Vowel Acoustics

November 2, 2012

Some Announcements• Mid-terms will be back on Monday…

• Today: more resonance + the acoustics of vowels

• Also on Monday: identifying vowels from spectrograms.

Back at the Ranch• Last time, we learned about resonance:

• when one physical object is set in motion by the vibrations of another object.

• In speech, the vocal tract resonates in response to…

• the periodic vibrations of the vocal folds.

• We can envision a resonating sound wave as a standing wave…

A Minor Disaster• The pressure waves of sound can set up standing waves in objects, too.

• Check out the Mythbusters video online:

• www.youtube.com/watch?v=PMg_nd-O688

Resonant Frequencies• This is important:

• a standing wave can only be set up in a tube if pressure pulses are emitted from the loudspeaker at the right frequency.

• What is the right frequency? That depends on:

• how fast the sound wave travels through the tube

• how long the tube is

• Basically:

• the longer the tube, the lower the frequency

• Why?

Establishing Resonance• A new pressure pulse should be emitted right when:

• the first pressure peak has traveled all the way down the length of the tube

• and come back to the loudspeaker.

Establishing Resonance• The longer the tube, the longer you need to wait for the pressure peak to travel the length of the tube.

• longer period between pressure pulses

• lower frequency

F0

F0

Making the Leap• First: let’s check out the pop bottle demo

• To relate resonance to speech, we need to add two elements to the theory:

1. It is possible for sound waves of more than one frequency to resonate in a tube at the same time.

2. The vocal tract is a tube that is open at one end (the mouth)…

• so it behaves a little differently from a closed tube.

Higher Resonances• It is actually possible to set up more than one standing wave in a tube at the same time.

First Resonance

Second Resonance

• In a closed tube, the second resonance frequency will be exactly twice as high as the first.

First ResonanceTime 1: initial impulse is sent down the tubeTime 2: initial impulse bounces at end of tubeTime 3: impulse returns to other end and is reinforced by a new impulse

• Resonant period = Time 3 - Time 1

Time 4: reinforced impulse travels back to far end

Second ResonanceTime 1: initial impulse is sent down the tube

Time 2: initial impulse bounces at end of tube + second impulse is sent down tube

Time 3: initial impulse returns and is reinforced; second impulse bounces

Time 4: initial impulse re-bounces; second impulse returns and is reinforcedResonant period = Time 2 - Time 1

Different Patterns• This is all fine and dandy, but speech doesn’t really involve closed tubes.

• Think of the vocal tract as a tube with:

• one open end

• a sound pulse source at the closed end

(the vibrating glottis)

• The vocal tract will vibrate in response to the sound pulses…

• at the particular frequencies that will set up standing waves down its length.

Just So You Know• A weird fact about nature:

• When a sound pressure peak hits the open end of a tube, it doesn’t get reflected back.

• Instead, there is an “anti-reflection”.

• The pressure disperses into the open air, and...

• A sound rarefaction gets sucked back into the tube.

Open Tubes, part 1

Open Tubes, part 2

Open Tube Resonances• Standing waves in an open tube will look like this:

1st Resonance Frequency: F1

tube length

2nd Resonance Frequency:

F2 = 3 * F1

3rd Resonance Frequency:

F3 = 5 * F1

An Evenly Spaced Spectrogram

• Go to Praat and check out:

• My neutral vowel

My “Open Tube” Vowel

formants

Spectral Analysis: Vowels• Remember: Fourier’s theorem breaks down any complex sound wave (e.g., speech) into its component sinewaves.

• For each component sinewave (harmonic), this analysis shows us:

• its frequency

• its amplitude (intensity)

• In vowels:

• resonating harmonics have higher intensity

• other harmonics will be damped (have lower intensity)

A Vowel Spectrum

Note:

F0 160 Hz

F1

F2

F3 F4

Different Vowels,Different Formants

• The formant frequencies of resemble the resonant frequencies of a tube that is open at one end.

