Absorción Acústica UNTREF

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Measuring the Absorption Coefficient

Ing. Alejandro [email protected]

www.untref.edu.ar

1

mailto:[email protected]

http://www.untref.edu.ar/

http://www.untref.edu.ar/

mailto:[email protected]



Basic Metrology:•Error:

Diferencia ente el “valor verdadero” y el valor medido.

•Precision:

Hace referencia a la repetibilidad (en el tiempo) del error.•Accuracy (Exactitud):

Es la medida del error que presenta un instrumento.

Exactitud baja.

Precisión alta.

Exactitud alta.

Precisión baja.

Exactitud alta.

Precisión alta.

2



Traditional measurements

Impedance tube: (for small samples)

•ISO 10534-1: 1996 Acoustics – Determination of sound absorption coefficient and

impedance in impedance tubes – Part 1: Method using standing wave method.

•ISO 10534-2: 1998 - Acoustics – Determination of sound absorption coefficient and

impedance in impedance tubes – Part 2: Transfer function method.

3



Absorción

2

1

incidente

reflejada

p

p

mínimaPresión

máximaPresión

1

1 22

1122

1122

ROE

ROE

ROE

cc

cc

I

I

i

r r

4



Impedance tube:

Road surface samples 5



Impedance Tube: Common error

6

(debido al corte incorrecto de las muestras del material - due to bad cutting the material samples)



Impedance Tube:

7

Analyzing road absorption coefficients: portable Impedance Tube.



Traditional measurementsReverberation chamber: (for large samples)

ISO 354:2003 Acoustics – Measurement of sound absorption in a reverberation room.

ASTM C-423 -09a: Standard Test Method for Sound Absorption and Sound Absorption

Coefficients by the Reverberation Room Method

Air Volume 180m3

8Scale reverberation chamber

American Society for Testing

and Materials (ASTM),



Reverberation chamber Absorption Measurement: ISO 354

9

Surface of material: 12m2

Air Volume 180m3

f Schroeder<120Hz

How would you measure (or

demonstrate) low modal density in a

room?



Rev Chamber: ISO 354 – Reverberation room

10

Shape of reverberation room:

The shape of the reverberation room shall be such that the following condition is fulfilled:

Where Imax is the length of the longest straight line which fits within the boundary of the

room (e.g. in a rectangular room it is the major diagonal), in metres;

V is the volume of the room, in cubic metres.

“In order to achieve a uniform distribution of natural frequencies (modes), especially in thelow-frequency bands, no two dimensions of the room shall be in the ratio of small whole

numbers.”

3max 9.1 V I

Diffusion of the sound field:

The decaying sound field in the room shall be sufficiently diffuse. In order to achieve

satisfactory diffusion whatever the shape of the room, the use of stationary or suspendeddiffusers or rotating vanes is, in general, required.

The volume of the reverberation room shall be at least 150 m3. For new constructions, the volume is

strongly recommended to be at least 200 m3. When the volume of the room is greater than about 500

m3, it may not be possible to measure sound absorption accurately at high frequencies because of air

absorption.




11

6.2 Test specimens

6.2.1 Plane absorbers

6.2.1.1 The test specimen shall have an area between 10 m2 and 12 m2. If the volume V of

the room is greater than 200 m3, the upper limit for the test specimen area shall beincreased by the factor (V/200 m3)2/3.

The area to be chosen depends on the room volume and on the absorption capability of

the test specimen.

The larger the room, the larger the test area should be. For specimens with small

absorption coefficient, the upper limit area should be chosen.

6.2.1.2 The test specimen shall be of rectangular shape with a ratio of width to length of

between 0,7 and 1. It should be placed so that no part of it is closer than 1 m to any edge

of the boundary of the room; the distance shall be at least 0,75 m. The edges of the

specimen shall preferably not be parallel to the nearest edge of the room. If necessary,

heavy test specimens may be mounted vertically along the walls of the room, and directly

resting on the floor. In this case, the requirement of at least 0,75 m distance need not be

respected.

