Lab2 Report Group4

8/8/2019 Lab2 Report Group4

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Abstract


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Contents

1 Introduction 1

2 Theory 12.1 Sound pressure level . . . . . . . . . . . . . . . . . . . . . . . 12.2 Octave bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Room acoustics and reverberation . . . . . . . . . . . . . . . . 22.4 Room absorption and absorption coefficients . . . . . . . . . . 2

3 Measurement method and equipment 33.1 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 WinMLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.4 Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Results 64.1 Average absorption factor . . . . . . . . . . . . . . . . . . . . 74.2 Fixed absorption factor . . . . . . . . . . . . . . . . . . . . . . 74.3 Decrease of reverberation time . . . . . . . . . . . . . . . . . . 84.4 Direct sound level . . . . . . . . . . . . . . . . . . . . . . . . . 84.5 Surface materials . . . . . . . . . . . . . . . . . . . . . . . . . 104.6 Diffuse sound eld . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Conclusions 11


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List of Figures

1 Illustration of an impulse response showing direct sound, earlyreections and reverberation . . . . . . . . . . . . . . . . . . . 3

2 Equipment used for measurements . . . . . . . . . . . . . . . . 43 Sketch of EL4 auditorium Elektroblokk B, Glshaugen campus 54 Microphone positions at EL4 . . . . . . . . . . . . . . . . . . . 65 Relative SPL as a function of distance in the 125 Hz to 4kHz

octave bands . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Sketch of an absorber - front view and side view . . . . . . . . 10

List of Tables1 Average absorption factor for each octave band . . . . . . . 72 Average absorption factor rs for the remaining surfaces . . . 73 Different positions and their distance to the loudspeaker / the

ceiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Value table generated by WinMLS for position 1 . . . . . . . . 135 Value table generated by WinMLS for position 2 . . . . . . . . 146 Value table generated by WinMLS for position 3 . . . . . . . . 147 Value table generated by WinMLS for position a . . . . . . . . 148 Value table generated by WinMLS for position b . . . . . . . . 14

9 Value table generated by WinMLS for position c . . . . . . . . 1510 Value table generated by WinMLS for position d . . . . . . . . 1511 Value table generated by WinMLS for position e . . . . . . . . 1512 Value table generated by WinMLS for position f . . . . . . . . 1513 Value table generated by WinMLS for position g . . . . . . . . 1514 Value table generated by WinMLS for position h . . . . . . . . 1615 Value table generated by WinMLS for position i . . . . . . . . 16


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1 Introduction

Room acoustics is an area of acoustic that deals with the behavior of soundin an enclosed space. Reverberation time is an important parameter in roomacoustic analysis. It denes sound persistence in a particular space after thesource is removed. The optimum reverberation time for a room depends onwhich use it is designed for.

The reverb can in fact have negative aspects, such as the risk of mask-ing syllables during a speech, and positive such as the reinforcement of thesources intensity. In this paper the measurement of the reverberation timeof an auditorium and the measurement of relative sound pressure level as afunction of distance are described. A brief introduction to basic concepts of

room acoustic analysis is also presented.

2 Theory

This section gives a basic overview of the theoretical background of recordingpressure levels, frequency selective analysis and room acoustic analysis.

2.1 Sound pressure level

The sound pressure p(x, t ) is the variation in air pressure around the static

air pressure ps so that ptot (x, t ) = ps + p(x, t ). Sound pressure is measured inPascal (Pa). Sound pressure level (SPL) is dened as ten times the logarithmof the ratio between the RMS square of the sound pressure prms and the squareof a reference value pref :

L p = 10 log10 prms 2

pref 2= 20 log10

prms pref

dB (1)

The commonly used reference sound pressure in air is pref = 20 Pa.SPL is measured in decibel (dB). In this paper, there is no calibration andonly relative sound pressure level is measured, as only the changes in soundpressure are relevant.

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2.2 Octave bands

In order to analyse the spectrum of the noise measured, Octave band lteringcan be used. This operation consists of using different lters that each havean octaves width and a central frequency at the corresponding octave centre.An octave is the interval between one musical pitch and another with half ordouble its frequency. The central frequencies of the different octaves are:

63Hz, 125 Hz, 250Hz, 500 Hz, 1 kHz, 2 kHz, 4 kHz, 8 kHz

In this way the signal can be decomposed and analysed, for example inorder to see in which frequency band the noise has its main components.

