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Chapter 2 What is sound?
vibration of an object- simple vibrations move in a sinusoid patternany object set into vibration has the potential to produce sound sinusoidal vibrations are the basic building blocks of all vibrations (and thus sound) TERM 2
Fourier series
DEFINITION 2
- any vibration = the sum of sinusoidal vibrations(sum of simple sine waves)- the sum of sinusoidal vibrations can describe almost any arbitrary vibration fourier analysis: derivation of these sinusoids TERM 3
vibrations
DEFINITION 3
- all vibrations have the potential to produce sound- if mass has inertia and elasticity, it can vibrate--> inertia: force that moves the mass--> elasticity: an object moves from one point to another and back again (RESTORING FORCE) (opposite of stiffness)mass and spring used as a model for air molecules- solution to simple harmonic oscillator is a sine tone- any system can vibrate if it has mass and elasticity TERM 4
physical properties of a sinusoid
DEFINITION 4 also called a sound wave- describes a particular relationship between displacement and time- sines tones are periodic 1. frequency --> how often per unit of time an object moves back and forth2. starting phase --> measures the relative position of the object at the instant in time it begins to vibrate3. amplitude - -> measure of displacement TERM 5
displacement
DEFINITION 5 distance the object moves--> sine wave: continuous regular back and forth displacement of a vibrating object--
sinusoidal vibration is symmetric in displacement --> period --> pattern repeats itself
complex vibration
vibration consisting of more than one sinusoid TERM 7
Sine Tone Equation
DEFINITION 7 D(t) = A sin ((2 pi f t) + theta)D(t) = instantaneous ampltidueA = measure of maximum amplitudef = measure of frequencyt = measure of timetheta = measure of starting phasesin = sine function TERM 8
changes in amplitude of sine wave
DEFINITION 8 perceived at loudness TERM 9
changes in frequency of a sine wave
DEFINITION 9 perceived as pitch TERM 10
locus of time stimulus
DEFINITION 10 changes in location of the stimulus --> two ears are stimulated with a difference in starting phase
Phase
phase is determined at t=0 (when sine wave begins) - changes the starting position of a sine tone- arbitrarily defined- relative phase differences matter most + phase: leads the other --
it reaches its maximum displacement first - phase: lags the other all about starting position0 phase :start at 0 and go up / rads (90 degrees) : start at the top and go down (180 degrees):
start at 0 and go down TERM 17
instantaneous phase
DEFINITION 17 phase difference figured at any point** if two sinusoids have the same frequency, the starting-phase difference always equals the instantaneous-phase difference** if two sinusoids have different frequencies, the starting phase will not be equal to instantaneous phase TERM 18
cosine wave
DEFINITION 18 if the wave starts at phase of 90 degrees TERM 19
chapter 2
summary
DEFINITION 19
- any vibration is capable of producing an audible sound2. any vibration is equal to a sum of sinusoidal vibrations3. sinusoid has 3 parameters- amplitude (displacement)- frequency (number of vibrations per unit time)- starting phase (where the wave begins)4. Fourier Analysis: shows that complex wave consists of many sinusoids5. mass (inertia), elasticity and resistance all contribute to a complete description of vibration TERM 20
(Amplitude) spectrum
DEFINITION 20 graphically represents the frequency content of a signal* fq content is the most important part of the sound because that is how the ear encodes it (it is a frequency analyzer)- fq on the x-axis- amplitude on the y
spectrum
- a pure sine tone technically has infinite duration- it has only one frequency- any operation (like filtering) leaves wave shape unchanged--> can only introduce phase shift, amplitude change- this is only true for sine tones TERM 22
vowel formants
DEFINITION 22
- vowels are characterized by the peaks (formants) in the amplitude spectrum TERM 23
spectrogram
DEFINITION 23
- plot frequency as a function of time- intensity shown by color- great for visualizing stimuli that change over time (Ex: speech) TERM 24
relationship to psychoacoustics
DEFINITION 24
- normal frequency range of hearing- loudness is related to amplitude- pitch is related to frequency- tone color is related to wave shape--> low fq sound dull--> high fq should shrill- complicated relationship to perception- ear is a frequency/spectrum analyzer- relates to place theory of hearing- connected to neural coding of sounds- sine tones are used by psychoacousticians and physiologists for experimental control TERM 25