6.2.1.3 The test specimen shall be installed in one of the mountings specified in Annex B,

unless the relevant specifications provided by the producer or the application details

provided by the user require a different mounting. The measurement of the reverberation

time of the empty room shall be made in the absence of the frame or the side walls of the

test specimen except for the barrier around a Type J mounting.




12

7.1.2 Microphones and microphone positions

The directivity characteristic of the microphones used for the measurement shall be

omnidirectional. The measurements shall be made with different microphone positionswhich are at least 1,5 m apart, 2 m from any sound source and 1 m from any room

surface and the test specimen. Decay curves measured at different microphone positions

shall not be combined in any way.

7.1.3 Source positions

The sound in the reverberation room shall be generated by a sound source with anomnidirectional radiation pattern. Different sound source positions which are at least 3

m apart shall be used.

7.1.4 Number of microphone and loudspeaker positions

The number of spatially independent measured decay curves shall be at least 12.

Therefore the number of microphone positions times the number of sound source

positions shall be at least 12. The minimum number of microphone positions shall be

three, the minimum number of sound source positions shall be two . It is permissible to

use more than one sound source simultaneously provided the difference in the radiated

power is within a tolerance band of 3 dB for each one-third-octave band. If more than

one sound source is used for excitation simultaneously, the number of spatially

independent measured decay curves may be reduced to six.



Medición del Coeficiente de Absorción

3

1

3

1

3

1

max

4:2:1: _

9.1

sugeridas Dim

V L Segundo

s5 5 5 4.5 3.5 2

Hertz 125 250 500 1K 2K 4K

RT60:

Cámara reverberante

13



Repetitividad y Reproducibilidad

14

The standard defines repeatability as the “value below which the absolute difference

between two single test results obtained with the same method on identical test

material, under the same conditions can be expected to lie with a probability of 95 %.”*1+

The reproducibility is the “value below which the absolute difference between two

single test results obtained with the same method on identical test material in a

different laboratory may be expected to lie with a probability of 95%.”

[1]: ASTMC423, Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the

Reverberation Room Method. 2002, ASTM International.

n

i

in

t r 1

2

1

12 Anexo C de ISO354

t : Factor de la distribución de Student.

t = 2.78 para n = 5;

t = 2.23 para n = 10;

n: cantidad de mediciones.



Repetitividad: valores de ejemplo

15



ISO 354: Repeatability

16

Repeatability of measured reverberation times:

The relative standard deviation of the reverberation time T20, evaluated over a 20 dB

decay range, can be estimated by the following formula (see ISO/TR 140-13 for details):

Ɛ20 (T): is the standard deviation of the reverberation time T20 ;

T: is the reverberation time measured [s] ;

F: is the centre frequency of the one-third-octave band [Hz] ;

N: is the number of decay curves evaluated.

An example of the standard deviation of measurement of T20 at 12 positions with 3 repetitions of

decay registration at each position is illustrated in next figure .

T f

N

T

T

59.342.2

20 , for each analysis band.



Rev Chamber absorption measurement: ASTM C-423

17

El método de la ASTM-C423 requiere de la medición de la absorción con el recint vacío y de la

absorción del recinto con la muestra en él.

Donde:A = absorption of the specimen, m2 or Sabins,

A1 = absorption of the empty reverberation chamber, m2 or Sabins, and

A2 = absorption of the reverberation room after the specimen has been installed, m2 or

Sabins.

El incremento en la absorción es dividido por el área de la muestra para obtener el “Coeficiente de

Absorción”.

Donde:

= absorption coefficient of the test specimen, no units or Sabins/ft2.

S = area of the test specimen, m2 or ft2, and

1= absorption coefficient of the surface covered by the specimen.

The absorption coefficient, 1, of the room surface covered by the specimen should be added

when it is significant. However, the absorption coefficients of a hard surface, such as the floor of

a reverberation chamber, are so small that they may be neglected and no adjustment should be

made for such a floor.

This coefficient is supposed to be dimensionless and is described in Sabins per square foot,

Sabins/ft2.