• For the average man (like Peter Ladefoged or me):

• F1 = 500 Hz

• F2 = 1500 Hz

• F3 = 2500 Hz

• However, we can change the shape of the vocal tract to get different resonant frequencies.

• Vowels may be defined in terms of their characteristic resonant frequencies (formants).

Artificial Examples• The characteristic resonant frequencies (formants) of the “corner” vowels:

“[i]” “[u]”

“ ”

Real Vowels

Real Vowels

What we need to worry about• There are 8 contrastive monophthong vowels in

Canadian English:

1. [i] “heed”

2. “hid” cap-i

3. “head”

4. [æ] “had” ash

5. “hod” / “hawed”

6. “hud” wedge

7. “hood” upsilon

8. [u] “who’ed”

More Vowels• There are also five diphthongs:

1. “bayed”

2. “bode”

3. “bide”

4. “bowed”

5. “Boyd”

• Diphthongs change vowel qualities within a syllable

• Each of these vowels/diphthongs has characteristic resonant frequencies (i.e., formants)…

• which are related to their articulatory properties.

Vowel Articulations• We learned (a long time ago) that vowels are articulated with characteristic tongue and lip shapes

Vowel DimensionsFor this reason, vowels have traditionally been described

according to four pseudo-articulatory parameters:

1. Height (of tongue)

2. Front/Back (of tongue)

3. Rounding (of lips)

4. Tense/Lax

= distance from center of vowel space.

The Vowel Space

Vowel Acoustics• But it turns out that we can get to the same chart a different way...

• Vowels are primarily distinguished by their first two formant frequencies: F1 and F2

• F1 corresponds to vowel height:

• lower F1 = higher vowel

• higher F1 = lower vowel

• F2 corresponds to front/backness:

• higher F2 = fronter vowel

• lower F2 = backer vowel

Reality Check• Let’s check out the formant values for Bruce Hayes’ vowels in Praat.

• And plot them on the board.

Things to Keep in Mind• Resonant frequencies (formants) are primarily based on the length of the speaker’s vocal tract.

• (the length of the open tube)

• The longer the vocal tract, the lower the formant frequencies.

• Thought Question #1:

• What effect might lip rounding have on formant frequencies?

Things to Keep in Mind• Thought Question #2:

• How might formant frequencies differ between men and women?

Male Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

[i][u]

[æ]

Female Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

[i] [u]

[æ]

Combined Formant Averages

200

300

400

500

600

700

800

900

1000

10001500200025003000

F2

F1

Women and Men• The acoustics of male and female vowels differ

reliably along two different dimensions:

1. Sound Source

2. Sound Filter

• Source--F0: depends on length of vocal folds

shorter in women higher average F0

longer in men lower average F0

• Filter--Formants: depend on length of vocal tract

shorter in women higher formant frequencies

longer in men lower formant frequencies

Prototypical Voices• Andre the Giant: (very) low F0, low formant frequencies

• Goldie Hawn: high F0, high formant frequencies

F0/Formant mismatches• The fact that source and filter characteristics are independent of each other…

• means that there can sometimes be source and filter “mismatches” in men and women.

• What would high F0 combined with low formant frequencies sound like?

• Answer: Julia Child.

F0/Formant mismatches• Another high F0, low formants example:

Roy Forbes, of Roy’s Record Room (on CKUA 93.7 FM)

• The opposite mis-match =

Popeye: low F0, high formant frequencies

In Praat• Check out:

Andre

Goldie

Julia

Popeye

Low-to-high F0

Pitch Shifting

In Conclusion• Everybody’s vowel space is different.

• A vowel space is defined by a speaker’s range of first formant (F1) and second formant (F2) frequencies.

• We identify vowels on the basis of the patterns formed by their formants within that acoustic space.

• F1 determines the height of vowels.

• F2 determines the front/backness of vowels.

• Questions?