# characterization absorber types absorption and impedance ...

### Transcript of characterization absorber types absorption and impedance ...

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

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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

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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

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resonance absorber:type Helmholtz

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

covers

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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 -

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introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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 -

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introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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

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resonance absorber:panels with holes or slits

(Helmholtz)

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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resonance absorber:micro-perforated absorber

(Helmholtz)

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 -

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introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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reverberation chamber

reverberation chamber at Empa:

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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

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absorption and impedance: normal

incidencesituation: plane wave in medium with impedance Z0 hitsa medium with Z1

Absorption -Reflection -

Transmission

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absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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

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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

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typical absorption values

I stone floor

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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typical absorption values

I parquet floor

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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typical absorption values

I carpet, thickness 5mm

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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typical absorption values

I plaster

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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typical absorption values

I window

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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typical absorption values

I heavy curtain

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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typical absorption values

I egg carton

Absorption -Reflection -

Transmission

introduction

absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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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

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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

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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

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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

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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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