Acoustics Flashcards
elasticity
Elasticity (internal stiffness) of the mass returns the mass back to its resting position (equilibrium)
inertia
Due to inertia, the mass moves beyond its rest position
Mass Spring Oscillator
The spring-mass oscillator consists of a spring (fixed at one end) that is attached to a mass which is resting on a special low-friction surface.
When not vibrating (at rest), the system is at equilibrium
Simple Periodic Signal
Always a sinusoidal waveform. Basically a pure tone. The waveform will repeat in equal periods.
What’s a waveform?
Change in some quantity over time. (Amplitude versus time)
What will determine the frequency of vibration?
the mass of the object &
the stiffness or elasticity of the object
Reduce Mass
Increases Frequency
Increasing Frequency
Reduces Mass
Are stiffness and frequency directly or inversely related?
Stiffness and Frequency have a direct relationship.
Are mass and frequency directly or inversely related?
Mass and Frequency have an inverse relationship.
What two properties determine the frequency of the spring-mass oscillator?
The spring-mass oscillator will vibrate at a frequency that is determined by its mass and stiffness
Period
the time it takes for one complete cycle of periodic vibration to occur
What is the x-axis of a wave form?
time
Frequency (f) and Period (T) are reciprocally related: (formula)
f (Hz) = 1/T (s) and T (s) = 1/f (Hz)
ex. If T = .01
1/.01 = 100 = F=100Hz
1000 milliseconds
1 second
50 milliseconds
.05 second
5 ms
.005 second
What determines the amplitude of vibration?
Magnitude of the force and degree of energy loss (damping)
damping
reduction of amplitude over time. (Energy Loss) The amplitude of vibration will gradually decrease because of energy losses in the system (friction)
For a lightly damped wave, amplitude decays slowly
For a heavily damped wave, amplitude decays rapidly
peak to peak amplitude
Distance between a waveforms peak and trough
peak to trough
peak amplitude
Distance between zero (equilibrium) and the waveform’s peak or trough
Propagation of a Sound Wave
Air particles, like the spring-mass oscillator, move in place around their rest position
How does a sound wave travel in air?
When air particles are disturbed, they behave like small masses connected to one another by springs. (Air, an elastic medium)
Simple sound waves in air
When a tuning fork is struck, air particles will move in place about their theoretical rest positions
Which is shorter in wavelength? Men or Women’s speech?
Typically women’s.
Which is lower in frequency? Men or Women’s speech?
Typically men’s.
Describe the relation of wavelength and frequency.
Wavelength and frequency are inversely related. Higher frequency sounds correspond to shorter wavelengths, and lower frequency sounds correspond to longer wavelengths.
wavelength equation using words
wavelength = velocity (of sound) X frequency.
How is frequency measured?
Hz
What answers the question “How Often”?
frequency
What answers the question “How fast”?
speed
Which material generally has the strongest bond between molecules? (solid, liquid, or gas?)
solids
Why does sound travel faster through solids?
strong bonds in solid materials allows particles to interact with each other more easily than weaker bonds.
How does air pressure influence the speed of sound?
Air pressure influences the density of the air. Greater pressure = increased density of particles.
How does temperature influence the speed of sound?
Temperature influences the strength og the interaction between particles. Higher temperature causes interaction between particles to become more elastic (they are more easily separated)
True or false: the speed of a sound wave is dependent upon its frequency or wavelength?
false: The speed of a sound wave can be altered only by the properties of the medium which it travels (density, temperature, etc.)
Why do sounds travel farther at night?
This effect is due to temperature and refraction. In the day air is warmer toward the ground than the higher air above. This causes refraction- A difference in velocity causes the sound to bend upward to the cooler air. At night, air is cooler toward the ground and the sound waves bend downward. As a result, the sound waves appear to be traveling farther, as they stay closer to the ground across a greater distance.
What is our perception of pitch based on?
It is strongly based on the frequency of the sound wave, but it is also influenced by the intensity of the sound.
What is our perception of loudness based on?
Our perception of loudness is primarily based on intensity, but is also strongly influenced by frequency.
What is the JND (just noticeable difference) between two sounds that can be measured?
about 1 decibel (but if very loud can drop to half a decibel)
If two sounds are equally “loud” (60 dB SPL) but at different frequencies, will they be perceived as equally loud?
