Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Acoustics I:
absorption-reflectiontransmission
Kurt Heutschi
2013-01-25
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
introduction
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
introduction
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
characterization of
absorption and reflection
Absorption Reflection Transmission
introduction
characterization of absorption and
reflection
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
absorption property → absorption coefficient (real,
0<α<1)
α=
absorbed energy
incident energy
Absorption Reflection Transmission
introduction
characterization of absorption and
reflection
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
reflection property → reflection factor (complex,
0 < |R| < 1)
R=
sound pressure reflected wave
sound pressure incident wave
Absorption Reflection Transmission
introduction
characterization of absorption and
reflection
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
relation between α and R for plane waves:
α = 1 − |R|2
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorber types
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
porous absorbers
Absorption Reflection Transmission
porous absorbers
introduction
absorption
characterization
absorber types
I
measurement methods
materials:
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absorption and impedance
typical absorption values
I
covers
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back
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absorption mechanism:
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glass fibers
organic fibers (e.g. wood)
open foams
sound particle velocity corresponds to oscillating
air in the pores
→ friction losses
placement:
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where sound particle velocity is high
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber:
type Helmholtz
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
I
absorption mechanism:
I
typical absorption values
spring-mass system
I
covers
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back
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spring = enclosed air volume
mass = oscillating air column
maximal absorption at resonance
resonance frequency f0 for stiffness s of the spring and
mass m:
ps
f0 =
m
2π
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
I
mass m = ?
stiffness of the spring s = ?
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
measurement methods
mass m:
absorption and impedance
typical absorption values
covers
back
I
mass of the oscillating air column:
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mass of cylinder of length l + end correction lcorr
lcorr ≈ 0.8R (radius of cylinder)
with S: cross sectional area of cylinder follows:
m = ρ0 (l + lcorr )S
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
stiffness s of the spring:
typical absorption values
covers
I
piston acting on air volume
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virtual experiment
back
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air cavity with volume V
piston with area S
external force F makes piston to sink in by ∆l
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
force F leads to a pressure change ∆P with
typical absorption values
covers
back
F
S
penetration depth ∆l corresponds to ∆V with
∆P =
∆V = ∆l · S
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
adiabatic state change (linearized):
∆V
∆P
= −κ
P0
V
inserted:
F
P0 S 2
= −κ
∆l
V
with
s
P0
c= κ
ρ0
follows
S2
F
= s = −c 2 ρ0
∆l
V
Absorption Reflection Transmission
resonance absorber: type Helmholtz
introduction
absorption
characterization
absorber types
resonance frequency:
measurement methods
absorption and impedance
c
f0 =
2π
typical absorption values
covers
back
I
s
S
V (l + lcorr )
for practical applications: introduction of porous
damping in the resonator neck (max. velocity)
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energy loss
lowering of the resonator quality
absorbing effect over a wider frequency range
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber:
panels with holes or slits
(Helmholtz)
Absorption Reflection Transmission
introduction
panel with holes
I
perforated panel in front of an air cavity (with
damping material)
I
spring-mass resonator where:
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
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spring: air cavity
mass: mass of the oscillating air columns in the
holes (end correction!)
damping: porous absorber in the cavity
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber:
micro-perforated absorber
(Helmholtz)
Absorption Reflection Transmission
introduction
micro-perforated absorber
I
panel with very fine holes in front of an air cavity
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spring-mass resonator where:
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
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spring: air cavity
mass: mass of the oscillating air columns (end
correction!)
damping: friction losses in the tiny holes
analytical description available
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
micro-perforated absorber
plate thickness
holes diameter
holes spacing
distance to wall
variant 1 variant 2
3 mm
3 mm
0.4 mm
2 mm
2 mm
15 mm
100 mm 50 mm
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
micro-perforated absorber
I
transparent solutions are possible!
