Measurement of the Acoustic
Properties of Acoustic Absorbers
Ralph T. Muehleisen
Civil, Architectural, and Environmental Engineering
Director of the Miller Acoustics Lab
muehleisen@iit.edu
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Outline
• Definitions
• Measuring Macro Properties
– Absorption Coefficients
• Measuring Bulk Properties
– Impedance, Wavenumber, Density, Bulk Modulus
• Measuring Microstructure Properties
–
–
–
–
Flow Resistivity
Porosity
Tortuosity
Characteristic Thermal and Viscous Lengths
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Defining Acoustic Absorbers
Absorbers are usually denoted as porous, panel
resonators or Helmholtz resonators, depending
upon the primary absorption mechanism.
»
– Helmholtz resonators are defined by their geometry
– Panel resonators are defined by their geometry and
structural vibration properties of panel
– Porous absorbers are defined by their geometry and
the acoustic properties of the porous material
In this talk we’ll limit our discussions to the
acoustic properties of porous absorbers
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Defining Acoustic Properties
The term “acoustic” properties of a porous absorbers is
open to interpretation. What is an acoustic property?
• Macro properties of absorbers assemblies
– Absorption coefficient and normal surface impedance
• Bulk properties of the porous material itself
– Characteristic impedance and wavenumber
• Microscale properties that create bulk properties
– Flow resistivity, Porosity, Tortuosity, Characteristic Lengths
– It is at the microscale that the porous material actually interacts
with the fluid
• Great reference, “Acoustic absorbers and Diffusers” by Trevor Cox
and Peter D’Antonio
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Rigid Frame and Poro-Elastic Media
Porous media are usually broken down further
into rigid and elastic frame
• In Rigid Frame absorbers, we assume that the solid
material (fibers, foam, ceramic, etc) is a rigid structure
and only participates with the acoustic wave through
viscous friction and heat transfer
• In Poro-Elastic absorbers the solid material supports
wave propagation and analysis and design involves
coupled solid and fluid waves. This is really hard stuff. I
think it is so hard that Rayleigh didn’t even work on it (Biot
did though). Alas, most foams are best modeled as elastic frame
media
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Absorption Coefficient, 
The absorption coefficient is
defined as the ratio of absorbed
energy to incident energy
Ea

Ei
– Some people define  as the ratio of
all energy not reflected to incident
energy, i.e
Er Ea  Et
  1 
Ei
Ei
– In general,  is a function of the
incident angle i . The normal
incidence value is denoted N
Er
Ei
 i r
Ea
Et
By Conservation
of Energy
Ei  Er  Ea  Et
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Normal Surface Impedance, Zn
• The reason energy reflects at a change in medium is
because of the change in wave impedance seen by the
wave.
• In general, the impedance seen at the surface of an
absorber depends on the porous media bulk properties,
the geometry of the absorber and the mounting conditions
of the absorber.
• The surface impedance is angular dependent, but if the
material is locally reacting, the effective surface
impedance at any angle is related to the normal surface
impedance, Zn by the formula
Zn
Z ( ) 
cos( )
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Measuring n and Zn
Probably the simplest methods for estimating normal
incidence absorption and surface impedance, n and Zn ,
are using plane wave impedance tubes
• Two industry standards
– ASTM C384/ISO 10534 Standing Wave Impedance Tube
– ASTM E1050/ISO 10534-2 Two Microphone Impedance Tube
• Both methods measure the magnitude and phase of the
pressure reflection coefficient, rˆ  r , and then
  1  rˆ  1  r
2
2
and
1  rˆ
ˆ
Zn 
1  rˆ
• For both methods, the upper frequency is limited to frequencies where
only plane waves can propagate in the impedance tube ( f < 0.586 c/d
where c =speed of sound and d = tube diameter )
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
ASTM C384-04
• Measure the ratio of peak amplitude to
min amplitudes of standing wave, the
standing wave ratio called SWR
• Measure distance from sample to the
closest pressure min, L-x.
• Use equations at right to get r and 
• This method is fairly foolproof, but it is
also only applicable for single frequencies
and is fairly time consuming
– No microphone calibration is required
• Lower frequency limited by tube length –
you must be able to support a half a
standing wave with at least one peak and
one null
A B
SWR 
A B
SWR  1
r
SWR  1
  2k  L  x  

