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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