05 Electroacoustics Flashcards
What is a lumped model?
A lumped model is a:
A way to simplify the model into the main compenents or simple equations
What condition applies in lumped models?
In lumped models, the wavelength (m) must be larger than the dimension of the system (m).
What is the formula to calculate frequency range for the human ear?
f = c / λ, where c is the speed of sound in m/s and λ is the wavelength.
What is the speed of sound?
The speed of sound is 343 m/s.
How can the maximum wavelength for the lumped model of the human ear be calculated?
max λ = c / f_min = 300 m/s / 100 Hz = 3 m.
How can the minimum wavelength for the lumped model of the human ear be calculated?
min λ = c / f_max = 300 m/s / 10,000 Hz = 3 cm.
What are the fundamental variables of electrical systems?
The fundamental variables are Voltage (U or V in volts), Current (I in amperes), and Resistance (R in ohms).
What does the Law of Ohm state?
The Law of Ohm defines the relation between voltage (U), current (I), and resistance (R) as U = I * R.
How is general impedance defined in electrical systems?
Impedance (Z) can be defined as Z = U / I.
What are the two forms of current in electrical systems?
The two forms of current are direct current (DC) and alternating current (AC).
How is resistance (R) defined graphically?
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
What is a phasor?
A phasor is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (φ) are time-invariant.
What is the relationship between current and voltage in an AC circuit?
In an AC circuit, the current (I) and voltage (U) may be out of phase, and this relationship can be described with impedance (Z).
How can the complex number of Impedence (Z) be described by the summation of two vectors?
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.
What are the 3 forms of electrical impedances?
There are three types of impedances:
- Resistor (R)
- Capacitor (C)
- Inductor (L).
Give the expressions of resistor, capacitor, and inductor as phasors
- Z_R = u(t)/i(t) = R
- Z_C = u(t)/i(t) = 1/jwC (phase difference of -90° = current leads voltage by 90°)
- Z_L = u(t)/i(t) = jwL (phase difference of +90° = voltage leads current by +90°)
What does conductance (G) represent?
Conductance (G) is the reciprocal of resistance (R), expressed as G = 1/R.
What is Hook’s law?
Hook’s law states that the force (F) exerted by a spring is proportional to its displacement (x), expressed as F = k * x.
What are the fundamental variables of mechanical systems?
The fundamental variables are Force (F in newtons), Velocity (v in m/s), Displacement (x in meters), and Acceleration (a in m/s²).
What are the three elements of a mechanical system?
Damper (resistor), mass (comparable to capacitor), spring (comparable to inductor)
What is the equation relating force and acceleration in mechanical systems?
F = m * (dv/dt), where m is mass.
(F = m*a)
What are the fundamental variables of acoustical systems?
The fundamental variables are Sound Pressure (P in pascals) and Volume Velocity (q in m/s).
What are the three main elements of acoustic systems?
Damper (Resistance) - Converts acoustic energy into heat
Acoustic Compliance - Compressed air (no temp. change)
Acoustic Mass (Inertance) - Accelerated but not compressed air
What is a Helmholtz resonator?
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
What is the ideal pressure conditions in an ideal (healthy) ear?
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)
How would flexibility be returned if you have an increased pressure in one of the sides? (either external auditory canal or the inner ear)
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
How does the resonance frequency relate to the acoustic resistance?
The resonance frequency corresponds to the frequency at which the impedance of the system is minimized.
What is the significance of the Bode diagram in acoustics?
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.
What do lumped models let us do?
They allow us to translate different engineering modalities using an element where we define an ACROSS and a THROUGH variable
