05 Electroacoustics

Question 1

What is a lumped model?

Answer 1

A lumped model is a:
A way to simplify the model into the main compenents or simple equations

Question 2

What condition applies in lumped models?

Answer 2

In lumped models, the wavelength (m) must be larger than the dimension of the system (m).

Question 3

What is the formula to calculate frequency range for the human ear?

Answer 3

f = c / λ, where c is the speed of sound in m/s and λ is the wavelength.

Question 4

What is the speed of sound?

Answer 4

The speed of sound is 343 m/s.

Question 5

How can the maximum wavelength for the lumped model of the human ear be calculated?

Answer 5

max λ = c / f_min = 300 m/s / 100 Hz = 3 m.

Question 6

How can the minimum wavelength for the lumped model of the human ear be calculated?

Answer 6

min λ = c / f_max = 300 m/s / 10,000 Hz = 3 cm.

Question 7

What are the fundamental variables of electrical systems?

Answer 7

The fundamental variables are Voltage (U or V in volts), Current (I in amperes), and Resistance (R in ohms).

Question 8

What does the Law of Ohm state?

Answer 8

The Law of Ohm defines the relation between voltage (U), current (I), and resistance (R) as U = I * R.

Question 9

How is general impedance defined in electrical systems?

Answer 9

Impedance (Z) can be defined as Z = U / I.

Question 10

What are the two forms of current in electrical systems?

Answer 10

The two forms of current are direct current (DC) and alternating current (AC).

Question 11

How is resistance (R) defined graphically?

Answer 11

Current goes through an element at voltage goes over it. When their values are plotted (in AC current) the difference between the 2 lines at their peak amplitudes makes up the resistance

Question 12

What is a phasor?

Answer 12

A phasor is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (φ) are time-invariant.

Question 13

What is the relationship between current and voltage in an AC circuit?

Answer 13

In an AC circuit, the current (I) and voltage (U) may be out of phase, and this relationship can be described with impedance (Z).

Question 14

How can the complex number of Impedence (Z) be described by the summation of two vectors?

Answer 14

The complex impedance (Z) can be described as the summation of resistance (R) and reactance (X) represented as vectors: Z = R + jX, where R is the real part (resistive component) and jX is the imaginary part (reactive component), with “j” being the imaginary unit.

Question 15

What are the 3 forms of electrical impedances?

Answer 15

There are three types of impedances:
- Resistor (R)
- Capacitor (C)
- Inductor (L).

Question 16

Give the expressions of resistor, capacitor, and inductor as phasors

Answer 16

1. Z_R = u(t)/i(t) = R
2. Z_C = u(t)/i(t) = 1/jwC (phase difference of -90° = current leads voltage by 90°)
3. Z_L = u(t)/i(t) = jwL (phase difference of +90° = voltage leads current by +90°)

Question 17

What does conductance (G) represent?

Answer 17

Conductance (G) is the reciprocal of resistance (R), expressed as G = 1/R.

Question 18

What is Hook’s law?

Answer 18

Hook’s law states that the force (F) exerted by a spring is proportional to its displacement (x), expressed as F = k * x.

Question 19

What are the fundamental variables of mechanical systems?

Answer 19

The fundamental variables are Force (F in newtons), Velocity (v in m/s), Displacement (x in meters), and Acceleration (a in m/s²).

Question 20

What are the three elements of a mechanical system?

Answer 20

Damper (resistor), mass (comparable to capacitor), spring (comparable to inductor)

Question 21

What is the equation relating force and acceleration in mechanical systems?

Answer 21

F = m * (dv/dt), where m is mass.

(F = m*a)

Question 22

What are the fundamental variables of acoustical systems?

Answer 22

The fundamental variables are Sound Pressure (P in pascals) and Volume Velocity (q in m/s).

Question 23

What are the three main elements of acoustic systems?

Answer 23

Damper (Resistance) - Converts acoustic energy into heat

Acoustic Compliance - Compressed air (no temp. change)

Acoustic Mass (Inertance) - Accelerated but not compressed air

Question 24

What is a Helmholtz resonator?

Answer 24

A Helmholtz resonator is a device that is used to determine the resonance frequency of a system and consists of a bottle-like shape with specific dimensions.

The “A” refers to the area of teh bottle opening

Question 25

What is the ideal pressure conditions in an ideal (healthy) ear?

Answer 25

The auditory canal is modelled as a small tube. In ideal conditions there is no pressure difference between the auditory canal (external ear canal [EAC]) and the middle ear (i.e. they are equal)

Question 26

How would flexibility be returned if you have an increased pressure in one of the sides? (either external auditory canal or the inner ear)

Answer 26

If there is a pressure increase on one side, there must be a pressure increase on the other too. And vice versa

This is regulated by the Eustachian tube in the middle ear

Unequal pressures can lead to a number of pathologies like tympanic membrane retraction

Question 27

How does the resonance frequency relate to the acoustic resistance?

Answer 27

The resonance frequency corresponds to the frequency at which the impedance of the system is minimized.

Question 28

What is the significance of the Bode diagram in acoustics?

Answer 28

The Bode diagram depicts the magnitude and phase of a complex impedance as a function of frequency, providing insights into the frequency response of a system.

Question 29

What do lumped models let us do?

Answer 29

They allow us to translate different engineering modalities using an element where we define an ACROSS and a THROUGH variable