No, the sensitivity of the ear is frequency dependent.
spectrum
amplitude (y axis) versus frequency (x axis)
What kind of sounds will have line spectra?
periodic
JB Fourier
Showed mathematically that all complex periodic sounds are made up of or can be broken down into a set of sine waves of different frequency, amplitude, and phase.
How does sound wave travel in air?
When a tuning fork is struck, air particles will move in place about their theoretical rest positions
As the disturbance moves away from the source, air particles will alternately become more densely packed (compression areas) and more widely dispersed (areas of rarefaction)
When air particles are disturbed, what do they behave like?
When air particles are disturbed, they behave like small masses connected to one another by springs. (Air, an elastic medium)
Sound wave in air is an example of a ….
Longitudinal wave
The particles of the medium move in _______________ as the wave.
The particles of the medium move in the same direction as the wave.
A ripple in water is an example of a ______ wave
A transverse wave
Sound in air is an example of a ________ wave.
A longitudinal wave
Propagation Velocity (C):
The speed of sound in air
Under normal atmospheric conditions (18o C), a sound wave will travel approximately 343 m/s
What is the speed of sound in air in normal atmospheric conditions (18o C)?
343 m/s
Wavelength
The distance in space spanned by one cycle of periodic wave motion; measured usually in meters
What’s the difference between period and wavelenth?
period is time; wavelength is distance
Symbol for wavelength
lambda λ
λ =
λ = CT (C=propagation velocity), Period = T
T=
1/F (period)
If a male has a 100Hz frequency what is the size of the wavelength?
(You need to know that speed of sound is always 343 m/s
use formula wavelength = C*T. Divide the 343 by the frequency (100) = 3.43 m
How do sounds cancel each other out?
When you have two sine waves with identical frequency that are 180 degrees out of phase toward each other, they will cancel each other out ( destructive interference)
What’s the minimum amount you have to shift a sine wave over another to quantify phase relationship
90 degrees; nothing can be greater than 180
Complex signals consist of
Complex signals consist of more than one frequency
What might you say to describe complex aperiodic sounds?
noise
Who discovered that any complex waveform can be broken down into a set of sine waves of different frequency, amplitude, and phase
J.B. Fourier
How are sine waves that make up complex periodic signal’s related?
harmonically related (occurring in different whole number intervals)
What’s a harmonic?
Whole number multiples of the fundamental
Each sine wave that makes up a complex periodic wave is an
harmonic
Describe the harmonic structure of the following complex periodic signals:
fo = 100 Hz fo = 250 Hz
The 100Hz will have the first harmonic (the most evergy) at 100 Hz, There will be another at 200, 300, and 400 (the spacing will be equal to the fundamental frequency)
How much of the glottal amplitude signal drops off
Generally it is 6-12 dB an octave below below 1000 Hz
What’s an octave?
a doubling of a frequency
What does a spectrum display?
A spectrum is an amplitude vs frequency display
What do the lines in a spectrum represent?
the harmonic
periodic waveforms have a
line spectra
Complex Aperiodic signals consist of
Complex Aperiodic signals consist of multiple frequencies, but the pattern of vibration does not repeat itself (random noise)
Are frequencies harmonically related?
Frequencies are not harmonically related
Rather, energy is distributed over a range of frequencies
transient complex
dissapears
continuous complex periodic sounds
continues
complex aperiodic sounds have what kind of spectrum?
continuous line spectrum
duration of noise can be described as
transient or continuous; this is only for complex aperiodic sounds
What can’t /m/ be described as continuous?
It is not noise, because it is quasi-periodic complex
Aperiodic sounds (noise) can be
transient or continuous
describe /s/
continuous aperiodic sound
Describe /g/
continuous aperiodic sound
continuous specta
consists of energy over a wide range of frequencies, with the max frequency concentrated (usually somewhere in the middle)
How are periodic sounds different from aperiodic sounds?
