SPPA 4030 Speech Science1 Sound Physics. SPPA 4030 Speech Science2 Outline What is sound? Graphic representation of sound Classifying sounds The

SPPA 4030 Speech Science 1

Sound Physics


Outline What is sound? Graphic representation of sound Classifying sounds The Acoustic Filter Resonance The decibel


What is sound? It may be defined as the propagation of a

pressure wave in space and time. propagates through a medium


Sound-conducting media Medium is composed of

molecules Molecules have “wiggle room” Molecules exhibit random

motion Molecules can exert pressure

A B


Spring Mass Model Mass (inertia) Elasticity Friction


Model of air molecule vibration (Time 1)

Rest positions

Air molecules sitting side by side










Model of air molecule vibrationTime

1

2

3

4

5

Distance

a b c d

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Wave action of molecular motionTime

1

2

3

4

5

Distance


Amplitude waveform

Position

Time


Amplitude waveform

Amplitude

Time

Question: How long will this last?


Model of air molecule vibrationTime

1

2

3

4

5

Pressure measuring deviceQuestions: Where is a region of compression?Where is a region of rarefaction?


For example…P

ress

ure

Time


Pressure vs. time (pressure waveform)

Pressure

Time

Amplitude

Period (T)

Phase: when a periodbegins

Frequency (F): rate that waveform repeats itself (1/T)

Phase (deg)


Phase


Initiating 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 vibration


Features of a pressure waveform Amplitude

Measured in pressure units peak amplitude peak-to-peak amplitude Instantaneous amplitude

Period and Frequency Period measured in time (basic quantity) Frequency is a rate measure (per unit time) expressed as Hertz (s-1) May be expressed as octaves, semitones, etc

Phase Measured in degrees (relative to period length) 0-360 degrees


Frequency representation: The octave Octave shift: doubling or halving of

frequency Non-linear


Spatial variation in pressure wave

wavelength () is the distance covering adjacent high and low pressure regions


For example…

Distance

Wavelength ()

Pre

ssur

e


Relation between frequency and wavelength

=c/F where

: wavelength

F: is the frequency

c: is sound speed in medium (33,600 cm/sec)


Additional Concepts Propagation of waves

Transmission Absorption Reflection Reverberation


Graphic representation of sound Time domain

Called a waveform Amplitude plotted as a

function of time

Frequency domain Called a spectrum Amplitude spectrum

amplitude vs. frequency

Phase spectrum phase vs. frequency

May be measured using a variety of “window” sizes


Same sound, different graphs

Time domain

Frequency domain

From Hillenbrand


Classification of sounds Number of frequency components

Simple Complex

Relationship of frequency components Periodic Aperiodic

Duration Continuous Transient


Simple periodic sound Simple: one frequency component Periodic: repeating pattern Completely characterized by

amplitude period (frequency) phase

Other names: sinusoid, simple harmonic motion, pure tone


Simple periodic sound: Graphic appearance

From Hillenbrand


Complex periodic sounds Complex: > one frequency component Periodic: repeating pattern Continuous Frequencies components have a special relation

Lowest frequency: fundamental frequency Symbol: fo

Frequency component with longest period

Higher frequency components: harmonics integer (whole number) multiples of the fo


Complex periodic sounds: Graphic appearance

Time domain: repeating pattern of pressure change within the cycle, things look complex

Frequency domain: spectral peaks at evenly spaced frequency

intervals “picket fence” appearance

Auditory impression: sounds ‘musical’


Complex periodic sounds: Graphic appearance

From Hillenbrand


(Complex) Aperiodic sounds Complex: > one frequency component Aperiodic: Does not repeat itself Frequency components are not systematically

related May be

Continuous Transient


Aperiodic sounds: Graphic appearance Time domain:

no repeating pattern of pressure change Frequency domain:

the spectrum is dense No “picket fence”

Auditory impression: sounds ‘noisy’


Aperiodic sounds: Graphic appearance

From Hillenbrand


Analysis of complex waves Waves can be summed Complex waves are the sum of simple waves Fourier: French Mathematician:

Any complex waveform may be formed by summing sinusoids of various frequency, amplitude and phase

Fourier Analysis Provides a unique (only one) solution for a given sound signal Is reflected in the amplitude and phase spectrum of the signal Reveals the building blocks of complex waves, which are sinusoids


The “envelope” of a sound wave Amplitude envelope:

imaginary smooth line that follows the peak of the amplitude of a sound pressure waveform

Spectrum envelope: Imaginary smooth line drawn on top of the

amplitude spectrum


Amplitude envelope

From Hillenbrand


Spectrum envelope

From Hillenbrand


Amplitude Spectrum: Window Size “instantaneous” vs. average spectrum


“Instantaneous” Amplitude Spectra


(Long Term) Average Amplitude Spectrum



What is a filter?


