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SPPA 6010 Advanced Speech Science1Topic 3 Physical Acoustics Review1WARNING!!!!This is a REVIEW.Mastery is ESSENTIAL to understand the material later in the course.If you found this material particularly challenging in previous courses it is, spend the time on it NOW.SPPA 6010 Advanced Speech Science2SPPA 6010 Advanced Speech Science3Learning ObjectivesOutline the physical processes underlying simple harmonic motion using the mass-spring modelDescribe the molecular basis of sound wave propagation3SPPA 6010 Advanced Speech Science4Spring Mass ModelMass (inertia)ElasticityFriction

4SPPA 6010 Advanced Speech Science5What is sound?It may be defined as the propagation of a pressure wave in space and time.propagates through a medium5We are going to need to talk more about the medium through which sound propagates. This will seem a little bit like a digression, but it should vastly improve your grasp of the material that we go into later. So we need to talk some physics and physical quantities.

SPPA 6010 Advanced Speech Science6Sound-conducting mediaMedium is composed of molecules Molecules have wiggle room Molecules exhibit random motionMolecules can exert pressure

AB6SPPA 6010 Advanced Speech Science7Model of air molecule vibration (Time 1)Rest positionsAir molecules sitting side by side

7SPPA 6010 Advanced Speech Science8Model of air molecule vibration (Time 2)

8SPPA 6010 Advanced Speech Science9Model of air molecule vibration (Time 3)

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Model of air molecule vibration (Time 4)10SPPA 6010 Advanced Speech Science11Model of air molecule vibration (Time 5)

11SPPA 6010 Advanced Speech Science12Model of air molecule vibration

Time12345Distanceabcd12SPPA 6010 Advanced Speech Science13Wave action of molecular motion

Time12345Distance13SPPA 6010 Advanced Speech Science14Amplitude waveform

PositionTime14SPPA 6010 Advanced Speech Science15Amplitude waveformAmplitudeTime

Question: How long will this last?15SPPA 6010 Advanced Speech Science16Model of air molecule vibration

Time12345Pressure measuring deviceQuestions: Where is a region of compression?Where is a region of rarefaction?16SPPA 6010 Advanced Speech Science17

For examplePressureTime17SPPA 6010 Advanced Speech Science18Learning ObjectivesDefine the key characteristics of sinusoidal motion (amplitude, frequency/period and phase)Outline the relationship between the frequency and wavelength of a sound wave

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Pressure vs. time (pressure waveform)PressureTimeAmplitudePeriod (T)Phase: when a periodbegins

Frequency (F): rate that waveform repeats itself (1/T)Phase (deg)19SPPA 6010 Advanced Speech Science20

Phase20SPPA 6010 Advanced Speech Science21Initiating a sound waves that differ only in phase

A force is applied to molecule at frequency f and time t

same force applied at frequency f at time t+a where a < the period of vibration21SPPA 6010 Advanced Speech Science22Features of a pressure waveformAmplitudeMeasured in pressure unitspeak amplitudepeak-to-peak amplitudeInstantaneous amplitudePeriod and FrequencyPeriod measured in time (basic quantity)Frequency is a rate measure (per unit time) expressed as Hertz (s-1)May be expressed as octaves, semitones, etcPhaseMeasured in degrees (relative to period length)0-360 degrees22SPPA 6010 Advanced Speech Science23Spatial variation in pressure wave

wavelength () is the distance covering adjacent high and low pressure regions23SPPA 6010 Advanced Speech Science24

For exampleDistanceWavelength ()Pressure24SPPA 6010 Advanced Speech Science25Relation between frequency and wavelength=c/F where

: wavelengthF: is the frequencyc: is sound speed in medium (35,000 cm/sec)25SPPA 6010 Advanced Speech Science26Additional ConceptsPropagation of wavesTransmissionAbsorptionReflectionReverberation

26SPPA 6010 Advanced Speech Science27Learning ObjectivesDraw and describe time-domain and frequency-domain representation of soundDistinguish between simple and complex sound sounds with regard to physical characteristics and graphical representationsDistinguish between periodic and aperiodic sounds with specific emphasis on terms such as fundamental frequency/period, harmonics, and overtonesDistinguish between continuous and transient sounds Describe how waves sum, define Fourier's theorem and be able to describe the basics of Fourier analysis27SPPA 6010 Advanced Speech Science28Graphic representation of soundTime domainCalled a waveformAmplitude plotted as a function of timeFrequency domainCalled a spectrumAmplitude spectrumamplitude vs. frequencyPhase spectrumphase vs. frequencyMay be measured using a variety of window sizes

28SPPA 6010 Advanced Speech Science29Same sound, different graphs

Time domainFrequency domainFrom Hillenbrand29SPPA 6010 Advanced Speech Science30Classification of soundsNumber of frequency componentsSimpleComplexRelationship of frequency componentsPeriodicAperiodicDurationContinuousTransient30SPPA 6010 Advanced Speech Science31Simple periodic soundSimple: one frequency componentPeriodic: repeating patternCompletely characterized byamplitudeperiod (frequency)phaseOther names: sinusoid, simple harmonic motion, pure tone31SPPA 6010 Advanced Speech Science32Simple periodic sound: Graphic appearance

