Acoustic Phonetics

3/9/00

Acoustic Theory of Speech Production

• Modeling the vocal tract

– Modeling= the construction of some replica of the actual physical object under study

– Tube to simulate the vocal tract

– Model gradually changes to what we know the vocal tract shape to be

Pipe Models

A. A uniform straight tube (closedat one end & open at the other)

*This tube is closed at one end to represent the closed vibrating vocal folds, The open end represents the lips separated for the production of vowel sounds.

l1

A.

Closed Open

Pipe Models

B. A uniform straight tube of a greater length than A. closed at one end and open at the other end.

* First modification of this model was to change the length.

l2

B.

Pipe ModelsC. A straight tube of varying cross-sectional diameter.

* Next modification is to shape the pipe so that the diameter varies along the length. Now the tube flares at its open end (lips).

C.

Pipe Models

D. A bent tube of varying cross sectional diameter.

* The final modification is a bent tube to represent the right angle of the vocal tract

D.

The Simple Pipe Model: Modeling One Vowel

• A. Closed at one and and open at the other: 17.5 cm long– Exhibits resonance under the right conditions:

• Frequency of sound; length of tube

• Odd-quarter wavelength

– Wavelength of a sound = Distance traveled by a soundwave during one period of vibration

• Wavelength depends on the frequency of vibration & speed of sound

= s/f (Where is the wavelength in meters, s is the speed of sound in meters/sec, and f is in frequency in hertz

The Simple Pipe Model: Modeling One Vowel• In this example the tube length is adjusted to the

wavelength of a tone (Similar to only a mid-central vowel in speech)

– Other resonance's occur when the tube changes shape

– The energy of human speech is concentrated at relatively low frequencies and higher areas can be neglected

• Concentration on first 3 resonance's of the vocal tract or formants.

– Formants are identified by formant number (F1, F2, F3)

• Typical Male (production of a mid central vowel): F1= 500 Hz, F2= 1500 Hz, F3= 2500 Hz

Adjusting the Length of the Tube: Modeling Vowels of Men, Women, & Children

• B. First modifications of the simple tube is

length.

– Length of the tube determines the frequencies of its

resonance's

– Longer tube has lower resonance frequencies

– Shorter tube has higher resonance frequencies

• Short tube = Child (8-10 cm)

• Moderately long= Women (15 cm)

• Long= Men (17.5 cm)

Calculated Formant Frequencies (F1, F2, F3)

F1 F2 F3

Neonate

Woman

Man

1094 3282 5470

583 1749 2915

500 1500 2500

* Neutral, or central, vowel in which the tongue and other articulators are positionedso that the vocal tract has a uniform cross-sectional area from the glottis to lips

Adjusting the Cross-Sectional Area of the Tube: Making More Vowels

• C. Length and cross sectional area variation– / i/ /u/, /a/ and /æ/ (Most frequently occurring in the English

language)

– Modifications to the pipe for this model is by varying the tube’s cross-sectional area so it resembles the vocal tract configurations of the specific vowel

– / i/- Back cavity enlarged relative to the front cavity• /u/- There is a constricted midway along the tube and at

its mouth

• /a/- The front cavity is enlarged relative to the back cavity

• /æ/- The front cavity is relatively enlarged compared to the back cavity

Vowels: Vocal Tract Configurations

Acoustic Vowel Quadrangle1. Defines the acoustic space of vowel production2. Interpret articulatory dimensions of the quadrangle can be interpreted acoustically

1. The high vowels / i/ & /u/have low F1, but low vowels

/ a / & /æ/ have high F1.*Relative value of F1 isassociated with tongue height

2. The back vowels /u/ & / a / have a low F2, but the front

vowels / i/ & /æ/ have a high F2.*Relative value of F2 is associatedwith A-P position of the tongue

i

æ

a

æ

a

uu

i

Women

Men

F1(kHz)

F2

(kH

z)

Example

• Using the vowel quadrangle, describe the difference in formant structure for the following word pair:– seat- suit

The Voice Source: Resonators

Harmonics

The Source-Filter Theory• Resonator & Source Energy

– Filter = Vocal tract• Energy passed in a frequency selective manner

• Production of different vowels changes the filter shape

– Source = Harmonic spectrum of voicing• Fundamental frequency & its harmonics

• Source spectrum is the acoustic energy activating the formants

• Source-filter theory of vowel production:– The energy form the source (vibrating vocal folds)

is modified by the resonance characteristics of the filter (vocal tract)

Source-Filter Theory of Speech Production

Source-Filter Theory• Radiation Characteristic- Exerts final shaping

on the acoustic signal

– Takes into account the way the vocal tract opens into the atmosphere (baffle effect)

– +6 dB increase at every octave

• Source energy has a -12 dB/octave and the radiation characteristic is +6 dB the result is -6 dB/octave fall-off in energy

– Result= Radiated pressure spectrum

Extending the Theory: Consonants

• Fricatives:– Voiceless fricative /s/

– Energy source: Not vocal fold vibration, but turbulent noise generated in the vocal tract

– Cavity lying in front of the noise source is the primary resonator• Length of front cavity determines lowest

frequency resonance– Short length: Labiodental (/f/, /v/)

– Longer length: Alveolar (/s/, /z/)

Model: Filtering of Frication Noise

Point of Noise Generation

Noise shaped by resonanceof the front cavity & sometimesback.

Different Filtering: Vowels vs. Consonants

• Filtering for consonants involves both formants & antiformants

– Anitformants= the opposite of formants in that they result in a loss of sound energy rather than enhancement

• Antiformants arise when:– Vocal tract is radically

constricted (stops, fricatives)

– Vocal tract is bifurcated or split into 2 passages (nasal)