“Acoustic” Filter holds back (attenuates) certain sounds and lets other

sounds through - selective.


Why might we be interested in filters? human vocal tract acts like a frequency selective

acoustic filter helps us understand how speech is produced and

perceived.

48

Frequency Response Curve (FRC)

Frequencylow high

Gai

n

+

-

Center frequency

lower cutofffrequency

upper cutoff frequency

passband

3 dB


Operation of a filter on a signal

NOTE: Amplitude spectrum describes a soundFrequency response curve describes a filter


Kinds of frequency selective filtersLow-pass filters

Lets low frequencies “pass through” and attenuates high frequencies

High-pass filters Lets high frequencies “pass through” and attenuates low

frequencies

Band-pass filters Lets a particular frequency range “pass through” and

attenuates other frequencies


Low Pass Filters

Frequencylow high

Gai

n

+

-


High Pass Filters

Frequencylow high

Gai

n

+

-


Band Pass Filter

Frequencylow high

Gai

n

+

-


Resonance


Free vibration

objects tend to vibrate at a characteristic or resonant frequency (RF)


Forced vibration

A vibrating system can force a nearby system into vibration

The efficiency with which this is accomplished is related to the similarity in the resonant frequency (RF) of the two systems


Forced vibration

If the RF of the two systems are the same, the amplitude of forced vibration will be large

If the RF of the two systems are quite different, the amplitude of forced vibration will be small or nonexistent


Resonance refers to

Natural vibrating frequency of a system The ability of a vibrating system to force

another system into vibration


Resonance

Acoustic (Cavity) Resonators Transmit sound frequencies with more or

less efficiency, depending upon the physical characteristics

Therefore, they act as filters, passing through (and even amplifying) some frequencies and attentuating others.


Resonance

Acoustic (Cavity) Resonators And 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


Resonator Features

Sharply tuned Broadly tuned


Resonator Features

An example of the resonance characteristics of the human vocal tract

Frequency

Gain


Sound pressure, intensity and the decibel scale


Signal amplitude vs. Signal loudness

The bigger the signal – the louder the signal

Loudness is our perception of signal amplitude


What units do we use to measure signal amplitude?

Up to this point, we’ve used pressure pressure = force/area cgs units = 1 dyne/cm2 = 1 barye = 0.1 pascal


What units do we use to measure signal amplitude?

Size may also be represented using intensity Intensity = Power/area

Power=Work/time Work=Force*distance

Units: watts/m2 – not cgs


Pressure-Intensity Relation Intensity is proportionate to Pressure2


What is the decibel scale? We use the decibel scale to represent signal

amplitude

We are used to using measurement scales that are absolute and linear

The decibel scale is relative and logarithmic


Linear vs. logarithmic

Linear scale: 1,2,3… For example, the difference between 2 and

4 is the same as the difference between 8 and 10.

We say these are additive

70

Linear vs. logarithmic Logarithmic scales are multiplicative Recall 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 1

Logarithmic scales use the exponents for the number scalelog1010 = 1

log10100 = 2

log 101000=3

log 100.1 = -1


Logarithmic Scale base doesn’t have to be 10 In the natural sciences, the base is often 2.7…

or e


Logarithmic Scale Why use such a complicated scale?

logarithmic scale squeezes a very wide range of magnitudes into a relatively compact scale

this is roughly how our hearing works in that a logarithmic scales matches our perception of loudness change


For example,

linear log

1 10

2 100

3 1000


Absolute vs. relative measurement

Relative measures are a ratio of a measure to some reference

Relative scales can be referenced to anything you want.

decibel scale doesn’t measure amplitude (intensity or pressure) absolutely, but as a ratio of some reference value.


Typical reference values Intensity

10-12 watts/m2 Threshold for normal hearing at 1000 Hz

Sound Pressure Level (SPL) 20 micropascals


However… You can reference intensity/pressure to

anything you want

For example, Post therapy to pre therapy Sick people to healthy people Sound A to sound B


Now, let us combine the idea of logarithmic and relative…

bel= log 10(Im/ Ir)

Im –measured intensity

Ir – reference intensity

A bel is pretty big, so we tend to use decibel where deci is 1/10. So 10 decibels makes one bel

dBIL = 10log 10(Im/ Ir)


Intensity vs. Pressure Intensity is difficult to measure. Pressure is easy to measure – a microphone is

a pressure measuring device. Intensity is proportionate to Pressure2


Extending the formula to pressure

Using some logrithmic tricks, this translates our equation for the decibel to

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

Documents

SPPA 4030 Speech Science1 Sound Physics. SPPA 4030 Speech Science2 Outline What is sound? Graphic representation of sound Classifying sounds The