From Hillenbrand32SPPA 6010 Advanced Speech Science33Complex periodic soundsComplex: > one frequency componentPeriodic: repeating patternContinuousFrequencies components have a special relationLowest frequency: fundamental frequencySymbol: foFrequency component with longest periodHigher frequency components: harmonics integer (whole number) multiples of the fo

33SPPA 6010 Advanced Speech Science34Complex periodic sounds: Graphic appearanceTime domain:repeating pattern of pressure changewithin the cycle, things look complexFrequency domain: spectral peaks at evenly spaced frequency intervals picket fence appearanceAuditory impression: sounds musical34SPPA 6010 Advanced Speech Science35Complex periodic sounds: Graphic appearance

From Hillenbrand35SPPA 6010 Advanced Speech Science36

36SPPA 6010 Advanced Speech Science37Amplitude vs. Phase Spectrum

Amplitude spectrum: different

Phase spectrum: same37SPPA 6010 Advanced Speech Science38

Amplitude vs. Phase SpectrumAmplitude spectrum: same

Phase spectrum: different38SPPA 6010 Advanced Speech Science39(Complex) Aperiodic soundsComplex: > one frequency componentAperiodic: Does not repeat itselfFrequency components are not systematically relatedMay be ContinuousTransient39SPPA 6010 Advanced Speech Science40Aperiodic sounds: Graphic appearanceTime domain:no repeating pattern of pressure changeFrequency domain:the spectrum is dense No picket fenceAuditory impression: sounds noisy40SPPA 6010 Advanced Speech Science41Aperiodic sounds: Graphic appearance

From Hillenbrand

41SPPA 6010 Advanced Speech Science42Analysis of complex wavesWaves can be summedComplex waves are the sum of simple wavesFourier: French Mathematician: Any complex waveform may be formed by summing sinusoids of various frequency, amplitude and phaseFourier AnalysisProvides a unique (only one) solution for a given sound signalIs reflected in the amplitude and phase spectrum of the signalReveals the building blocks of complex waves, which are sinusoids42SPPA 6010 Advanced Speech Science43Learning ObjectivesDraw and differentiate the waveform and the waveform envelopeDraw and differentiate the amplitude spectrum, the phase spectrum and the spectrum envelope43SPPA 6010 Advanced Speech Science44The envelope of a sound waveWaveform envelope:imaginary smooth line that follows the peak of the amplitude of a sound pressure waveformSpectrum envelope:Imaginary smooth line drawn on top of the amplitude spectrum

44SPPA 6010 Advanced Speech Science45Waveform envelope

Time45SPPA 6010 Advanced Speech Science46Spectrum envelope

From Hillenbrand46SPPA 6010 Advanced Speech Science47Thought QuestionCan an aperiodic and complex periodic sound have identical spectrum envelopes?SPPA 6010 Advanced Speech Science48Amplitude Spectrum: Window Sizeshort-term vs. long-term average amplitude spectrum48SPPA 6010 Advanced Speech Science49

Instantaneous Amplitude Spectra49SPPA 6010 Advanced Speech Science50

(Long Term) Average Amplitude Spectrum

50SPPA 6010 Advanced Speech Science51

51SPPA 6010 Advanced Speech Science52Learning ObjectivesDefine an acoustic filterDraw and label a frequency response curveDraw and differentiate different types of acoustic filtersDefine terms such as cutoff frequency, center frequency, roll off rate, gain, and bandwidthDefine and draw a basic filter system and relate that to the source-filter theory of speech productionSPPA 6010 Advanced Speech Science53What is an Acoustic Filterholds back (attenuates) certain sounds and lets other sounds through - selective.53SPPA 6010 Advanced Speech Science54Why might we be interested in filters?Human vocal tract acts like a frequency selective acoustic filterHuman auditory system behaves as a frequency selective filterhelps us understand how speech is produced and perceived.54SPPA 6010 Advanced Speech Science55Frequency Response Curve (FRC)FrequencylowhighGain+-Center frequencylower cutofffrequencyupper cutoff frequencypassband3 dB55SPPA 6010 Advanced Speech Science56Operation of a filter on a signal

NOTE: Amplitude spectrum describes a soundFrequency response curve describes a filter56SPPA 6010 Advanced Speech Science57Kinds of frequency selective filtersLow-pass filtersLets low frequencies pass through and attenuates high frequenciesHigh-pass filtersLets high frequencies pass through and attenuates low frequenciesBand-pass filtersLets a particular frequency range pass through and attenuates other frequencies57SPPA 6010 Advanced Speech Science58Low Pass FiltersFrequencylowhighGain+-58SPPA 6010 Advanced Speech Science59High Pass FiltersFrequencylowhighGain+-59SPPA 6010 Advanced Speech Science60Band Pass FilterFrequencylowhighGain+-60SPPA 6010 Advanced Speech Science61Learning ObjectivesDefine resonance, free and forced vibrationOutline how acoustic resonators behave like acoustic filtersSPPA 6010 Advanced Speech Science62Free vibrationobjects tend to vibrate at a characteristic or resonant frequency (RF)