2.3 Room acoustics and reverberationOne of the main aims of room acoustics is to study reection and absorptionof sound to improve the hearing experience. An important aspect to takeinto account is reverberation. An impulsive sound generated in a room willpersist for a certain time depending on room size, walls materials and shapes.

Reverberation time measures how long the sound remains audible and there-fore gives and indication of how it will mix with the following sound. In anauditorium, for example, a short reverberation time is desirable in order toavoid the masking of syllables. If the persistance of a syllable is too long,

it can mask the sound of the following one making the speech difficult tounderstand.

Reverberation time is generally dened as the time required for reectionsto decay by 60dB below the level of the direct sound. Its usually indicatedas T 60 . In order to calculate T 60 Sabines formula can be used:

T 60 0.161 V

A, (2)

where V is the volume of the room and A is the room absorption.

2.4 Room absorption and absorption coefficients

The absorption properties are strictly dependent on the materials used. Theabsorption coefficient of a material is a number between 0 and 1 which in-dicates the ratio between the absorbed sound and the incident sound. It is

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Figure 1: Illustration of an impulse response showing direct sound, earlyreections and reverberation

generally indicated with . According to Sabines formula, the total absorp-tion in a room can be calculated as:

A = 4mV + S , (3)

where is the average absorption coefficient and S is the total surface of the room. The average absorption coefficient can be described as:

= iS i i

S tot, (4)

where S i are the different surfaces of walls ceiling and oor, and i are therespective absorption coefficients. To modify the absorption of a room, andtherefore the reverberation time, panels with different absorption coefficientscan be used to cover ceiling and walls.

3 Measurement method and equipment

The laboratorys task is to perform measurements in an auditorium using theWinMLS measurement system. The recordings are done using microphone,

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an amplier, a laptop computer and a loudspeaker. Analysis of the recordings

is performed using the WinMLS software.

3.1 Equipment

For recording, a microphone, an amplierand a laptop computer are used.The microphone shown in gure 2(a) is a Norsonic Type 1206 microphone,which is connected to the amplifer. All measurements are performed withthe microphone facing upwards. Figure 2(b) shows the Norsonic Type 336amplifer that is used to amplify the microphones output. All measurementsexcept for one are performed with a 30 dB gain in order to achieve a highsignal-to-noise ratio.

(a) Norsonic Type 1206 microphone (b) Norsonic Type 336 amplier

(c) Genelec Active Monitor Model 1029A

Figure 2: Equipment used for measurements

The loudspeaker shown in gure 2(c) is a Genelec Active Monitor Model

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1029A and has a built-in amplier. The laptop computer is used to control

both microphone input and loudspeaker output with the WinMLS measure-ment software.

3.2 WinMLS

WinMLS measures impulse or frequency responses and transfer functionsusing a computer and a sound card. For this exercise, predened settings areloaded. The measurement type is swept sine with a duration of 20 seconds permeasurement. In addition, WinMLS is used to calculate the reverberationtime and the relative sound pressure level.

3.3 Room

The room chosen for the measurements is the EL4 auditorium ElektroblokkB, Glshaugen campus. It is a small auditorium with seven rows of sevenchairs each. The higher the distance from the rows to the lectern, the moreelevated the rows are, as shown in gure 3.

Figure 3: Sketch of EL4 auditorium Elektroblokk B, Glshaugen campus

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3.4 Positions

The measurements are performed at nine different microphone positionswhich are shown in gure 4. At each position, one measurement was per-formed for 20 seconds. All measurement results can be found in appendixA.

Figure 4: Microphone positions at EL4

4 Results

Preliminary to other calculations, the auditoriums geometrical propertieshave to be calculated. The dimensions are taken from gure 3.

S tot = 218 , 867m2 (5)

S chair = 33 , 422m2 (6)

V = 174 , 286m3 (7)

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4.1 Average absorption factor

Table 1 shows the average absorption factors in the room for each octaveband. WinMLS calculates only T 30 values, as T 60 are difficult to obtain inpraxis. Nevertheless, T 60 values can be attained by a multiplication with thefactor 2. This results in a slightly altered version of Sabines equation:

T 30 =0, 0805 sm V

S tot (8)

=0, 0805 sm V

S tot T 30(9)

Table 1: Average absorption factor for each octave bandOctave Band 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 5 kHz

Average absorption factor 0.078 0.121 0.132 0.134 0.135 0.140

4.2 Fixed absorption factor

Asumming that the chair (sloped) surface has an absorption factor of 0.7, the average absorption factor for the remaining surfaces is calculated.The calculations are performed for each octave band according to Sabinesformulad. The resulting absorption factors can be found in table 2.