2
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
ASTM E1050-98
• Measure the transfer function, H(f) between
two mics, spaced s apart, and a distance l
from sample to get r using the equation that
is to the right and below
• Frequency limited by mic spacing as well as
tube diameter – recommendations are for
0.05 c/s < f < 0.45 c/s
• If the microphone “switching” method not is
used, the microphones must be calibrated
for magnitude and phase and H must be
corrected before computation of r .
• Absorptive media put between source and
sample to damp out the standing waves
Hˆ  pˆ1 / pˆ 2
Hˆ  e jks j 2 k (l  s )
rˆ  jks
e
ˆ
e H
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Random Incidence Absorption Coefficient
• Since  is a function of angle, selecting a
representative value arbitrary incidence is hard
• If we average () over  we would get what we
call the random incidence coefficient rand
– For a locally reacting surface we can do that
analytically and would find that rand=(55)
• We could also try to measure a by placing a
material sample in a room and exposing it to a
diffuse sound field. That is done in ASTM
C423/ISO 354. This standard measures a
Sabine absorption coefficient.
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
ASTM C423/ISO 354
• This method measures the change in the
reverberant decay rate in a reverberant
room from the addition of a sample.
• Sabine equation is used to extract the
Sabine absorption coefficient , sab
 sab
–
–
–
–
–
V
 0.9210
 d2  d1   1
CS
V is room volume
c is speed of sound
S is surface area of sample
1 is absorption coefficient of covered surface
d1 and d2 are sound decay rates (dB/s) with
and without the sample
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
ASTM C423 and Sabine Absorption
Many of us are familiar with the absorption coefficients listed on
material data sheets measured by ASTM C423, the
Reverberation Room Method. These are sab
• sab  rand i.e. it is NOT a random incident absorption
coefficient, its only closely related. Numbers greater than unity
given on data sheets are not mistakes.
– sabis a measure of decay rate. It is only through the Sabine equation
that we equate it to absorption.
• sab is very useful measure if you want to predict the effect the
reverberation time of a room with that material.
• sab is a poor measure of absorption if you want to do other
types of noise control (such as line an engine shroud)
• There is no simple conversion from sab to rand or n
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
In-Situ measurement
• For some absorbers (especially
hanging aborbers), it is important
or only practical to measure the
absorption in-situ.
• The most popular methods are
free space variations of the
impedance tube and can be used
to measure angular dependent
absorption coefficients
• This method has been formalized
in the European Standard ENV
1793 (part 5)
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Bulk Properties
Bulk properties are those properties that describe the
material/sound wave interaction but are independent of
the material thickness and area (i.e. absorber size)
– In anisotropic materials such as layered fiberglass, the bulk
properties can be a function of direction so keep that in mind
Among the important bulk properties are
– Characteristic Impedance, Zc and characteristic wavenumber, kc
or alternatively dynamic density, e and dynamic bulk modulus, Ke
Z c  Ke e and kc  
e
Ke
– Imaginary part of kc is related to acoustic damping in the material,
the imaginary part of Zc is related to energy storage mechanisms
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Use of Zc and kc
We usually use Zc and kc directly
for designing absorbers. For
example, the normal surface
impedance of a layer of a porous
Zˆ n
material of against a wall with Zd is
ˆ  jZˆ tan(kˆ d )
Z
c
c
Zˆ n  Zˆ c d
Zˆ  jZˆ tan(kˆ d )
c
d
c
 
For Zˆ d  , Zˆ n   jZˆc cot kˆc d
Zˆc , kˆc
Zˆ d
d
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Measuring Bulk Properties
• We can use the impedance tube to estimate Zn
for two samples of differing d and/or Zd conditions
to estimate Zc and kc this is the two load method
– We need two conditions to solve for both Zc and kc
• We can use the four-mic transfer matrix method
of Song and Bolton to measure Zc and kc in one
measurement
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Four Mic Method
This is a variation on the standard
impedance tube using two pairs of mics.
• The mics measure both reflected and transmitted
waves to get Zc and kc with only one measurement.
• You can also estimate normal incident transmission
loss with the same measurements
• ASTM and ISO standards are currently under
development
• Works better for high porosity, low flow resistivity
materials than the two microphone impedance tube
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Microstructural Properties
The microstructural properties are the geometry details
that describe the interaction of the sound wave and
the material. These properties define the bulk
properties.
Knowledge of the microstructural properties is very
useful for designing aborber with specific bulk
properties.
Among the important microstructural properties are
–
–
–
–
Flow Resistivity
Porosity
Tortuosity
Characteristic Length
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Flow Resistivity
Back open to
atmosphere
• Flow resistivity  is the ratio of
static pressure drop P to a
volume flow U for a small
sample length, d
P

[Ns/m4 =MKS rayl/m]
Ud
• This can be measured using
ASTM C522
– To maintain laminar flow, the flow
velocity should be kept under 50
mm/s
P
Meter
U
Source
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Empirical Formula
• Many empirical formulae have been developed
that relate  to Zc and kc
The most famous is that of Delany and Bazley:
Zˆc  0c 1  0.0571X 0.754  j 0.087 X 0.732 

