUnits','data') % only do grids if hold is off if ~hold_state % make a radial grid hold on; if ~exist('params') rticks = 10; % default ticks lims = findscale(rho,rticks); % get click, rmax, rmin click = lims(1); rmax = lims(2); rmin = lims(3); rngdisp = rmax - rmin; else rmax = params(1); rmin = params(2); rticks = params(3); rngdisp = rmax - rmin; click = rngdisp/rticks; % clip the data where RHO<rmin (bug fix Jan 2014) [m,n] = find(rho<rmin); rho(m,n) = rmin; end set(cax,'userdata',[rngdisp rmax rmin]); % save variables for added plots % define a circle th = 0:pi/50:2*pi; xunit = cos(th); yunit = sin(th); % now really force points on x/y axes to lie on them exactly inds = 1:(length(th)-1)/4:length(th); xunit(inds(2:2:4)) = zeros(2,1); yunit(inds(1:2:5)) = zeros(3,1); % plot background if necessary if ~isstr(get(cax,'color')), patch('xdata',xunit*rngdisp,'ydata',yunit*rngdisp, ... 'edgecolor',tc,'facecolor',get(gca,'color'),... 'handlevisibility','off'); end

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% draw radial circles % angles for text labels c88 = cos(88*pi/180); s88 = sin(88*pi/180); c92 = -cos(92*pi/180); s92 = -sin(92*pi/180); for i=click:click:rngdisp tickt = i+rmin; if abs(tickt) < .001 tickt = 0; end ticktext = ['' num2str(tickt)]; hhh = plot(xunit*i,yunit*i,ls,'color',tc,'linewidth',1,... 'handlevisibility','off'); if i < rngdisp text(i*c88,i*s88, ... ticktext,'verticalalignment','bottom',... 'handlevisibility','off','fontsize',8) else text(i*c88,i*s88, ... [ticktext,' dB'],'verticalalignment','bottom',... 'handlevisibility','off','fontsize',8) end if fullplot if i < rngdisp text(i*c92,i*s92, ... ticktext,'verticalalignment','bottom',... 'handlevisibility','off','fontsize',8) else text(i*c92,i*s92, ... [ticktext,' dB'],'verticalalignment','bottom',... 'handlevisibility','off','fontsize',8) end end end set(hhh,'linestyle','-') % Make outer circle solid % plot spokes at 10 degree intervals th = (0:18)*2*pi/36; cst = cos(th); snt = sin(th); cs = [-cst; cst]; sn = [-snt; snt]; plot(rngdisp*cs,rngdisp*sn,ls,'color',tc,'linewidth',1,... 'handlevisibility','off') % label spokes in 30 degree intervals rt = 1.1*rngdisp; for i = 1:3:19 text(rt*cst(i),rt*snt(i),[int2str(90-(i-1)*10),'ô'],... 'horizontalalignment','center',... 'handlevisibility','off'); end if fullplot for i = 3:3:6

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text(-rt*cst(i+1),-rt*snt(i+1),[int2str(-90-i*10),'ô'],... 'horizontalalignment','center',... 'handlevisibility','off'); end for i = 9:3:15 text(-rt*cst(i+1),-rt*snt(i+1),[int2str(270-i*10),'ô'],... 'horizontalalignment','center',... 'handlevisibility','off'); end end % set view to 2-D view(2); % set axis limits if fullplot axis(rngdisp*[-1 1 -1.15 1.15]); else axis(rngdisp*[-1 1 0 1.15]); end end if hold_state v = get(cax,'userdata'); rngdisp = v(1); rmax = v(2); rmin = v(3); end % Reset defaults. set(cax, 'DefaultTextFontAngle', fAngle , ... 'DefaultTextFontName', fName , ... 'DefaultTextFontSize', fSize, ... 'DefaultTextFontWeight', fWeight, ... 'DefaultTextUnits',fUnits ); % transform data to Cartesian coordinates. % Rotate by pi/2 to get 0 degrees at top. Use negative % theta to have negative degrees on left. xx = (rho+rngdisp-rmax).*cos(-theta+pi/2); yy = (rho+rngdisp-rmax).*sin(-theta+pi/2); % plot data on top of grid if strcmp(line_style,'auto') q = plot(xx,yy); else q = plot(xx,yy,line_style); end if nargout > 0 hpol = q; end set(gca,'dataaspectratio',[1 1 1]), axis off; set(cax,'NextPlot',next); set(get(gca,'xlabel'),'visible','on') set(get(gca,'ylabel'),'visible','on') % Subfunction finds optimal scaling using "scope knob"

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% factors of 1, 2, 5. Range is limited to practical % decibel values. function lims = findscale(rho, rticks) clicks = [.001 .002 .005 .01 .02 .05 .1 ... .2 .5 1 2 5 10 20 50 100 200 500 1000]; lenclicks = length(clicks); rhi = max(rho); rlo = min(rho); rrng = rhi - rlo; rawclick = rrng/rticks; n = 1; while clicks(n) < rawclick n = n + 1; if n > lenclicks close; error('Cannot autoscale; unrealistic decibel range.'); end end click = clicks(n); m = floor(rhi/click); rmax = click * m; if rhi - rmax ~= 0 rmax = rmax + click; end rmin = rmax - click * rticks; % Check that minimum rho value is at least one tick % above rmin. If not, increase click value and % rescale. if rlo < rmin + click if n < lenclicks click = clicks(n+1); else error('Cannot autoscale; unrealistic decibel range.'); end m = floor(rhi/click); rmax = click * m; if rhi - rmax ~= 0 rmax = rmax + click; end rmin = rmax - click * rticks; end lims = [click rmax rmin];

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Assessment of directivity of real noise sources - Application ...746412/FULLTEXT01.pdfacoustic centre for each object was situated. Thereafter, the room correction factor was Thereafter,