acoustics ii: electrical-mechanical- acoustical analogiesisistaff/courses/ak2/... · mechanical...
TRANSCRIPT
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustics II:electrical-mechanical-
acousticalanalogies
Kurt Heutschi2013-01-18
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Motivation
I microphones, loudspeakers consist of mechanical,acoustical and electrical subsystems
I due to their interaction an analysis has to considerall subsystems in integral way
I the fundamental differential equations have identicalform in all systems
I introduction of analogies and conversion ofmechanical and acoustical systems into electricalones
I excellent tools available for analysis of electricalnetworks
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
mechanical systems
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Describing quantities
At a specific point of a mechanical system, the twoquantities of interest are:
I velocity u = dxdt
I force F
From u, further quantities are derived to describe themovement:
I displacement x =∫udt
I acceleration a = dudt
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
mechanical elements
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Mechanical massideal mass:
I incompressible → each point of the mass hasidentical velocity
I physical description: Fres = m · a (Newton)
ports 1 and 2:
u1 = u2 = u
F1 − F2 = mdu
dt
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Springideal spring:
I stiffness s independent of excursion x
I physical description: F = s · x (Hook’s law)
I no force difference along the spring
F1 = F2 = F
F = s
∫u1 − u2dt
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Frictionideal friction:
I proportionality between friction force and velocity
I physical description: F = R · uI no force difference along the friction element
F1 = F2 = F
F = R(u1 − u2)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Links
ideal link:
I connecting element for mechanical building blocks
I no mass and incompressible
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Lever
ideal lever:
I frictionless and massless
I mechanical transformer
F1l1 − F2l2 = 0
u1l2 + u2l1 = 0
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Mechanical sources
Mechanical sources:
I force sourceI example: conductor in a magnetic field → force∼ B × I but independent of velocity
I velocity sourceI example: motor with a flywheel → velocity
independent of load (force)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum
I given: external force: F (t) = F̂ sin(ωt)
I unknown: movement of massI excursion x(t)I velocity u(t) = dx/dtI acceleration a(t) = d2x/dt2
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum:
solution?
equilibrium of forces:
Facceleration + Ffriction + Fspring = F
differential equation for x in complex writing forharmonic excitation:
md2x
dt2+ R
dx
dt+ sx = F̂ e jωt
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum:
solution?
general solution of the differential equation:
x(t) =F̂ e jωt
(jω)2m + jωR + s=
F̂ e jωt
jω(jωm + R + s
jω
)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum:
solution?
withZm = jωm + R +
s
jω
the quantities become:
x(t) =F̂ e jωt
jωZm
u(t) =F̂ e jωt
Zm
a(t) =jωF̂ e jωt
Zm
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum:
solution?
amplitude responses:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
resonance system: spring pendulum
consequences for microphones:
I majority of mics use a membrane (mechanicalspring-mass resonance system)
I condition for flat amplitude response:I operation below resonance if electrical output
proportional to membrane excursionI operation at resonance if electrical output
proportional to membrane velocity
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
acoustical systems
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
describing quantities
fundamental acoustical quantities:
I sound pressure p
I sound particle velocity v or volume flow Q =∫SvdS
movie: rohr-open5-4
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical elements
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical mass
Acoustical mass:
I accelerated but not compressed air
I realization: tube of length l , diameter d whereλ� l and λ� d
∆F = ρAldv
dtNewton
whereρ: density of air
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical compliance
Acoustical compliance:
I compressed but not accelerated air
I realization: cavity V with opening area A (largestdimension l � λ)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical compliance
I experiment: virtual piston presses on opening A withforce F
I piston sinks in by ∆l = Fs
( s: stiffness of thecompliance )
with the assumption of adiabatic behavior (notemperature exchange):
s = c2ρA2
V
wherec : speed of sound
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical compliance
I position of the opening is irrelevant
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical resistance
Acoustical resistance:
I element introduces loss (conversion of sound energyinto heat)
I realization: porous material, small tube
resistance of a small tube:
∆p = v8lη
r 2
where∆p: sound pressure difference on both sidesv : sound particle velocityl : length of the tuber : radius of the tube (r � l)η: dynamic viscosity of air: 1.82× 10−5Nsm−2
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Acoustical resistance