= iS i i

S tot(10)

rs = S tot chair S chair

S rs(11)

Table 2: Average absorption factor rs for the remaining surfacesOctave Band 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 5 kHz

Average absorption factor rs -0.034 0.017 0.029 0.031 0.034 0.04

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4.3 Decrease of reverberation time

In the 1 kHz octave band, the average reveberation time T 60 is 0.96 seconds.This reverberation time is to be lowered to 0.5 seconds using sound absorberswith different absorption coefficients from 0.3 to 0.9. It is assumed that thechair surface still has an of 0.7 and that sound absorbers are used for theceiling only. Everything else is assumed to have a xed absorption value of 0.031, which is the average absorption factor of the room in the 1 kHz octaveband according to table 1.

T 60 =0.161 sm V

S tot (12)

= iS i i

S tot(13)

T 60 =0.161 sm V

iS i i

=0.161 sm V

S chair chair + S rest rest + S ceiling ceiling(14)

ceiling =

0.161 sm

V T 60

S chair chair S rest rest

S ceiling(15)

ceiling =

0.161 sm

174 .286m 3

0.5 s 33, 422m2 0.7 121.325m2 0.031

64.12= 0 .452

(16)Increasing only the ceilings absorption is on of the easiest solutions to in-

crease the average absorption. Of course, there are countless other solutions,for example covering parts of surface sections or use of multiple, varyingabsorber material for a single section.

4.4 Direct sound level

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Figure 5: Relative SPL as a function of distance in the 125 Hz to 4 kHz octavebands

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Figure 6: Sketch of an absorber - front view and side view

4.5 Surface materials

In auditorium EL4 there are two main absorbing surfaces - chairs and ab-sorber on the ceiling. Absorber on the ceiling as shown in gure 6 is perfo-rated material which is typical resonant absorber. Resonant absorbers areusually materials with holes and slots or perforated materials, like in the caseof auditorium EL4.A Resonant absorber is an absorber which is designed to absorb sound in anarrow frequency range. Resonance frequency can be calculated as follows:

f 0 =c

2 S holed S perhole lef f (17)lef f = l +

2

b (18)

S hole - cross section area of the holeS perhole - area behind each holed - distance from the walllef f - effective length of a holeb - radius of a hole

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Having in mind above formulae, f 0 is calculated:

lef f = l +2

b = 3 +2

1.52

= 4 .1781 10 3(m )

S hole =d 2

4= 1 .77 10 6(m 2)

S perhole = 6.52

4= 33 .183 10 6(m 2)

f 0

=344

2 1.77 10 6

0.3 33.183 10 6 4.1781 10 3 357.15(Hz )

4.6 Diffuse sound eld

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5 Conclusions

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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum.Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolorsit amet.Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diamnonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,

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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum.

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Position Distance to speaker gain Distance to ceiling

1 7,05 30 1,12 4,12 30 1,73 1,03 30 1,95

a 7,05 30 1,1b 6,07 30 1,4c 5,09 30 1,61d 4,12 30 1,7e 3,03 30 1,92f 2,01 30 1,95g 1,03 30 1,95h 0,5 30 1,95i 0,25 20 1,95

Table 3: Different positions and their distance to the loudspeaker / the ceiling

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 15,6 26,6 28,5 40,6 47,8 51,2 57,3 56,1 53edr[dB] 27,1 38,1 43,5 56,4 63,7 67 71,7 72,9 70,3EDT[s] 1,23 0,7 0,38 0,27 0,27 0,11 0,08 0,09 0T30[s] 1,33 0,9 0,52 0,47 0,44 0,43 0,42 0,36 0,29corr -1 -0,99 -0,99 -1 -1 -1 -1 -1 -1T20[s] 1,35 0,72 0,44 0,43 0,43 0,45 0,4 0,36 0,31corr -1 -1 -0,98 -1 -1 -0,99 -1 -1 -0,98

Table 4: Value table generated by WinMLS for position 1

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F[Hz] 63 125 250 500 1000 2000 4000 8000 16000

snr[dB] 10,6 20,9 25,7 36,2 42,2 44,9 47 50 43,8edr[dB] 23,1 34,3 42,7 51,3 59,4 60,6 64 65,7 60,2EDT[s] 1,28 0,84 0,38 0,49 0,43 0,47 0,36 0,32 0,17T30[s] 1,37 0,77 0,57 0,48 0,49 0,49 0,47 0,39 0,29corr -0,99 -1 -0,99 -1 -1 -1 -1 -1 -1T20[s] 1,37 0,78 0,53 0,46 0,47 0,48 0,46 0,39 0,27corr -0,99 -1 -0,98 -1 -1 -1 -1 -1 -1r[m] 4,2