Unlike periodic sounds that have energy present at discrete frequencies (harmonics), aperiodic sounds have a band of energy distributed over a wide range of frequencies.
describe /m/
complex quasi periodic
describe /ae/
complex quasi periodic
describe /l/
complex quasi periodic
describe /k/
transient complex aperiodic
describe /f/
continuous complex aperiodic
describe /v/
complex quasi periodic and continuous complex aperiodic (because from two sources)
describe /dʒ/
complex quasi periodic and transient complex aperiodic (because from two sources)
describe /b/ /d/ or /g/ initially
transient complex aperiodic sounds
describe /b/ /d/ or /g/ in a medial position
complex quasi periodic and transient complex aperiodic
Voice Onset Time (VOT)
the time it takes from the release of a stop to the vibration for the following sound
Voice Onset Time (VOT) for initial b
10-15 ms
What would have a VOT of 0
voiced sounds (truly voiced sounds), when the voicing happens the same time as the stop.
How are most consonants produced?
Most consonants are produced as a result of either vocal fold vibration (a complex quasi-periodic sound source) or noise created in the vocal tract/oral cavity (complex aperiodic sound source). One class of consonant sounds is produced by both sound sources simultaneously
Transient Complex Aperiodic
Voiceless Stops and Affricate /p, t, k, tš/ and the “voiced” Stops /b, d, g/ (in syllable releasing position: CV)
Aperiodic and Quasi-Periodic
Voiced Fricatives and Affricate
Which class of consonant sounds is produced by both sound sources simultaneously?
Aperiodic and Quasi-Periodic : Voiced Fricatives and Affricate
What is always the Y axis for a spectrogram?
Frequency
How to describe an acoustic spectra of a sound.
describe the range of energy, and where the maximum energy is.
What is the energy of vowels?
harmonics
How high do most vowels go?
3k Hz
Range for spectrograms for speech analysis should be what?
0 HZ- 8000 Hz
What kind of sounds have line spectra?
complex periodic sounds- transient and continuous
Everyday example of a mechanical filter?
A Brita, a coffee filter, Sorts things out by particle size and diameter.
Resonance Frequency (source-filter)
Has to do with the cavities of the super laryngeal vocal tract
what are the two ends of the vocal tract?
the larynx, the lips
What does changing the cross sectional area of the vocal tract do?
the resonance frequency
cross-sectional area (of the vocal tract)
Think of vowel quadrilateral,
How do you change the cross sectional area of the vocal tract?
Place of constriction, degree of constriction, and vocal tract length (rounding)
What is on the x axis of a vowel quadrilateral?
degree of tongue advancement
What is on the y-axis of a vowel quadrilateral?
tongue height
contrast /i/ and /u/ and cross sectional area.
Both high vowels, the place of constriction is moving from the pharynx to the oral cavity. The relative size of the cavity is shorted. The pharyngeal cavity becomes larger. I has retracted lips and u is rounded, U then has a longer vocal tract length.
What happens when you change the cross sectional area of a vowel?
the quality of the vowel changes
What is the simplest acoustic filter?
The Helmholtz filter (has one resonance frequency) Like a beer bottle
The Helmholtz filter
An enclosed body of air with a neck ( like a beer bottle) Frequency is determined by air volume.
How can you lengthen your vocal tract?
lip protrusion and lowering the larnyx
The Helmholtz filter
An enclosed body of air with a neck ( like a beer bottle) Frequency is determined by air volume. The air is acting like the spring component.
How can you lengthen your vocal tract?
lip protrusion and lowering the larynx
What is the double Helmholtz Resonator
In this model, oral and pharyngeal cavities are represented by separate volumes (2 coupled Helmholtz Resonators)
How many frequencies do you need to differentiate vowels?
Only 2
How does the double Helmholtz resonator work?
V1 (back cavity) and V2 (oral cavity) are connected by the neck cavity (tonue-palate) and V2 has a neck that represents the lips.
R1 (resonance 1)
The pharyngeal cavity
R2 (Resonance 2)
The oral cavity
As the place of constriction moves forward what happens to frequency?
F1 goes down and F2 goes up
When you round lips what happens to R1 and R2?
They lower
Anytime you change the cross sectional area of the vocal tract what happens to resonance?
Resonance frequencies change (formant structure and quality of what you hear)
What is the most constricted vowel we have?
/i/ (it’s also has the furthest separated f1 and f2)
What affect does going from rounded lips to spread lips have?
The vocal tract shortens, increasing the resonance of R1 and R2
Acoustic Transmission Line Model
Only valid for one vowel (the neutral vowel /ʌ?