I acoustical resistance of a tube is alwaysaccompanied by an acoustical mass
I mass behavior can be neglected for small diametersand low frequencies
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
analogies
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Analog quantities
potential quantity flow quantityelectrical system: voltage currentmechanical system: velocity u force Facoustical system: sound pressure p volume flow Q
→ dual analogy would be possible as well
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Analog quantities
Amplitude scaling:
I conversion of acoustical and mechanical quantitiesinto electrical ones requires amplitude and unitconversion factors
I arbitrary amplitude conversion factors are allowed
I here: = 1
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Analog quantities
mechanical → electrical:
U = G1u with G1 = 1Vs
m
I =1
G2F with G2 = 1
N
A
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Analog quantities
acoustical → electrical:
U = G3p with G3 = 1Vm2
N
I =1
G4Q with G4 = 1
m3
As
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: general
Conversion of mechanical and acoustical elements intoanalog electrical ones is performed using impedancedefinition:
impedance =potentialQuantity
flowQuantity
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: mechanical mass
impedance Z of the mechanical mass:
Z =u
F=
u
m dudt
with u = u0ejωt follows du
dt= u0jωe
jωt and finally
Z =1
jωm
I mechanical mass , electrical capacitor
I inertia of the mass is understood relative toreference system at rest → capacitors always atground potential
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: mechanical spring
impedance Z of the mechanical spring:
Z =u
F=
u
s∫udt
with u = u0ejωt follows
∫udt = u0
1jωe jωt and finally
Z = jω1
s
I mechanical spring , electrical inductance
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: mechanical friction
impedance Z of a mechanical friction element:
Z =u
F=
u
Ru=
1
R
I mechanical friction element , electrical resistance
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: acoustical mass
impedance Z of the acoustical mass:
Z =p
Q=
∆FA
Av=ρAl dv
dt
AAv
with v = v0ejωt follows dv
dt= v0jωe
jωt and finally
Z = jωρl
A
I acoustical mass , electrical inductance
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedance: acoustical compliance
impedance Z of the acoustical compliance:
Z =p
Q=
∆FA
Av=
c2ρA2
V∆l
AAv=
c2ρA2
V
∫vdt
AAv
with v = v0ejωt follows
∫vdt = v0
1jωe jωt and finally
Z =c2ρ
jωV
I acoustical compliance , electrical capacitor
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedance: acoustical resistance
impedance Z of the acoustical resistance:
Z =p
Q=
8lη
πr 4
wherel : length of the tuber : radius of the tube (r � l)η: dynamic viscosity in air = 1.82 ×10−5 Nsm−2
I acoustical resistance , electrical resistance
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: overview
electrical mechanical acoustical
Z = R resistance resistance resistance
Z = 1jωC
capacitor mass compliance
Z = jωL inductance spring mass
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedances: overview
electrical mechanical acoustical
Z = R R R = 1Rm
G1G2 R = RmG3G4
Z = 1jωC
C C = m 1G1G2
C = Vρc2
1G3G4
Z = jωL L L = 1sG1G2 L = ρl
AG3G4
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Examples of acoustical andmechanical networks
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical resonance circuit
combination of acoustical mass and compliance:
→
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical resonance circuit
combination of acoustical mass and compliance:
→ parallel resonance circuit
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical resonance circuit
combination of acoustical mass and compliance:
→
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical resonance circuit
combination of acoustical mass and compliance:
→ series resonance circuit
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical muffler
acoustical muffler:
I no damping for low frequency air flow
I high damping for high frequency sound
I → acoustical low pass filter
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical transmission line
description of tube-like structures (cross sect. area = A)but length > λ:
I subdivision of the tube into small sections of lengthl (l � λ)
I representation of each section by mass andcompliance properties
I equivalent network: L,C , L T-section withI L = ρl
2AI C = Al
ρc2
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical transmission line
numerical example:
I hard terminated tube of length 24 cm
I cross sectional area A = 10−4 m2
I discretization: l = 0.04 m
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: acoustical transmission line
Spice simulation of the voltage at the hard termination:
theoretically expected resonance frequencies:1λ4
= 0.24m → 354 Hz, 3λ4
= 0.24m → 1063 Hz
5λ4
= 0.24m → 1771 Hz, 7λ4
= 0.24m → 2479 Hz
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical resonance circuit
combinations of mechanical mass and spring:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical resonance circuit
combinations of mechanical mass and spring:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical resonance circuit
I sinusoidal force excitation
I analysis of the mechanical spring pendulum withhelp of an equivalent electrical circuit.
