Free field surface impedance measurements of sound-absorbing materials with surface coatings

Applied Acoustics 26 (1989) 199-207

Free Field Surface Impedance Measurements of Sound-absorbing Materials with Surface Coatings J. F. A l l a r d , C. D e p o l l i e r & P. G u i g n o u a r d * Laboratoire d'Acoustique Associ6 au CNR~-UA 1101, Facult6 des Sciences du Mans, Route de Laval, B.P. 535, 72017 Le Mans Cedex, France (Received 9 June 1988; accepted 14 September 1988)

A BS TRA C T A method has been previously worked out by one of the authors, to measure the surface impedance of glasswools and plastic foams in normal and oblique incidence, in free field, with two microphones. Using an improved version of this method, surface impedance measurements of two sound-absorbing materials with surface coating are presented and compared with measurements performed in a reverberant room. It appears that measurements with our method are possible, in normal and oblique incidence,for these materials.

INTRODUCTION Free field surface impedance measurements have been performed for a long time. A description of several methods can be found, for instance, in Ref. 1. One of the authors o f this paper has previously worked out a m e t h o d of measuring surface impedance in a free field, in normal and oblique incidence, 2"a which has been used to study the sound propagation in glasswools 4 and plastic foams, s This method has been improved 6 in order to be used in non-anechoic rooms, with usual sound-absorbing materials. A short description o f the m e t h o d is now given. As shown in Fig. 1, the material is set on a plane floor, in the acoustic field generated by a source S located at a distance h from the material. T w o microphones are set at M 1 and M2, close to the sample, on an axis perpendicular to the surface o f the material. Let M be the intersection o f the axis of the microphones with the * Present address: LASA (Laboratoire d'Applications des Sciences Acoustiques), BP 30, 78600 Maisons-Laffitte, France. 199 Applied Acoustics 0003-682X/89/$03'50 © 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain

200

J. F. Allard, C. Depollier, P. Guignouard S

M1 Id2 M

$'e

Fig. !.

Sketch of the measurementset-up; S is the source and S' the image of the source; microphones are set at M1 and M2.

surface of the material, and z the angle between MI, M2 and S M . In a first version, 2'3 the source is located at several meters from the material and it is possible to model the acoustic field close to the material, with incident and reflected plane waves. Measurements are performed in an anechoic room, or outdoors. Let H(tn) be the transfer function equal to the ratiop(M2)/p(M 0 of the acoustic pressures at M 2 and M1 in the frequency domain: H(o~) = p(M2)/p(Ml)

(1)

This quantity is measured with a dual-channel spectrum analyser. The surface impedance of the material is evaluated from H(m) under the hypothesis of plane incident and reflected waves. This method has been used to study the acoustic properties of glasswools and plastic foams, 4,5 but it is impossible, with this method, to study usual sound-absorbing materials such as carpets, or surfaced porous materials which have a rather small absorption coefficient. A NEW M E T H O D OF M E A S U R I N G S U R F A C E I M P E D A N C E 6 When the absorption coefficient is small, the acoustic field is strongly reactive, and the finite dimension effects can make measurements impossible. In order to diminish these effects, the distance from the source to the material and the microphones has to be decreased, the acoustic field becoming much smaller at the periphery of the material than under the microphones. Moreover, the relative contributions of the reflections from the ceiling and the walls of the room to the acoustic field around the

Free field surface impedance measurements

201

microphones can become negligible, and a non-anechoic room can be used. For small distances h from the sample, the acoustic field is not plane, and a better approximation of the acoustic field is obtained by adding two spherical waves generated by the source S and the image S' of S through the material. Let r 1, r2, r'1 and r~ be the quantities S M 1, S M 2 , S ' M I and S ' M 2 respectively, represented in Fig. 1. The transfer function, H(t~), with spherical modelization, is given by the following relation: H(o~) =

exp (ikr2)/r 2 + R s exp (ikr'2)/r'2 exp (ikrl)/r I + Rs exp (ikr'l)/r' 1

(2)

In this equation, R~ is the reflection coefficient of the material at angular frequency co, and k is the wavenumber in air. From eqn (2), R~ can be written (the time dependence is e -i'°') as: & =

exp (ikr2)/r 2 - H ( ~ ) exp (ikrl)/r 1 H(og) exp (ikr'~ )/r'l - exp (ikr'2 )/r'2

(3)

R, can be evaluated using eqn (3) from measured values of H(09). An estimate, Z~, of the true surface impedance, Z M, at M is: Z~ = p J v s

(4)

where v~ and p~ are the acoustic velocity component parallel to M I M 2 , and the pressure at M, calculated under the hypothesis of spherical incident and reflected waves. From a straightforward calculation, Z~ can be written: 6 Z~ = (1 + R~)/(cos z(1 - Rs)(1 - 1/(ikd)))