We can model the vowel tract as a uniform tube that is open at one end. The glottal end is considered closed because the vocal folds are rapidly vibrating, whereas the mouth is open.
Two characteristics of the Acoustic Transmission Line Model
the wavelength of R1 will be 4 times the length of the tube. Sometimes this is called a quarter length resonator.. Because at R1 only a quarter of the wavelength fits in the tube.
The other characteristic of quarter length resonators is that they resonate only at odd multiples. Meaning is the lowest resonance is 650 Hz, R2 3XR1, R3 5XR1
What do acoustic filters sort sounds by?
according to wavelength frequency
R1=
c/wavelength
Low pass filter
Only low frequencies pass, anything higher drops off
high pass filter
blocks low frequencies, anything higher is allowed to pass
a bandpass filter
two cut of frequencies (a high and low), alowing a band of frequencies in between to pass
describe the vocal tract as a filter
a multiple band pass filter
What makes up formant bands on a wide band spectrogram?
High energy harmonics; those that are closest to the natural resonate frequency
What makes up the formant bands on a narrow band spectrogram?
the harmonics
What’s the band width for a narrow band spectrogram?
45-50 Hz wide
What’s the band width for a wide band spectrogram?
about 300 Hz wide
Narrow Band Spectrogram advantage
Spectrogram is Frequency vs. time vs amplitude; Going to get improved y axis (frequency) resolution but will lose resolution of the time axis
Wide Band Spectrogram Advantage
Spectrogram is Frequency vs. time vs amplitude; Going to get improved x axis (time) resolution but will lose resolution of the frequency axis
What are the vertical bands (striations) on a spectrogram?
Vocal fold vibrations, The line is the opening (the puff of air) (source)
What do the dark bands (F1) (F2) represent?
locations of the resonant frequencies of the vocal tract
If you want to see clear harmonics, which spectrogram would you use (wide or narrow)?
Narrow= Because you can’t see any harmonics in a wide band.
What is shown on a spectrogram? (plotted on each axis)
x= frequency y=time
z axis of a spectrogram
amplitude (darkness// areas of grey on a paper)
How much time is needed for a spectrogram? (with 8K Hz)
2.2-2.5s
Why do we see formants (bands) on a wide band spectrogram?
poor frequency resolution- you can’t see individual harmonics
If you want to look at harmonic structure (hoarseness or roughness) - inter harmonic energy
narrowband
2 acoustic features that coorrelate very highly with vocal roughness/hoarseness
horse vowels have a lot of high frequency energy (noise) indicated by energy above 3000 hz (a good quality vowel would be white above 3000 hz), and interharmonic energy (the noise between harmonics)
What causes inter-harmonic energy?
nodules and other lesions in the larynx ? Causes turbulence in the air flow.
If the F0 doesn’t change for a vowel, what would the striations look like on a spectrogram?
striations are equally spaced
When frequency goes up, how do the striations of a spectrogram change? (like the end of a sentence in a question)
striations will compress and come closer together.
When frequency goes up, how do the striations of a spectrogram change?
striations will move closer together
A power spectrum
A graph of frequency and amplitude spectrum at an instant in time; like a snapshot of a part of a word.
What power spectrums would you see in the word “she” ?
sh= continuous /i/= line
What do the formant frequencies represent?
resonant frequencies (determined by the cross sectional area)
Loudness vs. intensity
Loudness is a psychological sensation of perceived intensity. The human ear perceives loudness differently depending on a sound’s frequency (and spectral characteristics)
That is, the ear is a more efficient transducer at certain frequencies and less efficient at others
What is a graph that illustrates an interesting phenomenon of human hearing where the actual loudness changes but the perceived loudness our brains hear will change at a different rate, depending on the frequency.
Fletcher Munson Curve
measure for amplitude on dB scale
dBSPL
measure for Intensity on dB scale
dBIL
How does the Fletcher-Munson curve work?
The Fletcher-Munson curves show us that sounds at the extreme frequencies must be of greater IL to be heard “as loud” as sounds in the middle frequencies (2-4 kHz) it shows that Because the ear perceives loudness differently depending on the sound’s frequency, not all equally intense sounds are perceived as equally loud.
the unit for loudness
phon
definition of loudness
Loudness, the psychological correlate of intensity, is scaled differently.
