Acoustics of Speech

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Acoustics of Speech

• Linguistics 414
• 10, 15, 17 October 07

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• The next slide describes the generation of
  alternating regions of air compression and
  rarefaction by the movement of a vibrating plate,
  and shows the propagation of these regions away
  from the plate.
• This is a (periodic) sound.

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P
P
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• The next slide depicts two different aspects of
  the same sound wave
• Differences in pressure (blue)
• Differences in the speed (velocity) of pressure
  change (red)
• Notice that where pressure is at an extreme,
  velocity of pressure change is 0, and vice versa.

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Pressure
Velocity
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Frequency and its reciprocals

• Period
• Wavelength

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• The next two slides show how a complex wave can
  be composed by adding simple waves together.
• Simple waves have energy at just one frequency.
• Complex waves have energy at more than one.
• Spectral analysis is the reverse of this process,
  decomposition of a complex wave into the simple
  waves (its components) that when added together
  would make that complex wave.

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Fundamental Frequency of a Complex Wave

• F0 largest common factor of the frequencies of
  its components

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• The next slide shows the spectra of the two
  complex waves displayed in the preceding slides,
  plus the spectra of two other complex waves that
  were not shown.
• The spectrum represents all you need to know at
  the components of a complex wave, their
• Frequencies
• Amplitudes
• Their shape is predicted by the sine function.

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• The next four slides show how the saw-toothed
  sound wave produced by vibrating the vocal folds
  can be decomposed into a large number of simple
  waves.
• Three voice qualities are illustrated, modal,
  lax, and tense voice, which differ in how rapidly
  energy drops off as the frequency of the
  components increases
• tense lt modal lt lax
• The spectra of these waves is shown in the fourth
  slide in this series.

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• The next slides show the evolution of a resonance
  from the point where the resonator is first
  disturbed until it establishes a stable standing
  wave.
• A standing wave is defined a wave in which the
  locations of maximal and minimal (0) displacement
  from rest are fixed along its length.
• This resonator is like a slinky in that it is
  fixed at one end but free at the other.

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• When the advancing wave reflects off the fixed
  end, energy is returned with opposite sign.
• When it reflects off the free end, it is instead
  returned without a change in sign.
• Wherever the advancing and reflected waves occupy
  the same stretch of the resonator the two waves
  add.
• If they have opposite signs, they cancel,
• If they have the same sign, they amplify.

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• The next slide shows the two alternating states
  of the resonator that produce the standing wave
  (although only for a portion of the wave)
• Cancellation
• Amplification.

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• The only important difference between the slinky
  and the column of air in your oral cavity as a
  resonator is that slinky molecules are displaced
  transversely (at right angles) to the propagation
  of the wave, while the air molecules are
  displaced longitudinally (in the same direction)
  as the propagation.

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• Two ends of oral cavity and slinky
• Closed end glottis Fixed
• Open end lips Free
• Longitudinal displacement of air molecules is
  maximally constrained at the closed end,
  maximally free at the open end.
• Longitudinal displacement Velocity of pressure
  change.
• Waves that fit have a velocity maximum at the
  open end and a velocity minimum at the closed end.

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• The next slide shows three waves that meet these
  criteria and fit inside the oral cavity.
• It also shows the relationship between the length
  of the resonator and the wavelengths of these
  resonances.

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Boundary Conditions
Closed at one end
Lips
Velocity Minimum
Velocity Maximum
Lvt(1/4)?1
Glottis
Open at other
Lvt(3/4)?2
Lvt(5/4)?3
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• In the next slide, we develop a general rule
  relating resonator length and wavelengths of
  resonances.
• Length rule
• In the one after, this rule is used to calculate
  the frequencies of these resonances for a
  resonator 17.5 cm long.

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Frequency is inversely proportional to cavity
length.
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F1
F2
F3
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MinMax Rule

• A constriction at a velocity maximum of a
  resonance lowers its frequency,
• A constriction at a velocity minimum raises its
  frequency.
• Velocity maxima odd quarters of ?
• Velocity minima even quarters of ?
• Locate constriction relative to even/odd quarter

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Locating Constrictions Relative to Minima and
Maxima
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Source-Filter Independence

• Filter response depends on
• Length of resonating cavity
• Location of constrictions and expansions
• Source depends on
• Subglottal air pressure
• Vocal fold position
• Vocal fold tension
• No physical connection!