12 A A A

1

12

S

A A




18

1

1

1

2

2

2

12

4355

4355

mV T cV A

mV T c

V A

S

A A

In case of having the

climating conditions

inside of the Rev

Chamber.

mV S

V

RT Sabine 4

161,0

60

Sabine + air absorption

correction from Ed Ledhert:

Climate conditions: ISO 9613-1With the specimen

Without the specimen

Surface of the specimen [m2]

Random incidence

absorption coefficient

Statistical Acoustics



Air Sound Absorption:


19



ISO 354

and

ASTM C-423comparison:

20

RT20

RT25



Diferencias entre ISO & ASTM :

21

What are the differences between the standards?

•

ASTM-C423 and ISO-354 require similar sample shapes and sizes but ISO-17497-1 requiresa circular sample.

•ASTM-C423, ISO-354 and ISO17497-1 can use different methods to measure the RT of the

reverberation room.

•All standards have different sample area requirements.

•All standards have different perimeter requirements.

•All standards give different “Coefficients of Absorption”.

A. What is the sample shape and size required by each standard? (ASTM-C423)

ASTM-C423 requires a rectangular sample with a size of 72 ft 2 (6.69m2). The dimensions

shall be a length of 9 ft (2.74m) and a width of 8ft (2.44m). The standard will accept, as

an option, a sample size of 64 ft2 (5.95m2) with a length and width of 8ft (2.44m).

B. What is the sample shape and size required by each standard? (ISO-354)

ISO-354 requires a rectangular sample with a size of 10m2 to 12m2. The dimensions of

the sample shall have a width to length ratio of 0.7 and 1.0.

C. What is the sample shape and size required by each standard? (ISO-17497-1)

ISO-17497-1 requires a circular sample with a minimum area of 7.068 meters2. The

dimensions of the sample shall have a minimum diameter of 3 meters.



Rev Chamber: some experimental results

22

MATERIAL: 15 elements of mineral wool (Rockwool type 211, thickness 100 mm and density of ca. 44 kg/m3) in a wooden casing (1 ,2*0,6m),

covered with a nonwoven fleece (Lantor type 3103HO) and an open wire mesh for protection. The back is made of a 3 mm hardboard.

“Improving the accuracy of sound absorption measurement according to ISO 354”. Vercammen M. L. S. Melbourne, Australia. ISRA 2010. 2010.



Rev Chamber: suggestions on diffusers

23

1:

2:



Rev Chamber: boundary diffusers

24



Difusores en Cámaras Reverberantes:

25

J.L. Davy et al.[2] investigated the suggested methods of ISO 354 and found an empirical

value for the optimal diffuser-to-chamber floor surface area ratio.

Davy defined δ as the ratio of the total diffuser area (both sides) to the chamber floor

area. He tested the absorption of a specimen, varying δ from 0 to 1.75 in two chambers,

with volumes of 200 and 600 m3. He found that for both chambers the sound absorptioncoefficient of a specimen increased linearly with δ, until δ was approximately 1.25±0.14

and remained constant thereafter [2]. Therefore, the optimum value of δ was 1.25.

For comparison, ASTM C423 and ISO 354 state that, in general, the optimum diffuser area

is 15-25% of the total chamber surface area.

Although the exact relationship depends on the chamber shape, these two conclusions

are not incompatible.

[2]: Davy, J.L., W. A. Davern, P. Dubout, Qualification of Room Diffusion for

Absorption Measurements. Applied Acoustics, 1989. 28: p. 177-185.

b ff l f d



Absorption coefficient vs. Real Life conditions

26

For Sabine Equation:

SabineS

V RT

161.060 If 1, RT60 0.

For Eyring Equation:

)1ln(

161.060

Eyring S

V RT

If 1, RT60 0.

The “Absorption Coefficient” is used in calculating the reverberation time of closed spaces such

as auditoriums, churches, working offices, theaters, classrooms, recording studios, etc. Some of

the equations for calculating the reverberation time are:

The perimeter is only used to simplify flexibility (for changing materials “cut and try”) geometrical models

“Edge diffraction” edge absorption

Millington Sette equation (1933):

ii MillingtoniS mV

V RT

1ln4

163,060




Absorption coefficients:Sabine & Eyring

Sabine: is that absorption coefficient measured from the initial and final RT60

variation inside a reverberant chamber as states in ISO 354 standard.