What is the phon scale?
The phon scale was arbitrarily created. A 10 dB IL sound presented at 1000 Hz has a loudness of 10 phons; a 20 dBIL sound at 1000 Hz is 20 phons, etc.
At what frequency is the ear more sensitive to hearing the difference in frequency?
The ear is more sensitive to frequency differences below 1000 Hz, than it is to frequency differences above 1000 Hz.
Consequently, 2 tones separated by the same frequency difference (100 Hz, e.g.), will be perceived as having a greater difference in pitch below 1000 Hz.
For Example, which pair of tones would the listener judge to have a greater difference in pitch?
1000 Hz - 1100 Hz (f = 100 Hz)
100 Hz - 200 Hz (f = 100 Hz)
What is pitch?
Pitch is a perceptual attribute of frequency
Relationship between frequency and pitch
Pitch is a perceptual attribute of frequency
Are pitch and frequency the same?
NOOO- and not a linear relationship about 1000 Hz
What diagram reveals the relationship between pitch and frequency?
The Stevens-Volkmann curve reveals the relationship between pitch and frequency
The relationship is linear below 1000 Hz, becoming nonlinear above 1k Hz
- (line starts with equal relationship then drops off)
semitone scale
devised to account for the nonlinear growth of pitch and frequency.
100-200 Hz and 1000-2000 Hz on a semitone scale
both are 12 ST
intensity
the power of a sound or power/area
amplitude
the pressure of a sound
A common unit of power
Watts
A common unit of area
cm 2 (squared)
How is Intensity usually measure (although inconveniently)?
watts per square centimeter
Why is it hard to describe intensity? (watts per cm 2)
the human auditory mechanism is sensitive to a wide range of powers, from the just detectable 10 to the minus 16 watts per centimeter (o dB) to a painfully loud 10 to the minus 2 watts per centimeter squared- represents a range of about 100 tillion to one) (you need smaller numbers, it’s inconvienent. 2) 3) our own interest in relative intensity
Why is it hard to describe intensity? (watts per cm 2)
1) the human auditory mechanism is sensitive to a wide range of powers, from the just detectable 10 to the minus 16 watts per centimeter (o dB) to a painfully loud 10 to the minus 2 watts per centimeter squared- represents a range of about 100 trillion to one) (you need smaller numbers, it’s inconvenient. 2) Relationship between intensity & loudness is not linear
3) our own interest in relative intensity
How is relative intensity quantified?
quantified as the logarithm of the ratio of an observed sound power/pressure to a standard reference power/pressure
What is a unit of relative intensity?
dB
dbIL
a ratio of two acoustic powers expressed on a log scale; the numerator is the observed power; it’s a unit of relative intensity and the standard reference will always be 10 -16 power
What is a synonym for logarithm?
exponent (a convenient mathematical shorthand)
What is the logarithm of 100?
2
What is the logarithm of 1000?
3
What is a power ratio?
Intensity Level
What is a power ratio?
Intensity Level (dBIL)
What is a pressure ratio?
Sound Pressure Level (dBSPL)
symbol for power
W
symbol for pressure
P
When would you use dBIL (intensity) in a logarithm?
When IL = 10 log (Wo/ Wr); where the standard reference power (Wr) is 10-16 W/cm2
If power is doubled in dBIL, how much will IL increase?
If power is doubled, IL will increase by 3 dB; a tenfold increase in power will result in a 10 dB IL increase
dBSPL (amplitude)
SPL = 20 log (Po/Pr); where the standard reference pressure (Pr) is 0.0002 dynes/cm2
If power is doubled in dB SPL, how much will SPL increase?
If pressure is doubled, SPL will increase by 6 dB; a tenfold increase in pressure will result in a 20 dB SPL increase
If two babies are crying at equally loud 80 dBIL, what will be the net dbIl?
83 dBIL because again If power is doubled, IL will increase by 3 dB;
dBGain
Gain expressed in decibels for voltage and pressure.
What is gain?
describes the properties of an amplifier; Gain is a ratio of an amplifiers output to the input.
What’s the log of 10?
1
How do we form s?
forming a major constriction near the alveolar ridge, but the constriction can happen in different ways.