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber:
membrane absorber
Absorption Reflection Transmission
resonance absorber: membrane absorber
introduction
absorption
characterization
I
absorption mechanism:
absorber types
measurement methods
I
spring-mass system
absorption and impedance
I
typical absorption values
covers
I
spring = enclosed air
mass = vibrating plate or membrane
back
I
maximum absorption at the resonance frequency
resonance frequency f0 for stiffness s 00 per unit area and
mass m00 per unit area:
q
f0 =
s 00
m00
2π
Absorption Reflection Transmission
resonance absorber: membrane absorber
introduction
absorption
characterization
stiffness of air cavity per unit area s 00 :
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
s 00 =
ρ0 c 2
lw
with
lw : distance to wall (thickness of air cavity)
and consequently:
q
c mρ000lw
f0 =
2π
Absorption Reflection Transmission
resonance absorber: membrane absorber
introduction
absorption
characterization
absorber types
measurement methods
I
absorption and impedance
typical absorption values
I
range of application: low frequency absorber
design rules:
covers
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back
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minimum plate area 0.4 m2
minimum plate dimensions 0.5 m
air cavity has to be filled with porous absorber
typical absorption α ≈ 0.6 in range of 1. . .2 octaves
sandwich combinations with porous absorber
possible
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: membrane absorber
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
measurement methods
Absorption Reflection Transmission
measurement of absorption
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
methods:
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Kundt’s tube
impedance tube
reverberation chamber
impulse response in situ
Absorption Reflection Transmission
measurement of absorption
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
properties of the methods
typical absorption values
covers
back
angle
phase
Kundt’s tube
normal
(no)
impedance tube
normal
yes
reverb. chamber
diffuse
no
impulse response arbitrary
yes
frequency
discrete
spectrum
third octaves
spectrum
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Kundt’s tube
Absorption Reflection Transmission
Kundt’s tube
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
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tube diameter λ (typ. 10 cm or 2 cm)
incident and reflected sinusoidal plane wave form an
interference pattern (standing wave)
from ppmax
, α can be calculated
min
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
Kundt’s tube
pe : sound pressure amplitude of incident wave
pr : sound pressure amplitude of reflected wave
√
pr
= 1−α
pe
back
sound pressure maxima: constructive interference:
pmax = pe + pr = pe (1 +
√
1 − α)
sound pressure minima: destructive interference:
pmin = pe − pr = pe (1 −
√
1 − α)
Absorption Reflection Transmission
Kundt’s tube
introduction
absorption
characterization
absorber types
measurement methods
from:
absorption and impedance
typical absorption values
covers
back
n=
pmax
pmin
follows the absorption coefficient:
α=1−
n−1
n+1
2
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
impedance tube
Absorption Reflection Transmission
impedance tube
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
I
tube diameter λ (typ. 10 cm resp. 2 cm)
determination of the transfer function between two
fixed microphone positions
Absorption Reflection Transmission
impedance tube
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
with the arbitrary reference pein (A) = 1 follows
H=
p(B)
e −jks + R · e −jk(s+2l)
=
p(A)
1 + R · e −j2k(s+l)
Absorption Reflection Transmission
impedance tube
introduction
absorption
characterization
resolved for R:
absorber types
measurement methods
absorption and impedance
R(f ) =
typical absorption values
covers
e −jks − H(f ) j2k(l+s)
e
H(f ) − e jks
back
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from R: impedance can be calculated (complete
information) and thus α
broadband excitation (white noise, frequency
discrimination with help of FFT)
high quality microphones necessary, calibration with
exchanged microphones
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
reverberation chamber
Absorption Reflection Transmission
reverberation chamber
introduction
absorption
characterization
absorber types
I
measurement methods
absorption and impedance
typical absorption values
covers
I
back
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measurement of the reverberation time T with and
without probe material (10. . .12 m2 )
by usage of empirical relation between α and T , α
can be determined
reverberation time formula found by Sabine (diffuse
field assumption!):
T =
0.16V
A
Absorption Reflection Transmission
reverberation chamber
introduction
absorption
I
characterization
absorber types
measurement methods
maximal accuracy for large differences with and
without material probe
I
absorption and impedance
typical absorption values
covers
back
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→ test chamber with minimal absorption
(reverberation chamber)
result: αS in third octaves or octaves
investigation in diffuse sound field corresponds to
averaging over all incident directions
αS > 1 is possible!