Eyring: It is a statistical descriptor. It is calculated from the flux

resistance or the acoustic impedance at normal incidence (Kundt’s

tube).

inicial total final

Material total final

final Material

Sabine RT S

S S RT cS

V 6060

13,55


BUT:

Into a Rev Chamber

27




Absorption coefficients:Sabine & Eyring

SabineS A Sabine:

Eyring: Eyring S A 1log3,2

Eyring Sabine 1log3,2 10


28




Absorption Coefficients:Sabine & Millington

“Acoustic Absorbers and Diffusers”. Cox, T. 200429



Absorption Coefficient:

Tubo de Kundt

30

Absorption coefficient



[9]

What if > 1?

31

p ff

EDGE EFFECT: In cases where the absorption footprint is larger than the area of the specimen,

the sound absorption coefficient is greater than 1.00. This is called the edge effect or

diffraction effect because it results from wave diffraction at the edges of the specimen.

Relative edge

length:

The effect increases with

decreasing frequency ,

decreasing specimen size,

increasing aspect ratio, and

increasing sound absorption

coefficient .

Perimeter

Perimeter E

S sta t

[9]: A. de Bruijn, The edge effect of sound absorbingmaterials “revisited”, NAG 2007 .

Valor medido

Absorption coefficient



Absorción

Frecuencia [Hz]

125 0.07

250 0.26

500 0.7

1K 0.99

2K 0.99

4K 0.98

75.04

)99.099.07.026.0(

NRC

NRC: Noise reduction Coefficient.

Es el promedio de los coeficientes de absorción en las frec. 250Hz, 500Hz, 1KHz y

2KHz, expresado al múltiplo más cercano a 0.05.

32

p ff

Fenómenos Físicos, Herramientas Acústicas



Absorción

,

33




AbsorciónCoeficientes de absorción de 1” de lana

de vidrio vs. espaciamiento de la pared

sólida trasera:

34




Absorción

La absorción de un material

depende de las condiciones de

montaje mecánico.

= f(Diferentes montajes):

35




Absorción

Efectos del montaje en la absorción de la superficie acústica:

36




Absorción Alfombra tipo “todo terreno”.

Coeficientes de absorción de

diferentes alfombras

37

T bl d fi i t d b ióFenómenos Físicos, Herramientas Acústicas



Absorción

Tabla de coeficientes de absorción:

38



Absorción

39



Absorción del Aire (m)

Absorción del Aire en función de la humedad relativa y de las frecuencias.

El aire atenúa más las altas frecuencias

que las medias y que las bajas.

En volúmenes importantes no tomarlo en

cuenta puede acarrear una pésima

predicción de la inteligibilidad de la

palabra.

Es un dato útil para el

control de ruidos al aire

libre.

40



Individual Experiment:

41

Measure the statistical absorption coefficient of a sample applying ISO 354, in 1/3

octave bands. Choose any room, describing it geometrically and in acoustic terms.

Use 2 (two) different arrangements of the sample under test.

Calculate the Repeatability.

Calculate the edge effect portion, as Ten Wolde results. Graphs in function of

frequency.

Produce conclusions on every related topic, including systematic errors.

Any programming or signal processing software development is very welcome.



42

In Geometric and Statistical Room Acoustic Models

the absorption coefficients of surfaces are required.

•How can these be determined if the room is

already built?

•May one use the Sabine absorption coefficients?

•Can one measure the absorption coefficient of asurface after it is installed?

In Situ measurements Motivation



In Situ measurements: Motivation

What if you don’t know the absorption coefficient of a material or you’re

not sure of its “real use” absorption coefficient?

ISO standard 13472-1 Acoustics -

Measurement of sound absorption

properties of road surfaces insitu - Part 1: Extended surface method.

43

An in-situ method of sound absorption coefficient measurement could be of use in many

industries including the automotive industry which could benefit from the ability to

measure surfaces such as seats, door panels, and headliners after installation.