What is a 2-2 model for the s sound?
an s constriction represented by a uniform tube open at both ends including a quarter length wave resonator and a halfway resonator.
Quarter wave resonators (open at one end) wavelength
the wavelength of the R1 is four times the length of the tube
Halfway resonator (open at both ends) wavelength
the wavelength of R1 is two times the length of the tube
For a half wave resonator what is resonance frequency for R2, R3, and R4 in relation to R1?
For a the second resonance frequency is 2R1,
For a third resonance frequency is 3R1,
For a 4th resonance frequency is 4* R1
For a quarter wave resonator, what is resonance frequency for R2, R3, and R4 in relation to R1?
For a the second resonance frequency is 3R1,
For a third resonance frequency is 5R1,
For a 4th resonance frequency is 7*R1
If the length of the tube in a half way resonator is 2.5 cm? How can you calculate the maximum energy of an s sound?
λ = CT (C=propagation velocity; always 343 m/s), Period = T;
Spectrogram benefits
It’s an acoustic signal (non invasive- just talking into a microphone). Tells us what is going on at the physiological level of the vocal tract. Tell us valuable information about what’s going on with the sound source and the vocal tract filter.
What is a spectrogram?
a hard copy of from spectrography; a 3d visual representation of sound; y axis is frequency, x axis is time, z-axis is intensity/amplitude (in grey or black)
When should formants not be changing in a spectrogrom?
a sustained vowel?
What kind of spectrogram shows formants?
Narrow band
Formats are indicative of source or filter in a spectrogram?
filter
Vertical bands (striations) are indicative of source or filter on a spectrogram?
source
If vertical striations are moving farther apart or closer together on a spectrogram for a sustained vowel, where in the vocal tract does the instability lie?
source
Change in formants means what?
change in filter (cross sectional area)
In a wideband spectrogram if vertical striations are more closely spaced it means that there is a _______FO in comparison to another sound.
a higher FO
When is the end of VOT?
When voicing begins; on a spectrogram at the first vertical striations that passes through f1 and f2; it is relatively short for “voiced” stops and it is longer for “voiceless” stops. A simple temporal measure used for stops.
VOT is a good measure of a speakers ability to coordinate __________
____ ______________
__________________events.
VOT is a good measure of a speakers ability to coordinate laryngeal and superlaryngeal articulatory events.
laryngeal event in VOT
vocal fold vibration
superlaryngeal in VOT
release of a stop
If the vertical striations in a side band spectrogram move further apart, what does this mean about F0 and most likely why?
F0 is dropping (lowering)- for a declarative sentece
Hallmarks of /m/,/n/ and /ng/ on a wideband spectrogram?
vertical striations and structure will be very light compared to a vowel because of damping and energy loss when they pass through the nasal cavity.
How to (manually) find F0 on a wideband?
Count the verticle striations but you need to know the time interval (difficult)
How to (manually) find F0 on a narrowband?
You need to know the frequencies (on the y-axis); find a convenient harmonic, high on the page that you can count up to reliably. Find which harmonic it is (for ex. 20th harmonic at 3500 Hz) (3500/20= 175 Hz)
Harmonics are wider or closer spaced for higher f0s
Wider
Verticle Striations in a wide bad
those in the glottal source that fell closest in frequency to the resonant frequencies in the vocal tract
What spectrogram would you need to see interharmonic energy?
Spectrogram - the only one you will see harmonincs?
sound source for /a/
vocal fold vibration
Narrow band higher FO then harmonics are ……
higher f0 harmonics are more widely spaced
wide band, higher FO the verticle striations are…
verticle striations are closer together
If a first harmonic is 4 HZ, What is the 20th harmonic?
4 times 20 = 80 Hz
Harmonics are multiples of the first harmoinic.
sound sources for /dg/
vocal fold vibrations and noise in the oral cavity
/dg/
transient complex aperiodic, and complex quasi periodic
What spectrum would voiced /th/ have?
combined spectrum
What spectrum would /f/ have?
continuous
vocal fold vibration spectrum
line spectrum
noise in the oral cavity specturm
continuous spectrum
/h/ sound source
glottis (vocal folds) but not vibration
sound spectrum for /h/
continuous spectrum (it’s noise)
How long is VOT for voiceless stops?
anything over 20 milliseconds
