characterization absorber types absorption and impedance
TRANSCRIPT
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Acoustics I:absorption-reflection-
transmission
Kurt Heutschi2013-01-25
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 ofabsorption and reflection
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
characterization of absorption and
reflection
I absorption property → absorption coefficient (real,0 < α < 1 )
α =absorbed energy
incident energy
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
characterization of absorption and
reflection
I reflection property → reflection factor (complex,0 < |R| < 1)
R =sound pressure reflected wave
sound pressure incident wave
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
characterization of absorption and
reflection
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
porous absorbers
I materials:I glass fibersI organic fibers (e.g. wood)I open foams
I absorption mechanism:I sound particle velocity corresponds to oscillating
air in the poresI → friction losses
I placement:I 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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
I absorption mechanism:I spring-mass system
I spring = enclosed air volumeI mass = oscillating air column
I maximal absorption at resonance
resonance frequency f0 for stiffness s of the spring andmass m:
f0 =
√sm
2π
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
I mass m = ?
I stiffness of the spring s = ?
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
mass m:
I mass of the oscillating air column:I mass of cylinder of length l + end correction lcorr
I lcorr ≈ 0.8R (radius of cylinder)I with S : cross sectional area of cylinder follows:
m = ρ0(l + lcorr)S
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
stiffness s of the spring:
I piston acting on air volume
I virtual experimentI air cavity with volume VI piston with area SI external force F makes piston to sink in by ∆l
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
force F leads to a pressure change ∆P with
∆P =F
S
penetration depth ∆l corresponds to ∆V with
∆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):
∆P
P0= −κ∆V
V
inserted:
F
∆l= −κP0S
2
V
with
c =
√κP0
ρ0
follows
F
∆l= s = −c2ρ0
S2
V
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: type Helmholtz
resonance frequency:
f0 =c
2π
√S
V (l + lcorr)
I for practical applications: introduction of porousdamping in the resonator neck (max. velocity)
I energy lossI lowering of the resonator qualityI 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
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
panel with holes
I perforated panel in front of an air cavity (withdamping material)
I spring-mass resonator where:I spring: air cavityI mass: mass of the oscillating air columns in the
holes (end correction!)I 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
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
micro-perforated absorber
I panel with very fine holes in front of an air cavity
I spring-mass resonator where:I spring: air cavityI mass: mass of the oscillating air columns (end
correction!)I damping: friction losses in the tiny holes
I analytical description available
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
micro-perforated absorbervariant 1 variant 2
plate thickness 3 mm 3 mmholes diameter 0.4 mm 2 mmholes spacing 2 mm 15 mmdistance to wall 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
backresonance absorber:membrane absorber
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: membrane absorber
I absorption mechanism:I spring-mass system
I spring = enclosed airI mass = vibrating plate or membrane
I maximum absorption at the resonance frequency
resonance frequency f0 for stiffness s ′′ per unit area andmass m′′ per unit area:
f0 =
√s′′
m′′
2π
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: membrane absorber
stiffness of air cavity per unit area s ′′:
s ′′ =ρ0c
2
lw
withlw : distance to wall (thickness of air cavity)and consequently:
f0 =c√
ρ0
m′′lw
2π
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
resonance absorber: membrane absorber
I range of application: low frequency absorber
I design rules:I minimum plate area 0.4 m2
I minimum plate dimensions 0.5 mI air cavity has to be filled with porous absorber
I typical absorption α ≈ 0.6 in range of 1. . .2 octaves
I sandwich combinations with porous absorberpossible
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
measurement of absorption
I methods:I Kundt’s tubeI impedance tubeI reverberation chamberI impulse response in situ
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
measurement of absorption
properties of the methods
angle phase frequencyKundt’s tube normal (no) discreteimpedance tube normal yes spectrumreverb. chamber diffuse no third octavesimpulse response arbitrary yes 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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Kundt’s tube
I tube diameter � λ (typ. 10 cm or 2 cm)
I incident and reflected sinusoidal plane wave form aninterference pattern (standing wave)
I from pmax
pmin, α can be calculated
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Kundt’s tube
pe : sound pressure amplitude of incident wavepr : sound pressure amplitude of reflected wave
prpe
=√
1− α
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
Kundt’s tube
from:
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
impedance tube
I tube diameter � λ (typ. 10 cm resp. 2 cm)
I determination of the transfer function between twofixed microphone positions
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
impedance tube
with the arbitrary reference pein(A) = 1 follows
