Building Acoustics

Sound absorbers 205

()

( )

()

()

c

12

12

c

sinh cos

cosh cos

cos

sinh cos

cos cosh cos

Zd

d

pp

vvd

d

Z

φ

φ

φ

φ

φφ

⎡⎤Γ⋅

⎢⎥Γ⋅

⎡⎤⎢⎥⎡⎤

⎢⎥=⎢⎥⎢⎥

⎣⎦ Γ⋅ ⎣⎦

⎢⎥⋅Γ⋅

⎢⎥⎣⎦

(5.85)

It should be noted that cosφ could be a complex quantity; see discussion on Snell’s law
in Chapter 3 (section 3.5.3).
A concentrated layer, such as a membrane, thin plate etc. will result in a much
simpler transfer matrix. In this case we get

1 w (5.86)
12

1

,

01

ppZ

v

⎡⎤⎡⎤⎡⎤

⎢⎥=⎢⎥⎢⎥

⎣⎦⎣⎦⎣⎦

2

v

where Zw is the so-called wall impedance, which is given by the ratio of the sound
pressure difference across the layer to the velocity of the layer. We thereby assume that
the velocity is equal on both sides of the layer. Equations (5.85) and (5.86) are the ones
used in a number of the illustrations in this chapter (see e.g. Kristiansen and Vigran
(1994)).

5.8 References

ISO 9053: 1991, Acoustics – Materials for acoustical applications – Determination of
airflow resistance.
ISO 10534: 1996, Acoustics – Determination of sound absorption coefficient and
impedance in impedance tubes. Part 1: Method using standing wave ratio. Part 2:
Transfer-function method.
ISO 13472–1: 2002, Acoustics – Measurement of sound absorption properties of road
surfaces in situ. Part 1: Extended surface method.
ISO 354: 2003, Acoustics – Measurement of sound absorption in a reverberation room.

Allard, J. F. (1993) Propagation of sound in porous media. Modelling sound absorbing
materials. Elsevier Applied Science, London and New York.
Allard, J. F., Castanede, B., Henry, M. and Lauriks, W. (1994) Evaluation of the
tortuosity in acoustic materials saturated by air. Review of Scientific Instruments,
65, 754–755.
Attenborough, K. (1983) Acoustical characteristics of rigid fibrous absorbents and
granular materials. J. Acoust. Soc. Am., 73, 785–799.
Attenborough, K. (1992) Ground parameter information for propagation modelling. J.
Acoust. Soc. Am., 92, 418.
Brouard, B., Lafarge, D. and Allard, J. F. (1995) A general method for modelling sound
propagation in layered media. J. Sound Vib., 183, 129–142.
Champoux, Y., Stinson, M. R. and Daigle, G. A. (1991) Air-based system for the
measurement of porosity. J. Acoust. Soc. Am., 89, 910–916.
Delany, M. E. and Bazley, E. N. (1969) Acoustical characterisation of fibrous absorbent
materials. NPL Aero Report AC 37.
Delany, M. E. and Bazley, E. N. (1970) Acoustical properties of fibrous materials.
Applied Acoustics, 3, 105.