characterization absorber types absorption and impedance ...

Absorption -Reflection -

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absorption

characterization

absorber types

measurement methods

absorption and impedance

typical absorption values

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Acoustics I:absorption-reflection-

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Kurt Heutschi2013-01-25


Transmission

introduction

absorption

characterization

absorber types

measurement methods



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Transmission

introduction

absorption

characterization

absorber types

measurement methods



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introduction


Transmission

introduction

absorption

characterization

absorber types

measurement methods



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back absorption


Transmission

introduction

absorption

characterization

absorber types

measurement methods



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characterization ofabsorption and reflection


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introduction

absorption

characterization

absorber types

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characterization of absorption and

reflection

I absorption property → absorption coefficient (real,0 < α < 1 )

α =absorbed energy

incident energy


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absorption

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reflection

I reflection property → reflection factor (complex,0 < |R| < 1)

R =sound pressure reflected wave

sound pressure incident wave


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absorption

characterization

absorber types

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reflection

I relation between α and R for plane waves:

α = 1− |R|2


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absorption

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back absorber types


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absorption

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absorber types

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back porous absorbers


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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


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absorption

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resonance absorber:type Helmholtz


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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


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I mass m = ?

I stiffness of the spring s = ?


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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


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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


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force F leads to a pressure change ∆P with

∆P =F

S

penetration depth ∆l corresponds to ∆V with

∆V = ∆l · S


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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


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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


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resonance absorber:panels with holes or slits

(Helmholtz)


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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


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resonance absorber:micro-perforated absorber

(Helmholtz)


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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


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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


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micro-perforated absorber

I transparent solutions are possible!


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backresonance absorber:membrane absorber


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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


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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


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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


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absorption

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absorption

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measurement of absorption

I methods:I Kundt’s tubeI impedance tubeI reverberation chamberI impulse response in situ


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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


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back Kundt’s tube


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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


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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)


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Kundt’s tube

from:

n =pmax

pmin

follows the absorption coefficient:

α = 1−(n − 1

n + 1

)2


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absorption

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back impedance tube


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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


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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)


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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


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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


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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)


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reverberation chamber at Empa:


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backin situ impulse response

measurement


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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


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example transparent noise barrier:


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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)


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back normal incidence


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absorption and impedance: normal

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


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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


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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


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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


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back oblique incidence


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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


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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


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I stone floor


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I parquet floor


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I carpet, thickness 5mm


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I plaster


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I acoustically optimized plaster, thickness 20mm


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I window


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I heavy curtain


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I egg carton


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I glass fiber panel, thickness 50 mm


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I panel resonator, 4 mm wood, 120 mm air layer


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I audience on upholstered chairs


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back covers for porous absorbers


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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


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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


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frequency response of the degree of transmission of acover with holes:


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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∗


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I design of covers:I f0.5 typically chosen ”sufficiently high”I f0.5 at specific frequency for mid frequency

absorber


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characterization absorber types absorption and impedance ...

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