Concept

44

Th



Theory

the sound absorption coefficient is estimated through the sound reflection

coefficient measurement.

2

2 )(

11)( f R

a f p

Pressure Reflection Coefficient

45

)( r r d p

)( ii d p

Reflected and incident sound pressures are function of

frequency and sound paths distances.

IR F d p

Pressures are the Fourier Transforms of the reflected and

incident Impulse Responses.

2

2

2

f p

f p f R

i

r Reflection coefficient is the fraction between reflected

and incident energies.

Distance

compensation

coefficient

Measurement Setup



Measurement Setup

Pseudo “Free field” thru

time windowing.

46

ds

dm

dmds

dmdsa

Attenuation coefficient:

Absorber sample radius “r” (considering spherical sound spreading):

TW: Time window length

W W W

W

W

aSampledAre T cT cdmT c

dsT cdmds

T cdmds

r

2

2

1

Attenuation due todivergence of spherical

waves



Methods:

47

Windowing.

IR Substraction.

Reference wall: relative

absorption coeff.

Direct path.

In situ Absorption

Measurement

Half Blackman-Harris.Rectangular.

2

1 f H

f H f

all referencew

absorber

Using the attenuation

coefficient “1/a2”

(inverse square law)Direct IR substraction from direct + reflected IR.

Direct IR should be taken in an anechoic sound field.

IR Substraction:The subtraction technique allows the

i h b l d l



IR Substraction:

48

Parasitic

reflections:

Windowed

out

microphone to be placed very close to

the surface-under-test and to make a

temporal window around the reflection

limited only by the next-arriving

(parasitic) reflection from the

environment

Cancellation requires an exact inverse of the direct wave. Even a one sampledifference or slight phase shift will result in incomplete cancellation.



IR Substraction

Example:

49

10101dB x

Direct wave measured

in anechoic field (or

equivalent).

X dB should be always negative

10

)Re(

101

fl Dir



IR Substraction

Example:

50

Att ti d Ab ti C ffi i t



Attenuation and Absorption Coefficient:

51

Values in yellow mean “anechoic situation”.



Distance attenuation coefficient:

52Source of error: If S.U.T. has an irregular surface, Drefl distance is uncertain.

Is this the distancefrom the surce at

wich sperical waves

really spread off?

To apply to the source – reflected IR.

Attenuation due to

the larger sound path

Irregularsurface

under test

Regular

surface

under test

Impulse response:



Impulse response:

Reflections isolation by

using a Rectangular or ½Blackman Harris time

window.

53

“In situ measurements of acoustic

properties of surfaces”. Mallais, S. 2009.

Impulse Response Windowing:



Impulse Response Windowing:

54

E l A



Example Arrays:

55



Example Arrays:

56

Systematic errors:



Systematic errors:

57

•Parasitic reflections: proper windowing.•Small sample size.

•Inaccurate acoustic center (compact source aproximation: 2b << )

•Not enough low freq data: duration of the time windowing.

•Irregular geometric absorber surface.

•Low freq resolution when trying impulse substraction.

•Diffraction from sound source.



Effects of Systematic Errors:

58

P i i fl i

Systematic errors:



Parasitic reflections:

proper windowing:

59

Rectangular

window with half-

Hann portions on

either side:

Recommended

“In Situ Measurements

of Acoustic

Properties of Surfaces”.

Mallais, S. 2009.

Inaccurate Acoustic Center:Systematic errors:



Inaccurate Acoustic Center:

60

(f): correction factor to the propagation distance for low frequencies.

The compact source approximation is valid when the source is much smaller than the

wavelength of its radiation:

b2

source (speaker or baffle) radius

From the IEC standard [7], the “acoustic centre” of a sound source is: “For a sound emitting

transducer, for a sinusoidal signal of given frequency and for a specified direction and

distance, the point from which the approximately spherical wavefronts, as observed in a

small region around the observation point, appear to diverge.” The thrust of this definition

may be to ensure that the amplitude of the acoustic pressure accurately follows a 1/r

dependence.

dmds

dmdsaCorrection (when needed ):

2

2

2

11)(

f p

f p

a f

i

r

(“Direct path” method)

b

c f

b

c f

b

c f

2

2

2

0

¿¿¿???