(5)

In this equation: d = h/cos z (6) The true normal surface impedance is different from Z,, the reflected field being a spherical wave only in a first approximation. A more precise description of the acoustic field above a surface of constant normal impedance has been given by Nobile and Hayek. We have worked out a simple iterative procedure 6 using eqns (B 1) and (16) of Nobile and Hayek, ? which supplies a better estimate, Z, of the surface impedance, from the measured value of Z~. In normal incidence, this method has been used to evaluate the surface impedance of a thick carpet in a cafeteria. 6 New measurements, in normal and in oblique incidence, on materials with surface coatings, are now presented. SURFACE I M P E D A N C E M E A S U R E M E N T S The materials

Two materials are studied. The first material is a compressed rockwool of high flow resistance, of thickness equal to 1"5 cm (Tatra, manufactured by

J. F. Allard, C. Depollier, P. Guignouard

202

: •

..¢

"

.¢ ,-

I

I,

o

¢r

J

p...

• ~'~q

"~

•

iI,

[

I ..

A) ~'

P

B r

Fig. 2.

~r

q' .4"

.i,f

•

*

•

'

Z

,,,,Qa

~ •

• ,,

%

•

The material with a perforated coating: the area is equal to 10 × lOcm.

Armstrong). The material, shown in Fig. 2, is covered with a perforated facing. The second material is a glasswool of thickness equal to 1.5cm, covered with an impervious film (Spanglas, manufactured by Isover). The frame of the first material is very stiff, and the frame of the second material is flexible. The

measurements

Impedance measurements are performed in normal and oblique incidence with our method, in an anechoic room. The source is a pipe excited by a compressor driver, and two small electret microphones (KE4 Sennheiser) are used. Measurements are performed in pure tone. Impedance measurements are also performed, up to 1500Hz, in normal incidence, with a Kundt interferometer, for the first material. For the second material, the Kundt interferometer has not been used; the absorption in the second material is due to surface vibrations, and the behaviour of the surface must be different in a Kundt interferometer, and when a large area of material is placed on a floor. Measurements at low frequencies are limited to 400 Hz for the first material and 300 Hz for the second material, the acoustic field becoming too reactive at lower frequencies for accurate measurements. The area of the samples is about 4 m 2. In oblique incidence, the distance, h, from the source to the material is equal to 8cm. In spite of this very small distance,

Free field surface impedance measurements

203

measurements at very large angles of incidence are inaccurate, and measurements in oblique incidence are presented only for cos z = 0-632. The absorption coefficient, ~, of the two materials in normal and oblique incidence is calculated at M as follows: 0t = 1 -- I(Z - Zc/cos z)/(Z + Z J c o s z)l 2

(7)

Z~ being the characteristic impedance in air. The incident field is not plane, and eqn (7) is valid only for a given angle of incidence. The microphones being close to the sample, z is rather close to the specular angles of incidence for both microphones, and eqn (7) is used for the sake of simplification. This absorption coefficient is compared, for the first material, with measurements in random incidence performed in the reverberant room of the CEBTP (Centre Experimental de Recherche et d'Etude du B~timent et des Travaux Publics). Measurements in the reverberant room are performed according to the international standard ISO/DIS 354, with a one-third octave band analyser. Measurements on the first material

Surface impedance measurements in normal and oblique incidence are presented in Figs 3 and 4 for the first material. Measurements in normal incidence, with a Kundt interferometer, up to 1500 Hz, are very similar to

Re Z

(PaJms

2000

•

Q

-1)

•

•

•

• •

m

•

o

,

•m•

10001

i

i

J

,

i I

,

!

,

,

I 2

,

F (kHz)

Fig. 3. The real part of the surface impedance for the first material: distances of microphones from material are 0-8 cm and 2.6 cm. I , Normal incidence, distance from source material 0.24 m; , , oblique incidence, distance from source material 8 cm, cos z = 0.626.

204

J. 1~ A/lard, C. Depollier, P. Guignouard Im Z

(Pa/ms-1)

2000

1000

IIII

i

l

I

I

I

•

•

,

I

1

• o

I

•

• I 2

• I

l

IO •

F (kHz)

Fig. 4.