0.7
0.732
ˆ
kc   1  0.0978 X
 j 0.087 X

c
Here we see Zc and kc are complex. The imaginary part
of Zc represents stored energy and the imaginary part
of kc represents damping in the medium.
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Porosity, 
Porosity is the ratio of interconnected void volume to total
volume of a material and is surprisingly hard to measure.
– Note: There is no standard variable name for porosity
You would think you can just measure the volume and mass of
an absorber sample but it is not that simple …
• It is hard to measure in open cell foams because it is hard to
determine which cells are really open and interconnected.
• It is hard to measure accurately for fibrous absorbers because
measuring the exact volume of a compressible sample can be
hard
• Porosities of 95-98% if fibrous absorbers are not uncommon
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Measuring Porosity
• One method is to fill the sample
pores with a liquid and
measure that volume. But that
can contaminate the sample
and preclude making other
parameter measurements.
• Another popular method uses
thermodynamics.
– Sample is placed in a chamber
which is compressed by V. The
internal pressure will increase by
P according to Boyles law.
P0  P
V0  Vt  
V
P
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Tortuosity, q
• Tortuosity is a measure of the “non-straightness”
of the pore structure of the porous material.
– The more complex the path, the more time a wave is in
contact with the absorbent.
– Note: there is no standard variable name for tortuosity
• One method is to saturate the sample with an
electrically conducting fluid and measure the
electrical resistivity of the saturated sample, rs,
and compare to the resistivity of the fluid alone, rf
then q= rs/rf
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Using Ultrasonics
• Fellah, et. al. have shown that
by using ultrasonic time domain
reflectometry to measure the
complex surface reflection
coefficient at ultrasonic
frequencies.
• At ultrasonic frequencies the
surface reflection coefficient
depends primarily on the
tortuosity and porosity of the
porous sample.
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Characteristic Lengths,  and ’
Two more important microstructural properties are the
characteristic viscous length  and thermal length ’
which relate to viscous and thermal losses.
– The thermal length ’ is the twice
ratio of volume to surface area in
connected pores. This is
geometric and can be measured
directly.
– The viscous length, , is nearly
the same, but each integral is
weighted by the square of the
fluid velocity in the pore. This
cannot be measured directly
dV
V

'  2

 dS S
sample
pore walls
v

2
v
2
fluid
dV
2
fluid
dS
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Measuring Thermal Length
• Leclair et. al. showed that ’ can be
measured by finding the pressure,
P required to draw a wetting liquid
through the sample (kind of a liquid
flow resistivity).
– P is related to the surface tension of
the liquid and the total surface area of
the pores in contact with the liquid
• Lauriks estimated both
characteristic lengths via more
time domain reflectometry and
curve fitting
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
The Curve Fitting Approach
• Probably the most popular way of finding out all
these microstructure constants is through curve
fitting.
– One measures the bulk parameters and then uses
non-linear multivariable curve fitting to get the best
estimates of , , q, , and ’. This works best if one
can estimate at least some of the variables (such as
flow resistivity, ) by other means.
– By working in the ultrasonic region like Fellah and
Lauriks have it is easier to isolate individual
microstructural variables or at least only have two
coupled together in a particular measurement.
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
Poro-Elastic
• Poro-elastic systems are even tougher to model
as they additionally require knowledge of the
structural characteristics of the porous frame as
well as coupling coefficients between the frame
waves and the acoustic waves.
• All those extra variables make my head start to
hurt so I’ll end my talk now.
R. T. Muehleisen, muehleisen@iit.edu, Measurement of Acoustic Properties
References
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Cox, T. J. and P. D'antonio (2004). Acoustic Absorbers and Diffusers, Spon Press.
ASTM C384 (2003). Standard Test Method for Impedance and Absorption of Acoustical Materials by the Impedance
Tube Method.
ASTM C423-07a (2007). Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the
Reverberation Room Method.
ASTM C522 (2003). Standard Test Method for Air Flow Restance of Acoustical Materials.
ASTM E 1050 (1998). Standard Test Method for Impedance and Absorption of Acoustical Materials Using a Tube,
Two Microphones and a Digital Frequency Analysis System.
European Standard EN 1793-5, Road traffic noise reducing devices –test method for determining the acoustic
performance – Part 5: Intrinsic characteristics In situ values of sound reflection and airborne sound insulation.
Champoux, Y., M. R. Stinson, et al. (1991). "Air-based system for the measurement of porosity." Journal of the
Acoustical Society of America 89(2): 910-916.
Leclaire, P., O. Umnova, et al. (2003). "Porosity measurement by comparison of air volumes." Review of Scientific
Instruments 74(1366-1370).
Leclaire, P., M. J. Swift, et al. (1998). "Determining the specific area of porous acoustic materials from water
extraction data." Journal of Applied Physics 84(12): 6886-6890.
Leclaire, P., L. Kelders, et al. (1996). "Determination of the viscous and thermal characteristic lengths of plastic
foams by ultrasonic measurements in helium and air." Journal of Applied Physics 80(4): 2009-212.
Song, B. H. and J. S. Bolton (2000). "A transfer-matrix approach for estimating the characteristic impedance and
wave numbers of limp and rigid porous materials." Journal of the Acoustical Society of America 107(3): 1131-1152.
Muehleisen, R. T. and C. W. Beamer IV (2002). "Comparison of errors in the three- and four-microphone methods
used in the measurement of the acoustic properties of porous materials." Acoustic Research Letters Online 3(4):
112-117.
Muehleisen, R. T., C. W. Beamer IV, et al. (2005). "Measurements and empirical model of the acoustic properties of
reticulated vitreous carbon." Journal of the Acoustical Society of America 117(2): 536-544.