Chapter 3: sound transmission and sound
propagation
DEFINITION 25 transmission = how vibration from ann object (sound) travels to reach the ear- object causes air molecules next to it to vibrate; the motion of the air molecules is propagated (transferred) through air toward ear
identifying frequency in a wave propagation
number of waves per secondv = (f) (wavelength) TERM 32
speed of sound
DEFINITION 32 344 m/s in air* it does depend on the temperature, density and humidity as well--> hot and humid = higher speed--> cold and dry = slower speed--> high density = slower speed TERM 33
speed of sound equation
DEFINITION 33 v = (wavelength) (fq)v = m/swavelength = metersfq = Hz (1/s)m/s = (m) (1/s)a- when velocity is the greatest, displacement is smallestfq increases, wavelength decreasesspeed increases, wavelength increases TERM 34
atmospheric pressure
DEFINITION 34 the force per unit area exerted against a surface by the weight of air particles in earth's atmosphere* high in atmosphere - no air pressure* close to sea level = high air pressure TERM 35
sound pressure variation in air
DEFINITION 35 we are sensitive to a huge range of pressures- atmospheric pressure- threshold of hearing- threshold of pain
power, intensity, level
- pressure is a positive and negative quantity- intensity (and power and energy) is a positive only quantity I is proportional to P and is proportional to p^2 proportional = multiplied by a constant TERM 37
decibels (dB)
DEFINITION 37 relative measure (not absolute)- dB SL = sensation level- dB =- dB SPL =- find threshold of hearing for individual person for a given stimulus- play stimulus X dB above the level** DB never changes, just the reference level doesdifference of two levels:L2 - L1 = 10 log (I2 / I1)L2 - L1 = 20 log (p2 / p1) TERM 38
combining sound properties
DEFINITION 38 only intensities can be added linearly TERM 39
threshold of hearing at 1000
Hz
DEFINITION 39 p0 = 20 uPaI0 = 10^-12 W/m^ TERM 40
constructive interference
DEFINITION 40 known as reinforcement
distance is halved
4I
TERM 47
power halved
DEFINITION 47 I/2* if power is less, intensity is less* intensity is proportional to power - if I goes down by half so does the other TERM 48
pressure doubled
DEFINITION 48 4I TERM 49
Concept problem
DEFINITION 49 living in a 2 dimensional world --> would there be an inverse square law?I = 1/r1 dimension world?I = KP/2- half of the every goes one way and half goes the other way- no r in the equation - goes on forever TERM 50
doubling intensity
DEFINITION 50 level change of 3 dB
doubling pressure
level change of 6 dB TERM 52
Chapter 4
DEFINITION 52 Complex sounds TERM 53
time domain vs fq domain
DEFINITION 53 they give the same infoIf you're looking for temporal properties --> waveform is easier to useIf you're looking for fq properties --> spectrum is better TERM 54
real world sounds like speech..
DEFINITION 54 have multiple frequencies and they are multiples of some fq* complex sounds have a fundamental fq and harmonics TERM 55
complex tone equation
DEFINITION 55
- complex tone waveforms can change a lot from small variable changes--> changing the phase can completely change the way the waveform looks
complex tone fq spectrum
each line is an individual sound --> when plotted on the spectrum, peaks are formed- formats determine which vowel it is TERM 62
duration of real world sounds
DEFINITION 62 they are finite ** duration is proportionate to 1/BW or shortening a sound causes spectral smearing TERM 63
sine tone with finite duration
DEFINITION 63 x(t) = A sin (2pi f t) + phaset1 < t < t2 ( otherwise)waveform:ampltidue spectrum:phase spectrum:- finite duration tone = continuous spectra- zeros at 1/2D (2/2D, 3/2D ect)- shorter duration, more smearing (more smearing for finite duration)- spectrum represents infinite # of sine tones (continuous = all fqs) TERM 64
line spectra vs continuous spectra
DEFINITION 64 discrete = line = infinite (1 fq)continuous = finite = all fqs TERM 65
condensation and rarefaction click
DEFINITION 65 click = signal turns on then offx(t) = A00 < t < D ( otherwise) condensation: positive amplitude and +90 degree phase rarefaction: negative amplitude and -90 degree phase* amplitude spectrum still stays positive (same as condensation spectrum) only phase spectrum is different zeros are at 1/D
what is the first spectral zero for a click with a
20 micro sec duration
50 kHz (1/.00002) TERM 67
what frequencies are the first spectral zeroes
for a 50-ms 1000 Hz tone?