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical spring pendulum
I x = FF/s
I u = FR/R
I a = FM/m
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical vibration damper
I strategy in case of sinusoidal vibration →implementation of an additional resonance system
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Example: mechanical vibration damper
I additional series resonance circuit
I at resonance: impedance → 0
I short-circuit for the excitation force
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Measurement of acousticalimpedances
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Measurement of acoustical impedances
I investigation of unknown acoustical impedancesI e.g. quality control of wind instrumentsI e.g. audiometric tests → input impedance of the
middle ear
I measurement methodsI combination of sound pressure and sound particle
sensor, e.g. µFlownI two pressure sensors and known acoustical
resistance
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Measurement of acoustical impedances
method with two pressure sensors and known acousticalresistance
evaluation strategies:
I loudspeaker signal controlled for constant differencep1 − p2 → p2 ∼ Z
I calculation from measured spectra
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acousticalelements
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
I simulation of acoustical behavior of long tubes:I series of short sections, each represented by
lumped elementsI or introduction of a distributed acoustical element→ four pole
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
I assumption: 2 plane waves traveling in oppositedirections
p̌(x) = Ae−jkx + Be jkx
v̌(x) =A
ρce−jkx − B
ρce jkx
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
I definition:I p̌(x = 0) ≡ p̌1 and p̌(x = d) ≡ p̌2
I v̌(x = 0) ≡ v̌1 and v̌(x = d) ≡ v̌2
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
insert above definition:
I p̌(x = 0) = p̌1 and p̌(x = d) = p̌2
I v̌(x = 0) = v̌1 and v̌(x = d) = v̌2
in:
p̌(x) = Ae−jkx + Be jkx
v̌(x) =A
ρce−jkx − B
ρce jkx
and resolve for p̌2 and v̌2
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
yields the four pole equations:
p̌2 =p̌1
2e−jkd +
p̌1
2e jkd +
v̌1ρc
2e−jkd − v̌1ρc
2e jkd
= p̌1 cosh(jkd)− v̌1ρc sinh(jkd)
v̌2 =1
ρc
p̌1
2e−jkd − 1
ρc
p̌1
2e jkd +
v̌1
2e−jkd +
v̌1
2e jkd
= −p̌11
ρcsinh(jkd) + v̌1 cosh(jkd)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
representation of the above four-pole relations by T-typecircuit:
with:
Z1 = jρc1− cos(kd)
sin(kd)
Z2 =−jρc
sin(kd)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
distributed acoustical elements
impedance at the entrance of tube of length d with hardtermination:
p̌1
v̌1= Z1 + Z2
p̌1
v̌1=
jρc − jρc cos(kd)− jρc
sin(kd)= −jρc cot(kd)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
coupling of mechanical,acoustical and electrical
systems
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
interfaces
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
interfaces
”linking” of different subsystems:
I transformation of different physical quantities byhelp of interfaces:
I type 1: conversion of potential quantity intopotential quantity and flow quantity into flowquantity
I type 2: conversion of potential quantity into flowquantity and vice versa
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Interfaces: transformer
interface type 1: transformer
relations for the transformer:
U2 = nU1 (1)
I2 =1
nI1 (2)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
interface: gyrator
interface type 2: gyrator
relations for the gyrator:
U2 = I1m (3)
I2 = U11
m(4)
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Dual conversion
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Dual conversion
motivation: elimination of gyrators
I selection of an arbitrary conversion factor r
I dual conversion of a suitable region of the network(cut in half all gyrators)
I gyrators → transformers
I series arrangement → parallel arrangement
I parallel arrangement → series arrangement
I L → C , C → L, R → 1/R
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Dual conversion
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Dual conversion
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
application:thin absorber
in front of a hard wall
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Thin absorber in front of a hard wall
discussion of the behavior of a thin porous layer in frontof a hard wall by an equivalent network for perpendicularincidence
→ equivalent electrical network?
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Thin absorber in front of a hard wall
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Thin absorber in front of a hard wall
I absorption: dissipated power according to iR · uI max. absorption for
I ZS → 0I RS = Z0
I m→∞ and f →∞
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
application:measurement of the
impedance at the earETH-Diss. Alfred
Stirnemann
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Impedance measurement for the diagnosis
of middle ear diseases
idea:
I estimation of middle-ear transfer characteristicsfrom measured impedance at the entrance of theear canal
I detection of possible diseases in the middle-ear
I e.g. Otosclerosis
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Measurement of the impedance at the ear
- principal structure
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Model of the middle ear - equivalent
network
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Model of the middle ear - equivalent
network
complete equivalent network
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Model of the middle ear - equivalent
network
dual conversion
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Model of the middle ear - equivalent
network
network after dual conversion and neglect of irrelevantelements
vTR : velocity of ear drumvST : velocity of inner ear window
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Diagnosis
diagnosis:
I measurement of the input impedance
I estimation of the element values
I comparison with limits → indication for possibledisease
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Experimentsexperiments - model fit:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Experiments
experiments - comparison of impedances:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
Experiments
experiments - velocity of inner ear window:
analogies
mechanicalsystems
describing quantities
mechanical elements
Mechanical sources
Mechanical resonance -spring pendulum
acoustical systems
describing quantities
Acoustical elements
analogies
potential and flowquantities
Impedances
Measurement of acousticalimpedances
distributed elements
coupling
interfaces
Dual conversion
thin absorbers
measurement ofthe impedance atthe ear
Model of the middle ear
Diagnosis
Experiments
back
eth-acoustics-2