F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 16 21,9 22,3 31 39,3 43,1 47,6 47,9 42,1edr[dB] 29,6 36,7 37,6 47,2 54,6 59 63,4 64,4 59,3EDT[s] 1,08 0,79 0,45 0,5 0,34 0,3 0,3 0,21 0,14T30[s] 1,38 0,79 0,5 0,51 0,51 0,5 0,48 0,4 0,31corr -1 -1 -1 -1 -1 -1 -1 -1 -1T20[s] 1,36 0,84 0,51 0,49 0,51 0,49 0,45 0,38 0,29corr -1 -1 -0,99 -1 -1 -1 -1 -1 -0,99r[m] 7,2


F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 16 21,9 22,3 31 39,3 43,1 47,6 47,9 42,1edr[dB] 29,6 36,7 37,6 47,2 54,6 59 63,4 64,4 59,3G[dB] 101,6 101,2 99,2 100,3 105,2 106,4 108,1 108,1 103,4r[m] 7,2

Table 7: Value table generated by WinMLS for position a

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 11,6 22,6 24,9 34,4 41,2 43,2 48,5 48,6 40,5

edr[dB] 27,2 33,1 38,2 50,2 58,1 58,8 63,3 65 58,4G[dB] 97,2 100,3 99,7 103,3 106,7 106,8 108,1 109,3 103,2r[m] 6,2

Table 8: Value table generated by WinMLS for position b

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F[Hz] 63 125 250 500 1000 2000 4000 8000 16000

snr[dB] 11,3 21,8 24,9 36,9 42,4 44,4 49,7 48,7 42,8edr[dB] 23,5 34,3 40 53,3 58,4 60,8 64,7 65,4 59,4G[dB] 96,1 100,8 100,3 104,9 107,1 107,3 109,3 109,1 104r[m] 5,2

Table 9: Value table generated by WinMLS for position c

]

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 11 20,1 26,3 36,1 42,9 43,6 47,9 49,7 44,3edr[dB] 24,1 34 43 52,1 58,2 60,6 64,1 65,5 61,2G[dB] 94,7 100,7 102 104 106,9 108,2 110,2 110,1 105,9

r[m] 4,2Table 10: Value table generated by WinMLS for position d

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 13,8 21,1 26,5 37,7 43,4 47,2 51,8 51,8 47,2edr[dB] 28,6 34,6 41,9 54 60 62,9 66,9 68,3 64,2G[dB] 99,2 101,6 102,1 105,5 108,5 109,1 112,3 112,6 108,7r[m] 3,2

Table 11: Value table generated by WinMLS for position e

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 15,1 21,5 29 38,9 45,5 45,4 52,3 53,5 48,8edr[dB] 28,9 34,7 44,9 56 63,3 62,4 63,7 68,2 65,5G[dB] 99,6 101,6 105,6 107,4 110,8 112,2 114 113,7 110,5r[m] 2,1

Table 12: Value table generated by WinMLS for position f

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 17,1 25,3 29,7 42,5 50,5 54,7 58 57,6 54,4

edr[dB] 27,9 38 44,4 55,4 65,7 69,7 73,2 74 70,8G[dB] 101,5 105,2 108,5 111,2 115,3 117,2 118,9 119 116,1r[m] 1,2

Table 13: Value table generated by WinMLS for position g

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F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 20,1 32,6 38,8 50,8 55,8 56,4 59,8 63,6 60,5edr[dB] 33,2 43,6 50,6 62,1 66,3 72,9 74,6 79,5 77,3G[dB] 105,6 111,2 113,9 116,9 120,6 123,2 124,4 126 123,9r[m] 0,2

Table 14: Value table generated by WinMLS for position h

F[Hz] 63 125 250 500 1000 2000 4000 8000 16000snr[dB] 24,3 38 43 54,5 60,7 64,1 63,6 65,4 61,7edr[dB] 39,7 50,3 60,2 68,1 77,2 75,9 73,5 81,3 78,8G[dB] 101,7 108,6 111,3 113,8 117,5 119,1 117,6 120,1 118,7r[m] 0,4

Table 15: Value table generated by WinMLS for position i

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