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Sound attenuation by hearing aidearmold tubing

Comsol conference 2008

Mads J. H. JensenWidex A/S, Denmark

Presented at the COMSOL Conference 2008 Hannover

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Contents

MotivationModeling

• Model setup• Theory … hopefully not too many equations• Boundary conditions

ResultsConclusion

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Motivation: why “sound attenuation”Introductory study in preparation for modeling a full hearing aid device

Feedback in hearing aids:• Mechanical stability• Acoustic feedback:

– Leaks and/or vent– Sound radiation (tubing)?

feedback

receiver or loud speaker

microphones

earmold

earmold tube

Thicker tubes?Other materials?Include in future models?

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Virtual measurement set-up

Real attenuation = Ltube – L0

Measured attenuation = Lmic – L0

L. Flack, R. White, J. Tweed, D.W. Gregory, and M.Y. QureshiBrit. J. of Aud., 29, 237 (1995)

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Model setup

FEM domain:Fluid (air)

Solid (tube)PML

In: Electro-acoustic

equivalent

Out: Electro-acoustic

equivalent

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Theory: electroacoustic model

Electric analogue to an acoustic system

An acoustic system may also be terminated by an acoustic impedance Zac

For this model to hold we assume plane waves!

paQa

pbQb

Q

Zac

Q Q

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Theory: thermoviscous acoustics

Assuming harmonic variations a small parameter expansion of the Navier-Stokes, continuity, and the energy equation yields:

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Theory: elastic waves in solids

Assuming small deformations in a solidMomentum:

Stress (elastic) and strain tensor (linearized):

Modeling losses Young’s modulus is represented as

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FEM domain (axisymmetric)

σ = 0.45 (Poisson ratio)

E = 4.1 107 Pa (Young’s modulus)

η = 0.019 (loss factor)

ρ = 1220 kg/m3 (density)

Ê = E(1 + ηi) (complex Young’s modulus)

Frequency: f [Hz]

Temperature: T [K]

Atmospheric pressure: p = 105 Pa

Density: ρ [kg/m^3]

Speed of sound: c [m/s]

Dynamic viscosity: μ [Pa·s]

Heat conductivity: κ [W/(m · K)]

Specific heat (@ const. p): Cp [J/(kg·K)]

Ratio of specific heats: γ = Cp/Cv

measured properties of solid

other parameters

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Weak formulation for FEM and PML

Governing (fluid domain)

Perfectly matched layer (PML, open boundary)

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AIBC: Inlet boundary condition

Electroacoustic relation for BCRequires plane wave at inlet ∂Ωe

Solve for the non-evanescent eigen-solution ue on inlet ∂Ωe

Apply BC as weak constraint and scale uwith Lagrange multiplier

∂Ωe

n

δe

Ω

**

VI Q

pQ Zac

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Other BCs

Sound hard wall (isothermal):

Solid fluid coupling (continuity of normal stress and displacement):

Outlet BC as inlet BC (no source):p = Q Zac

solidfluid

n

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Results: sound pressure level

L=20 log(p/pref) where pref = 20 μPa

f = 1000 Hz

0 5 10 15 20 25-40

-20

0

20

40

60

80

100

120

R (mm)

SP

LR

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Results: sound attenuation

102 103 10460

70

80

90

100

110

120

130

140

150

160

f (Hz)

Sou

nd a

ttenu

atio

n (d

B)

Lcoupler – L0

Ltube – L0

Flack et al.

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Results: acoustic feedback

102 103 104-60

-40

-20

0

20

40

60

80

f (Hz)

gain

(dB

rel.

1V)

2.0 mm vent

1.0 mm vent

0.5 mm vent

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Conclusions

2D model to analyze sound radiationPML for thermoviscous acoustic systemCoupling between electroacoustic model and FEM with AIBC

Order of magnitude OK (Flack et al.)Attenuation is high for standard earmold tubing (> 80 dB) Feedback @ high frequencies? More detailed study needed.

Some numerical effects/instabilities in the system –comments are welcome after the session!

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Results: pressure / stress level

10 dB SPL

-50 dB SPL

130 dB SPL

110 dB SPL

10 dB SPL

28 dB SPL

L=20 log(p/pref) where pref = 20 μPa f = 1000 Hz