Acoustic Center ( Cabinet Center):Systematic errors:



Acoustic Center ( Cabinet Center):

61

It is defined in [1] and [2] as the position of the point from which spherical wavefronts

appear to diverge, and in [3] and [4] as the position from which the

sound pressure varies inversely as the distance.

Knowledge of the acoustic center is of concern whenever a well-defined distance to a

source is needed.

The acoustic centre is that point for which the polar response is truly omni -directional

at frequencies for which the wavelength is large compared to the source size.

[1]: C. L. Morfey, Dictionary of Acoustics (Academic, San Diego, 2001).

[2]: IEC International Standard 61094-3, ‘‘Measurement microphones, Part 3: Primary methods for free-field

calibration of laboratory standard microphones by the reciprocity technique,’’ 1995.

*3+: IEC International Standard 50(801), ‘‘International electrotechnical vocabulary,’’ 1994.

*4+: American National Standard ANSI S1.1, ‘‘Acoustical Terminology,’’ 1994.

*5+: J. R. Cox, Jr., ‘‘Physical limitations on free-field microphone calibration,’’ Massachusetts Institute of

Technology, Ph.D. thesis, 1954.

[6]: K. Rasmussen, Acoustic centre of condenser microphones, The Acoustics Laboratory, Technical University of

Denmark, Report No. 5, 1973.

*7+: “Polar plots at low frequencies: the acoustic centre”. Vanderkooy, J., Henwood, D. AES. 2006.

In general the acoustic center of a source varies with the frequency, with the

direction of the observer, and with the distance from the source [1] as

demonstrated theoretically in [5] and [6]. Also with cabinet and speaker size [7].





62

For wavelengths much larger than the size of the cabinet, the “acoustic flow”

pattern shows a very simple symmetry at some distance from the cabinet, essentially

pointing to the real natural centre of the system. In addition this leads to a verypleasing set of nested polar responses versus angle for the lower frequencies [7].

Acoustic Center:



63

Acoustic Center:



Acoustic Center:

64

Acoustic responses have frequency character that scales inversely with size. At low

frequencies the wavelength is much larger than the loudspeaker, and distance to the

acoustic centre δ will be scaled by the loudspeaker size, R, so that the ratio δ/R is the

relevant variable.

12

1

180

0

180

0

S S

S

S d

Pressure decay: = 1/r

R (Half) Speaker

Cabinet radius.

Acoustic Center:



Acoustic Center:

65

= { a ~ 0.66 a ~ 0.5 a}

Just for frequencies with much larger than speaker size.

a a a

“For typical loudspeaker boxes, the acoustic centre concept is valid up to about 200 Hz, hence the whole sub-bass

region of the spectrum is encompassed. The concept remains useful to even higher frequencies.” [8]

[7]: “Polar plots at low frequencies: the acoustic centre”. Vanderkooy, J., Henwood, D. AES. 2006.

*8+: “Applicatins of the Acoustic Centre”. Vanderkooy, J. 122nd AES Convention. Vienna. Austria. 2007.

[7], [8]

Acoustic Center: And what for intermediate frequencies?



Acoustic Center: And what for intermediate frequencies?

66

For very high frequencies, the “new method” gives an acoustic centre position which is

essentially at the source, and the curve of the above figure would hover near zero

position for frequencies above 1kHz. This is reasonable, since at very high frequencies,

we would expect a point source to send out spherical waves precisely from where it is

located, and line-of-sight ray tracing would be appropriate.Another point to make regarding the acoustic centre at intermediate frequencies is that

the concept does not break down quickly as frequency rises. The flow pattern near the

source does show some modification as the wavelength goes down and approaches the

source size, but this process is gradual. If one is fairly close to a transducer, the acoustic

centre concept may be useful well into the region in which the response is no longer

quite omnidirectional. [8]

N h l f d

Systematic errors:



Not enough low freq data:

67

The low end of the usable frequency range is determined by the (limited) length of the timewindows.