62SPPA 6010 Advanced Speech Science63Forced vibrationA vibrating system can force a nearby system into vibrationThe efficiency with which this is accomplished is related to the similarity in the resonant frequency (RF) of the two systems63SPPA 6010 Advanced Speech Science64Forced vibrationIf the RF of the two systems are the same, the amplitude of forced vibration will be largeIf the RF of the two systems are quite different, the amplitude of forced vibration will be small or nonexistent64SPPA 6010 Advanced Speech Science65Resonance refers toNatural vibrating frequency of a systemThe ability of a vibrating system to force another system into vibration

65SPPA 6010 Advanced Speech Science66ResonanceAcoustic (Cavity) ResonatorsTransmit sound frequencies with more or less efficiency, depending upon the physical characteristicsTherefore, they act as filters, passing through (and even amplifying) some frequencies and attentuating others.

66SPPA 6010 Advanced Speech Science67ResonanceAcoustic (Cavity) ResonatorsAnd since they act as filters, they have most of the same features of a filter, even though we might use different names.Center frequency is often termed the resonant frequency.Frequency response curve often termed the resonance curve.Resonators may be sharply or broadly tuned which refers to the roll-off frequency

67SPPA 6010 Advanced Speech Science68Resonator Features

Sharply tunedBroadly tuned68SPPA 6010 Advanced Speech Science69Resonator Features

An example of the resonance characteristics of the human vocal tractFrequencyGain69SPPA 6010 Advanced Speech Science70Learning ObjectivesExplain what the decibel is and why it is a preferred way to quantify amplitudeSPPA 4030 Speech Science71Signal amplitude vs. Signal loudnessThe bigger the signal the louder the signalLoudness is our perception of signal amplitude

71SPPA 4030 Speech Science72What units do we use to measure signal amplitude?Up to this point, weve used pressurepressure = force/areacgs units = 1 dyne/cm2 = 1 barye = 0.1 pascal

72SPPA 4030 Speech Science73What units do we use to measure signal amplitude?Size may also be represented using intensityIntensity = Power/area Power=Work/timeWork=Force*distanceUnits: watts/m2 not cgs

73SPPA 4030 Speech Science74Pressure-Intensity RelationIntensity is proportionate to Pressure274SPPA 4030 Speech Science75What is the decibel scale?We use the decibel scale to represent signal amplitude

We are used to using measurement scales that are absolute and linearThe decibel scale is relative and logarithmic75SPPA 4030 Speech Science76Linear vs. logarithmicLinear scale: 1,2,3For example, the difference between 2 and 4 is the same as the difference between 8 and 10.We say these are additive7677Linear vs. logarithmicLogarithmic scales are multiplicativeRecall from high school math and hearing science

10 = 101 = 10 x 1100 = 102 = 10 x 101000= 103 = 10 x 10 x 100.1 = 10-1 = 1/10 x 1Logarithmic scales use the exponents for the number scalelog1010 = 1log10100 = 2log 101000=3log 100.1 = -177SPPA 4030 Speech Science78Logarithmic Scalebase doesnt have to be 10In the natural sciences, the base is often 2.7 or e78SPPA 4030 Speech Science79Logarithmic ScaleWhy use such a complicated scale?logarithmic scale squeezes a very wide range of magnitudes into a relatively compact scalethis is roughly how our hearing works in that a logarithmic scales matches our perception of loudness change79SPPA 4030 Speech Science80For example,linearlog11021003100080SPPA 4030 Speech Science81Absolute vs. relative measurementRelative measures are a ratio of a measure to some reference Relative scales can be referenced to anything you want.decibel scale doesnt measure amplitude (intensity or pressure) absolutely, but as a ratio of some reference value.81SPPA 4030 Speech Science82Typical reference valuesIntensity10-12 watts/m2 Threshold for normal hearing at 1000 HzSound Pressure Level (SPL) 20 micropascals

82SPPA 4030 Speech Science83HoweverYou can reference intensity/pressure to anything you want

For example,Post therapy to pre therapySick people to healthy peopleSound A to sound B

83SPPA 4030 Speech Science84Now, let us combine the idea of logarithmic and relativebel= log 10(Im/ Ir)Im measured intensityIr reference intensity

A bel is pretty big, so we tend to use decibel where deci is 1/10. So 10 decibels makes one beldBIL = 10log 10(Im/ Ir)

84SPPA 4030 Speech Science85Intensity vs. PressureIntensity is difficult to measure.Pressure is easy to measure a microphone is a pressure measuring device.Intensity is proportionate to Pressure2

85SPPA 4030 Speech Science86Extending the formula to pressureUsing some logrithmic tricks, this translates our equation for the decibel to

dBSPL= (2)(10)log 10(Pm/ Pr) = 20log 10(Pm/ Pr)

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