H =p(B)
p(A)=
e−jks + R · e−jk(s+2l)
1 + R · e−j2k(s+l)
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
impedance tube
resolved for R :
R(f ) =e−jks − H(f )
H(f )− e jkse j2k(l+s)
I from R : impedance can be calculated (completeinformation) and thus α
I broadband excitation (white noise, frequencydiscrimination with help of FFT)
I high quality microphones necessary, calibration withexchanged microphones
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back reverberation chamber
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
reverberation chamber
I measurement of the reverberation time T with andwithout probe material (10. . .12 m2)
I by usage of empirical relation between α and T , αcan be determined
I reverberation time formula found by Sabine (diffusefield assumption!):
T =0.16V
A
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
reverberation chamber
I maximal accuracy for large differences with andwithout material probe
I → test chamber with minimal absorption(reverberation chamber)
I result: αS in third octaves or octaves
I investigation in diffuse sound field corresponds toaveraging over all incident directions
I αS > 1 is possible!I sound field with absorber violates diffuse field
assumptionI 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
backin situ impulse response
measurement
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
in situ impulse response measurement
I in situ determination of absorption coefficients:I already installed surfaces (e.g. room acoustical
analysis of existing objects)I elements that can’t be brought to the laboratoryI 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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
in situ impulse response measurement
I points to consider:I the size of the element under test has to be large
enough (critical at low frequencies → Fresnelzone)
I measurement geometry should allow to separatedifferent contributions (critical at low frequencies)
I reflection contributions have to be compensatedfor the additional geometrical divergence
I relatively large measurement uncertainty fornon-flat surfaces
I 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
incidencesituation: plane wave in medium with impedance Z0 hitsa medium with Z1
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: normal
incidenceincident wave: pI, vI with
pI
vI= Z0
reflected wave: pII, vII with
pII
vII= Z0
On the surface holds:
p = pI + pII
v = vI − vII
with:
p
v= Z1
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: normal
incidence
from
pI + pII = Z1
(pI
Z0− pII
Z0
)follows:
pII
pI= R =
Z1 − Z0
Z1 + Z0
I Z1 = Z0 → R = 0, α = 1
I Z1 � Z0 → R → 1, α→ 0
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: normal
incidence
I porous absorber in front of hard wall:I hard termination increases resulting impedance →
reduction of the absorptionI thickness of the absorber > λ/4 (if possible)I 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
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: oblique
incidence
I locally reacting absorberI only sound propagation in the absorber
perpendicular to the surface (often reasonableassumption due to refraction)
I impedance is independent of the incident angle
I laterally reacting absorberI relevant sound propagation component parallel to
the surface
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
absorption and impedance: oblique
incidence
I for locally reacting absorber:
pII
pI= R =
Z1 − Z0
cos(φ)
Z1 + Z0
cos(φ)
withφ: angle of sound incidence direction relative to thesurface normal direction
I Z1 = Z0
cos(φg )→ R = 0, α = 1
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I stone floor
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I parquet floor
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I carpet, thickness 5mm
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I plaster
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I acoustically optimized plaster, thickness 20mm
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I window
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I heavy curtain
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I egg carton
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I glass fiber panel, thickness 50 mm
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
I panel resonator, 4 mm wood, 120 mm air layer
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
typical absorption values
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
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
I porous absorbers are usually covered by mechanicalprotection
I plates with holes or slitsI requirement: no significant influence on absorption→ no relevant transmission loss
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
I reason for transmission loss?I inertia of the mass of the oscillating air columns in
the openingsI 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 acover with holes:
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
I parameters of the cover:I ε: ratio of the area of the holes relative to the area
of the panel in %I hole diameter r [mm]I panel thickness l [mm]I end correction 2 ·∆l [mm]I effective panel thickness l∗ = l + 2 ·∆l [mm]
I calculation of the frequency f0.5 for a degree oftransmission of 0.5:
f0.5 ≈ 1500ε
l∗
Absorption -Reflection -
Transmission
introduction
absorption
characterization
absorber types
measurement methods
absorption and impedance
typical absorption values
covers
back
covers for porous absorbers
I design of covers:I f0.5 typically chosen ”sufficiently high”I 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
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