DEFINITION 67 20 Hz (double check that this is correct) TERM 68
click trains
DEFINITION 68 infinitely long- basic psycho-acoustical stimulus- important for cochlear implants (trains of electrical pulses that are amplitude modulated and relay speech info) - stilldiscrete lines/harmonics on thespectrum waveform:amplitude spectrum:Phase spectrum: TERM 69
Beats
DEFINITION 69 type of modulation --> 2 sine tones that are close together in fqequation: (envelope) (carrier)waveform:amplitude spectrum:phase spectrum:- times when the fqs are in phase - -> amplitude is the greatest- amplitudes cancel out when fqs are completely out of phase TERM 70
envelope
DEFINITION 70 slowly varying part that really isn't theregives it its shape
noise
noise has continuous spectrum (think really small component spacing, like 1 Hz)- noise has random phases TERM 77
white noise
DEFINITION 77 flat power spectrum TERM 78
pink noise
DEFINITION 78 spectrum level decreases with increasing fq- double fq --> 1/2 power TERM 79
wideband waveforms
DEFINITION 79
- wide bandwidth = very fast modulations phase spectrum: random phases --> each component has a random phaseamplitude spectrum: also random --> flat spectrum TERM 80
narrowband waveform
DEFINITION 80
- more structure- carrier fq is around the same --> more tonal- narrow bandwidth = slow modulations** know how to draw spectrum in terms of bandwidth and center fq
3 big ideas in ch 4
- as things get shorter there is more smearing2. harmonics imply periodicity- periodic signal has to have harmonics- if harmonics present, must be a periodic signal3. modulations add sidebands (extra frequencies to the signal) TERM 82
spectral smearing
DEFINITION 82
- caused by shortening a sound- the shorter the sound, the more smearing TERM 83
finite vs. infinite sounds
DEFINITION 83 finite duration sounds = continuous spectrainfinite sounds = discrete spectra TERM 84
envelope vs. fine structure
DEFINITION 84 envelope = general shape of the sound (dotted lines)fine structure = specific form of the wave - shown in solid lines TERM 85
stiffness and resonance
DEFINITION 85 as things get stiffer, they don't want to vibrate slowly
stiffness limited vs stiffness limited
stiffness limited: as things get stiffer they don't want to vibrate slowly mass limited: bigger mass, lower fq it wants to vibrate at(draw figure) TERM 92
complex
resonators
DEFINITION 92 more than one resonant frequency within an object- most objects have complex resonance patterns (think of an object as consisting of several single resonators) TERM 93
tubes
DEFINITION 93 tubes have resonance patters (ex: a flute or your vocal tract)- particularly, this will have implications for the ear canal which is an open-closed tube- resonant frequency of ear canal near 3-4 kHz TERM 94
interference effects
DEFINITION 94 locations of minimum vibratory displacement (nodes) alternate over space with locations of maximal vibratory displacement (antinodes) TERM 95
filters
DEFINITION 95 filters are resonators designed to modify the amplitude and phase spectraphysiological: ear canal, middle ear bones, inner ear, ect.man-made: digital filters, computer algorithms
Octaves
octave: doubling the fq before- first octave = doubling the fundamental fqfirst 3 octaves of 100 Hz200, 400, 800 TERM 97
octaves can never be harmonics
DEFINITION 97 FALSE TERM 98
four types of filters
DEFINITION 98 low passhighpassbandpassbandreject TERM 99
cuff off attenuation per octave
DEFINITION 99 cut off: last fq in which is not affected by the filterattenuation per octave: how much sound is reduced per octave TERM 100
low pass filter
DEFINITION 100 everything below cutoff is allowed to pass (unaffected)