The direct sound time window cannot be made so long as to overlap the reflected response,

whereas the reflected sound time window is limited by the tail of the direct response, and the

parasitic reflections.

Both windows can be extended by using the subtraction technique as described by E. Mommertz

in “Angle-dependent in-situ measurements of reflection coefficients using a subtraction

technique” ( Applied Acoustics, Vol.46, 1995, pp. 251-263).

wT f

1min

It can be seen that a frequency resolution on the order of 10Hz requires a time window of onetenth of a second, corresponding to a nearest surface of about 17m away. This is half the distance

that the reflected sound wave travels. On the other hand, a frequency resolution on the order of

one 100Hz is achieved with a nearest surface of almost 2m. It is therefore clear that the frequency

resolution of a measurement is limited by the geometry of the experimental setup.

Systematic errors:



Not enough low freq data:

68

1) The difference between the arrival time of the reflected wave and the arrival

time of the incident wave: tri = tref - tinc.

2) The difference between the arrival time of the foor reflection and the arrival

time of the reflected wave: tfr = tfloor - tref .

3) The difference between the arrival time of the speaker reflection and the arrival

time of the reflected wave: tsr = tspk - tref .

t = min{tref - tinc; tfloor - tref ; tspk – tref }

Diffraction from sound source:Systematic errors:



69

Spherical

speaker

“Tube”speaker

“Auratone”

Id l U if di t ib ti R l G i di t ib ti



Ideal Uniform distribution vs. Real Gaussian distribution

of impinguing sound energy over the sample:

70

Therefore, a non-dimensionalized parameter, ke , which is multiplication of the wavenumber and thecharacteristic length of a sample, is introduced to effectively indicate the general trend of the

relative errors. A high value of ke means a high frequency and/or a large sample.

2 k Wavenumber

The angular distribution of energy density incident on a sample has been simulated for arectangular room and a reverberation chamber with non-parallel surfaces by using the beam

tracing method. A large variation in incident energy density was found depending on the source

position. To achieve a uniform distribution, the source should be located perpendicularly from the

boundary of the target surface, as close as possible to the target surface. Therefore a room with

non-parallel walls is advantageous for obtaining a uniform distribution. A long distance from a

source to a target surface results in a concentration of acoustic energy near the normal direction.

The simulated reverberant energy distribution plays the role of a weighting factor in calculating theangle-weighted absorption coefficient. The importance of non-uniform incident energy becomes

significant for high ke values. For smaller values of ke, the calculated absorption coefficient

adopting fairly uniform distribution agrees well with the measurement, while the averaged

Gaussian-like weighting function agrees better with the measurement for high ke.

Cheol – Ho Jeong. “A correction of random incidence absorption coefficients for the angular distribution of acoustic

energy under measurement conditions”. Acoustic Technology, Department of Electrical Engineering. Technical

University of Denmark (DTU).



Ke & error from uniform absorption coefficient:

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Cheol – Ho Jeong. “A correction of random incidence absorption coefficients for the angular distribution of acoustic

energy under measurement conditions”. Acoustic Technology, Department of Electrical Engineering. Technical

University of Denmark (DTU).

Relative error

Rev chamber

measurements

Individual Experiment:



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Main Objetive:

Comparison between the statistical calculation of the reverberation

time by measuring the individual absorption coefficients, and themeasured RT60 with Log Sine Sweep techniques.

Secondary objetives:

•Description of the sound field inside the room in relation with the

experimental results.

•Comparison of the obtained absorption coefficients with the available

commercial information of each one.

•Analysis of the systematic errors. Develop a proposal to minimize them.

Instructions:

Choose any room. Measure the in situ absorption coefficients. Calculate

the statistical RT60 (total and by bands). Get conclusions on every related

topic, including systematic errors. Give explanations of applied practices.

Any programming or signal processing software development is very welcome.

Butacas: Método de Kath & Kuhl

Absorción Acústica UNTREF

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