The imaginary part of the surface impedance for the first material: same conditions as in Fig. 3. O, Normal incidence; n , oblique incidence.

free field measurements, and they are not reported. From previous predictions, 8 the surface impedance does not depend on the angle of incidence. Measurements in oblique incidence exhibit a systematic difference from measurements in normal incidence. The imaginary part of impedance is larger in oblique incidence, but this difference is small. In Fig. 5, measurements of the absorption coefficients in the anechoic room and the reverberant room are compared. The measured real part of surface impedance lies around 1800 Pa/ms-1 in the whole range of frequencies studied. The surface impedance being not strongly dependent on the angle incidence, the absorption coefficient must increase with the angle of incidence up to large values of this angle. The absorption coefficient must be larger in random incidence than in normal incidence. It appears that the absorption coefficient in random incidence is close to the values obtained with eqn (7) in oblique incidence for cos z--0.632. Measurements on the second material

The surface impedance of the second material, measured in normal and oblique incidence in a free field, is shown in Figs 6 and 7. Measurements have not been performed in the dashed frequency intervals; the acoustic field is very reactive, and measurements are not accurate in these intervals. In normal incidence, the imaginary part of the impedance is equal to zero for

Free fieM surface impedance measurements

205

C~ Absorption coefficient

0-5

,

,

,

,

I

,

,

i

i

I

i

i

i

F (kXz)

Fig. 5. The absorption coefficient of the first material. 0 , Normal incidence; ll, oblique incidence; &, random incidence (reverberant room).

Re Z (Pa pros -1 )

2000

I

I

I|illi IIII

J

1

I

|||||i ll|i

I

J

2 F(kXz)

Fig. 6. The real part of the surface impedance for the second material: distances of microphones from material are 0.8 cm and 2.6 cm. Q, Normal incidence, distance from source material 0"24 m; l , oblique incidence, distance from source material 8 cm, cos ~ = 0.626.

J. F. A/lard, C. Depollier, P. Guignouard

206

I m Z ( P a , ' m s -1 )

1000

I •

i

•

llnlli IIII

•

i,l -1

I

IIIIII IIII

•

l

l

•

2

F (kHzl

-1000 m

-2000

Fig. 7.

The imaginary part of the surface impedance for the second material: same conditions as in Fig. 6. O, Normal incidence; n , oblique incidence.

,I o

l

Absorption c o e f f i c i e n t

,

,

A

I

1

Fig. 8.

I

I

I

i

I

2 F lkHz)

The absorption coefficient o f the second material measured in a reverberant room.

Freefield surface impedance measurements

207

frequencies equal to 400Hz, 980Hz and 1820Hz. At first sight, the behaviour of the surface impedance indicates three resonances of the material at these frequencies. We have not provided further interpretation. It must be pointed out that these resonances also appear in oblique incidence at the same frequencies, as shown in Figs 6 and 7. The real part of the impedance is not very different in oblique and normal incidence, and the imaginary parts of the impedance are very similar. The absorption coefficient, measured in the reverberant room, is shown in Fig. 8. Two peaks appear at 400 Hz and 1000 Hz, but there is no significant enhancement at the frequencies 1600 Hz and 2000 Hz, probably due to the one-third octave band analysis. CONCLUSION Free field measurements of surface impedance can be more difficult to perform on usual surfaced sound-absorbing materials than on strongly absorbing materials such as thick samples of glasswool or reticulated foams. Probably because of finite dimension effects, it is not possible to perform measurements in the whole range of the acoustic frequencies and at large angles of incidence. These limitations are more drastic than for better absorbing materials. Nevertheless, these m e a s u r e m e n t s can supply important information, which is lost in the traditional measurements performed in a reverberant room. REFERENCES 1. Legouis, T. & Nicolas, J., Phase gradient method of measuring the acoustic impedance of materials. J. Acoust. Soc. Am., 81 (1986) 44-50. 2. Allard, J. F. & Sieben, B., Measurements of acoustic impedance in a free field with two microphones and a spectrum analyzer. J. Acoust. Soc. Am., 77 (1985) 1617-18. 3. Allard, J. F., Bourdier, R. & Bruneau, A. M., The measurement of acoustic impedance at oblique incidence with two microphones. J. Sound Vibr., 101 (1985) 130-2. 4. Allard, J. F., Bourdier, R. & L'Esperance, A., Anisotropy effect in glass wool on normal impedance in oblique incidence. J. Sound Vibr., 114 (1987) 233-8. 5. Ailard, J. F., Champoux, Y. & Depollier, C., Modelization of layered sound absorbing materials with transfer matrices. J. Acoust. Soc. Am., 82 (1987) 1792q5. 6. Allard, J. F. & Champoux, Y., In situ free-field measurements of the surface acoustic impedance of materials. J. Noise Control Engng (in press). 7. Nobile, M. A. & Hayek, S. I., Acoustic propagation over an impedance plane. J. Acoust. Soc. Am., 78 (1985) 1325-35. 8. Ingard, U. & Bolt, R. H., Absorption characteristics of acoustic material with perforated facings. J. Acoust. Soc. Am., 23 (1951) 533-7.