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• The following slide shows the spectra of six
  vowels produced by a male speaker of American
  English (the first set) and a female speaker of
  New Zealand English (the second set). They are
  arranged
• front, unrounded back, rounded
• i u high
• e o mid
• æ ? low (unrounded)

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• The arrows identify the first three formants, and
  the vertical lines can be used to see how these
  formant frequencies differ from the neutral
  values predicted from a tube without any
  constrictions.
• Use these deviations, the pictures from slide 26,
  repeated to the right, and the MinMax rule to
  work out where the constrictions are in each
  vowels.

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• The next three slides show the acoustic effects
  of a bilabial, alveolar, and velar constriction
  on the formant frequencies at the edges of
  flanking vowels in utterances consisting of
  ?Cæ.
• Place of articulation is indicated by differences
  in F2 and F3
• F2 F3
• bilabial b ? ?
• alveolar d -- ?
• velar g ? ? Note the velar pinch
• Why is F1 lowered by constrictions at all three
  places of articulation?

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?
æ
Stop closure
F3
F2
F1
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F3
F2
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F3
F2
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• The four slides show the acoustic effects of
  bilabial, alveolar, and velar constrictions in
  the context of following i, æ, ?, and u,
  respectively.
• Note how F2 and F3 differ simultaneously as a
  function of place of articulation and vowel
  quality.

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F3
F2
F3
F2
F3
F2
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F3
F2
F3
F2
F3
F2
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F3
F2
F3
F2
F3
F2
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F3
F2
F3
F2
F3
F2
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• The next four slides repeat the four you have
  just seen, but now the F2 values at the onset of
  the following vowel have been pulled out.

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1600
1900
2000
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1400
1700
2000
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900
1500
1200
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1100
1500
1300
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• The F2 values are tabulated on the next slide.
• Note that F2
• b lt d or g in all four vowel contexts,
• g gt d before front vowels,
• g lt d before back vowels.

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• The next three slides show a different way of
  determining how a constriction alters
  resonance/formant frequencies.
• The constriction divides the oral cavity into a
  number of resonating cavities,
• Whose resonance frequencies are determined by
  their length and boundary conditions.
• The first three formants are the lowest three
  resonances produced by this combination of
  resonators.

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Both resonating cavities are closed at one end
and open at the other.
Back cavity is closed at both ends, the front
cavity open at both ends. See the next slide.
The Helmholtz resonance.
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Maximum
Maximum
Minimum
Minimum
Lrc?1/2
Maximum
Maximum
Minimum
Minimum
Lrc2?1/2
Maximum
Maximum
Minimum
Minimum
Lrc3?1/2
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Resonance frequencies predicted from the three
configurations on the previous slide as the
constriction is moved from 2 cm above the glottis
to the lips. For any constriction location,
simply read up the three lowest frequencies from
the bottom to determine what the first three
formants would be.
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• The next six slides apply this approach to
  predicting the differences in F1 and F2 between
  different vowels.

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First Resonance Formant F1 Tongue Height
i heed
? hid
? head
æ had
i lt ? lt ? lt æ
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Articulation Height
high i heed
LONG
high i F1 low
lower high ? hid
low mid ? head
low æ had
low ? F1 high
SHORT
low ? hod
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The length rule F1

• Longer cavities have lower frequency resonances
  (AKA formants).
• Frequency is inversely proportional to length.
• F1 varies inversely with length of cavity behind
  lingual constriction.

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Second Resonance Formant F2 Tongue Backness
and Lip Rounding
i gt u ? gt ? ? gt ? æ gt ? Front gt
Back
? head
? law
i heed
u whod
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Articulation Backness and Rounding
front
back
front unrounded i heed
unrounded
rounded
back rounded u whod
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Length rule again F2

• F2 varies inversely with the length of the cavity
  in front of the lingual constriction.
• Lip rounding lengthens that cavity even more.