Final Exam Flashcards
Force (Inertial)
Force (inertial) = mass * acceleration
- newton’s second law of motion
- measured in Newtons
F=ma
Pressure
Pressure = Force/Area
- measured in Pascals or Newton/m^2
- 1 pascal = 1 Newton/m^2
P=F/a
Force (Stiffness)
Force (stiffness) = -k*displacement - stiffness is measured in kg/sec
- force of stiffness happening is measured in Newton
Work
Wok = force*displacement
- measured in Joules
Total (forcing force/driving force)
Total (or forcing force) = (Mass * acceleration) + (damping or resistance * velocity) + (k*displacement)
For sinusoids ONLY rms is?
rms of sinusoid = .707
How does natural frequency relate to mass and stiffness?
- natural frequency is directly proportional to square root of stiffness
- inversely proportional to square root of mass (directly proportional to 1/square root of mass)
What is the definition of angular velocity?
angular velocity = 2f
What is the wavelength in reference to speed and frequency of sound
(lambda) = s/f - speed of sound over frequency
- wavelength gets longer as frequency goes down, shorter as it goes up
Mass Reactance
Xm= 2(pi)fm
- frequency
- mass
Compliant/Stiffness Reactance
Xc=1/ [2(pi)fc]
- frequency
- compliance
Magnitude of Impedance
Z = Sq root [R2 + (Xm-Xc)2]
Law of exponents
Xa * Xb = Xa+b
Xa/Xb = Xa-b
Law of Logarithms
log (a*b) = log a + log b
log (a/b) = log a - log b
log ab = b log a
log 1/a = -log a
Log10 1
Log10 2
Log10 3
Log10 1 = 0.0
Log10 2 = 0.3
Log10 3 = 0.48
Decibels for ratio of intensities
dB = 10 log10 (Ix/Ir)
Decibels for ratio of presures
dB = 20log10 (Px/Pr)
Reference for intensity level (IL)
10-12 watt/m2
Reference for pressure level (SPL)
20*10-6 Pa = 20mu pascals
=.00002 Pa
Lps / Lpc
- amount of pressure or energy in 1 Hz band
Lps = SPLwb-10 log10 (change in)fwb
SPLnb
SPLnb = SPLwb-10log10 [(change in) fwb / (change in) f]
% of harmonic distortion
% harmonic distortion = 100 * [(V22 + V32 +… +Vn2)/V12]
Write a sentence using thefollowing words and phrases: “input signal” “output signal” loudspeaker” “electrical-to-mechanical transducer system” “voltage waveform” and “acoustic waveform”
What types of systems perform mechsnical to electrical transformations?
The cochlea.
What type of system performs acoustic to mechanical transformations?
The middle ear.
Periodic
When a signal continualy traces the same path, repeats itself, those that do not are aperiodic
Uniform Circular Motion
single point on located in the circumference of a circle traces a sinusoidal function
- refers to constant speed of the point, rather than velocity because velocity refers to direction as well, however, in this case the point is following around a circle, the direction is set
Length of circumference
2πr
r is radius
2πr = 360 degrees
Equation for any sinusoid
Acos(2πft+ø)
cosine starts at peak (sin instead starts at 0 and goes up)
f = frequency (Hz)
t = time (sec)
Ø = phase angle (degrees)
How are clicks and noise similar?
HINT: frequency domain
Both have continuous frequency spectra with infinite bandwidth
Impulses and white noise, however, have different waveforms. Why do they differ?
HINT: Frequency domain
white noise phases are random
impulse spectral components have the same phase D
Define “Peak-to-peak” amplitude
Measuring amplitude from the distance betwen the highest peak and the lowest valley. Must specify this is the “peak-to-peak” amplitude or else you can’t tell the difference.
Peak Amplitude
Measuring the amplitude from the high point of the peak to 0.
Root Mean Square
Square each of the points, add them together and divide that by the number of points. Then you take the square root of that number. This is the average of the wave taking into account the negative numbers. If you just take an average of all of the points you might just wind up with zero. For any sine wave the rms is .707
Why is rms amplitude the most important way of specifying the amplitude of a signal?
It presupposes the use of a related quantity - intensity. For a sound wave, intensity ina free or completely diffuse fild is proportional to amplitude square.
How do you translate from Intensitys to dB?
dB = 10 log10 (I/Iref)
How do you translate from pressure to dB?
dB = 20 log10 (P/Pref)
What reference is most important for using SPL?