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sound field with absorber violates diffuse field
assumption
edge effects (diffraction along the border of the
probe)
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
reverberation chamber
reverberation chamber at Empa:
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
reverberation chamber
reverberation chamber at Empa:
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
in situ impulse response
measurement
Absorption Reflection Transmission
in situ impulse response measurement
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
in situ determination of absorption coefficients:
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already installed surfaces (e.g. room acoustical
analysis of existing objects)
elements that can’t be brought to the laboratory
investigation for specific angles of incident
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
in situ impulse response measurement
example transparent noise barrier:
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
in situ impulse response measurement
example transparent noise barrier:
Absorption Reflection Transmission
in situ impulse response measurement
introduction
absorption
characterization
absorber types
measurement methods
I
points to consider:
I
absorption and impedance
typical absorption values
covers
back
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the size of the element under test has to be large
enough (critical at low frequencies → Fresnel
zone)
measurement geometry should allow to separate
different contributions (critical at low frequencies)
reflection contributions have to be compensated
for the additional geometrical divergence
relatively large measurement uncertainty for
non-flat surfaces
standardized procedure: EN 1793-5 (Adrienne)
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
normal incidence
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: normal
incidence
situation: plane wave in medium with impedance Z0 hits
a medium with Z1
Absorption Reflection Transmission
introduction
absorption
absorption and impedance: normal
incidence
incident wave: pI , vI with
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
pI
= Z0
vI
reflected wave: pII , vII with
back
pII
= Z0
vII
On the surface holds:
p = pI + pII
v = vI − vII
with:
p
= Z1
v
Absorption Reflection Transmission
introduction
absorption and impedance: normal
incidence
absorption
characterization
absorber types
from
measurement methods
absorption and impedance
typical absorption values
pI + pII = Z1
covers
back
pII
pI
−
Z0 Z0
follows:
pII
Z1 − Z0
=R=
pI
Z1 + Z0
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Z1 = Z0 → R = 0, α = 1
Z1 Z0 → R → 1, α → 0
Absorption Reflection Transmission
introduction
absorption and impedance: normal
incidence
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
porous absorber in front of hard wall:
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hard termination increases resulting impedance →
reduction of the absorption
thickness of the absorber > λ/4 (if possible)
thin layers should be mounted with distance to the
hard termination
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
oblique incidence
Absorption Reflection Transmission
introduction
absorption and impedance: oblique
incidence
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
I
locally reacting absorber
covers
I
back
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only sound propagation in the absorber
perpendicular to the surface (often reasonable
assumption due to refraction)
impedance is independent of the incident angle
laterally reacting absorber
I
relevant sound propagation component parallel to
the surface
Absorption Reflection Transmission
introduction
absorption and impedance: oblique
incidence
absorption
characterization
absorber types
measurement methods
I
for locally reacting absorber:
absorption and impedance
typical absorption values
covers
Z1 −
pII
=R=
pI
Z1 +
back
Z0
cos(φ)
Z0
cos(φ)
with
φ: angle of sound incidence direction relative to the
surface normal direction
Z0
cos(φg )
◦
→ R = 0, α = 1
I
Z1 =
I
φ → 90 → R → −1, phase = 180◦ , α → 0
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
stone floor
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
parquet floor
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
carpet, thickness 5mm
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
plaster
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
acoustically optimized plaster, thickness 20mm
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
window
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
heavy curtain
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
egg carton
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
glass fiber panel, thickness 50 mm
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
panel resonator, 4 mm wood, 120 mm air layer
Absorption Reflection Transmission
typical absorption values
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
audience on upholstered chairs
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
Absorption Reflection Transmission
covers for porous absorbers
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
I
porous absorbers are usually covered by mechanical
protection
I
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plates with holes or slits
requirement: no significant influence on absorption
→ no relevant transmission loss
Absorption Reflection Transmission
covers for porous absorbers
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
I
reason for transmission loss?
back
I
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inertia of the mass of the oscillating air columns in
the openings
acceleration of the air columns has to be low
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
frequency response of the degree of transmission of a
cover with holes:
Absorption Reflection Transmission
covers for porous absorbers
introduction
absorption
I
parameters of the cover:
characterization
I
absorber types
measurement methods
absorption and impedance
typical absorption values
I
covers
I
back
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: ratio of the area of the holes relative to the area
of the panel in %
hole diameter r [mm]
panel thickness l [mm]
end correction 2 · ∆l [mm]
effective panel thickness l ∗ = l + 2 · ∆l [mm]
calculation of the frequency f0.5 for a degree of
transmission of 0.5:
f0.5 ≈ 1500
l∗
Absorption Reflection Transmission
covers for porous absorbers
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
I
design of covers:
back
I
I
f0.5 typically chosen ”sufficiently high”
f0.5 at specific frequency for mid frequency
absorber
Absorption Reflection Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
eth-acoustics-1