20 micropascals = 20*10-6Pascals = .0002 for use in equation
Power
power = energy transformed/unit time
measured in joules/sec = watt
joule = Newton * meter (1 joule is a force of 1 newton acting through a distance of 1 meter)
Intensity
Acoustic Power/ unit area
watts/m2
I=P/a
General Property of a logrithm
LogB (X) = Y so BY = X
What is a system?
A system is something which performs some operation on, or transformation of, an input signal to produce an output signal.
What do amplifiers do?
An amplifier adds energy to a system to increase the power or intensity of a signal.
What does an integrator do?
?
What makes a system linear?
A system is linear if the transformation that it performs fulfill the requirements of homogeneity (or propotionality) and additivity.
Proportionality (homogeneity)
Proportionality: k*inp(t) -> k*outp(t)
Additivity
if inp1(t) -> outp1(t) and inp2(t) -> outp2(t), inp1(t) + inp2(t) -> outp1(t) + outp2(t)
Time invariant
A system that does not change over time.
When can you predict responses to a system’s input?
As long as a system is linear and time invariant (LTI), we only need to know its response to sinusoidal inputs in order to predict its response to any input.
Sinusoidal input signals to an LTI system always lead to a sinusoidal output of the same frequency.
Given that we know the response of an LTI system to sinusoidal stimuli we can predict the system output to any input signal that can be expressed as a sum of sinusoids of the appropriate frequencies and phases (which according to Fourier’s theorem, can be done for nearly any real-world signal).
The recipe for predicting outputs of LTI systems:
1) determine the transfer function (e.g. the ratios of output-to-input magnitudes and the phase differences, at all necessary frequencies)
2) analyze any arbitrary input into sinusoids (again: amplitudes and phases)
3) synthesize the desired output by a) multiplying the input amplitudes and the system output-to-input magnitudes and b) by summing the input phases with system phases
What are the two parts of the transfer function?
Amplitude or magnitude response
Phase response
Amplitude response
Amplitude response = A(f) = output amplitude(f)/input amplitude (f)
What is a filter?
System that lets some frequencies pass better than others
What are the basic types of filters?
band-pass
high-pass
low-pass
band-reject/stop
How do you find the overall amplitude response of two or more cascaded LTI filters?
Cascades of LTI filters combine linearly: to find the overall amplitude response of two or more cascaded LTI filters, all we need to do is multiply the respective amplitude response (gain) curves together (and add the corresponding phases). Note that if the amplitude responses of the LTI filters are expressed in dB, then the dB of the filters are simply added together.
What is the “quality factor” of resonant filters?
Q - fcf/bandwidth
What do we call each resonance of the vocal tract?
A Formant
What’s so special about a phase response that is a straight-line passing through the origin?
A system with a phase response like this has a special property - every sinusoid passed through it is delayed by exactly the same amount of time
Amplitude spectrum of sawtooth wave:
all harmonics of fundamental, with amplitude of 1/f
Amplitude spectrum of a square wave?
odd harmonics of fundamental, with amplitude of 1/f
amplitude spectrum of triangular wave?
odd harmonics of the fundamental, with amplitude of 1/f
Amplitude Spectrum of a pulse train
DC plus all harmonics of fundamental, with lobed envelope and notches at inverse pulse duration and its multiples
From a periodic train of pulses to an impulse (transient, aperiodic signal)
indefinitely decrease pulse duration and increase inter-pulse interval
6 Steps of the “laborious method”
1) analyze the signal into its component sinusoids, specifying the frequency, amplitude, and phase of each of the components (in other words, establish the amplitude and phase spectra of the signal)
2) obtain the amplitude response of the system
3) obtain the phase response of the system
4) for each sinusoid present in the input, use the amplitude response of the system to ascertain the amplitude of each sinusoidal output
5) similarly, taking each sinusoidal input component in turn, establish its output phase from the phase of the input and the phase response of the system
6) now that the amplitude and phases of all the sinusoidal output components are known, the output waveform can be synthesized
How do we speed up the “laborious method”
By handling the amplitude and phase curves in toto as continous functions and paying attention tot he overall patterns of variation with frequency (e.g. frequency ranges of flat curves, ranges of constant decay or growth)
As long as the both the input amplitude spectrum and the amplitude response are expressed in dB…
all you need to do is add the two together at corresponding frequencies in order to obtain the amplitude spectrum of the output (again in dB). In a simalr way, the phases of the output componentscan be obtained by adding together the input phases and the phase responses at corresponding frequencies.
Wide Bandwidth: Time Resolution, Frequency Resolution & Impulse Response
Time Resolution: Good
Frequency Resolution: Bad
Impulse Response: Short
Narrow Bandwidth: Time resolution, frequency resolution, impulse response
Time: Bad
Frequency: Good
Impulse Response Long
