Homework - Chapter 6-8
CGSC 433/633
Due: May 2, 2013
Resonant frequencies for tubes closed at both ends:
fk =
kc
2L
Resonant frequencies for tubes closed at one end and open at the other:
fk =
(2k − 1)c
4L
Chapter 6
1. A vocal tract is 14 cm long. Assume the speed of sound is 35,000 cm/s.
(a) (3 points) Draw a multitube model for the vowel [a]. Label the lengths of each of
the tubes, as well as the glottis and the mouth.
Solution: glottis
mouth
7cm
7cm
(b) (3 points) What are the F1, F2, and F3 of the front tube?
Solution: F1 = 35,000/28 = 1250Hz.
F2 = 3 × F1 = 3750Hz.
F3 = 5 × F1 = 6250Hz.
(c) (3 points) What are the F1, F2, and F3 of the back tube?
1
Solution: F1 = 35,000/28 = 1250Hz.
F2 = 3 × F1 = 3750Hz.
F3 = 5 × F1 = 6250Hz.
(d) (6 points) What are the F1, F2, and F3 of the whole tube system? Assume acoustic
coupling offsets the numbers by 20%.
Solution: F1 = 80% of 1250 = 1000Hz.
F2 = 120% of 1250 = 1500Hz.
F3 = 80% of 3750 = 3000Hz.
2. Answer the following questions using the nomogram in Figure 6.4 on page 136 and
consider the constriction to be 8cm from the glottis.
(a) (1 point)
A.
B.
C.
D.
E.
Which is the F1 of the whole tube system?
The Helmholtz resonance
The F1 of the front tube.
The F1 of the back tube.
The F2 of the front tube.
The F2 of the back tube.
(b) (1 point)
A.
B.
C.
D.
E.
Which is the F2 of the whole tube system?
The Helmholtz resonance
The F1 of the front tube.
The F1 of the back tube.
The F2 of the front tube.
The F2 of the back tube.
(c) (1 point)
A.
B.
C.
D.
E.
Which is the F3 of the whole tube system?
The Helmholtz resonance
The F1 of the front tube.
The F1 of the back tube.
The F2 of the front tube.
The F2 of the back tube.
3. (4 points) (From Johnson 2011, page 150 #3). Figure 6.12 (page 151) shows the F3
standing wave with articulatory landmarks for typical male and female speakers. Using
pertubation theory, describe the articulations that will produce the lowest F3 in [ô] How
do the ‘best’ articulations differ in men and women?
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Solution: According to perturbation theory, the articulations that will lower F3 are
constrictions formed at velocity antinodes. For men, these are at the lips, between
the velum and below the pharynx. For women, these are at the lips, at the velum,
and at the pharynx. So apart from forming a constriction at the lips, men have to
form constrictions a little further back in the vocal tract than women to acheive the
same acoustic effect.
4. In this exercise, you will estimate the length of your vocal tract. With Praat, record
yourself making an extended schwa. For example, relax your tongue and jaw, and say
[@@@@@@]. If it helps, say the word about with the first vowel very exentended. Be careful
not to overarticulate!!
Using Praat, measure the first 3 formants of your [@] from the middle of the vowel. When
it’s about 60 degrees Fahrenheit, the speed of sound is actually closer to 34,000cm/s. So
use that value for the speed of sound in this exercise.
(a) (2 points) Using the equations for finding the resonant frequencies for tubes open
at one end and closed at the other, write the equation for F1 , substituting your [@]
F1 value and the value for c. Solve for L, the length of your vocal tract.
Solution:
(b) (2 points) Solve for L again this time using F2 .
Solution:
(c) (2 points) Solve for L again this time using F3 .
Solution:
(d) (2 points) Average your results. That’s a pretty good estimate of your vocal tract
length!
Solution:
Chapter 7
5. Consider the saggital section for the fricative [s] below, and answer the following questions.
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B
C
D
E
A
(a) (1 point) Which location is the point of highest particle velocity (assuming a constant volume velocity throughout the mouth)?
(a)
D
(b) (1 point) Which location (if any) is the point where channel turbulence is generated? If there is no channel turbulence, answer “none”.
(b)
C
(c) (1 point) Which location (if any) is the point where obstacle turbulence is generated? If there is no obstacle turbulence, answer “none”.
(c)
B
(d) (1 point) Yes/No. Is the glottis a source of noise in the production of this fricative?
(d)
6. (Johnson 2011, page 167, sufficient jargon.) Define the following terms.
(a) (1 point) particle velocity.
Solution: Particle velocity refers to the speed of air particles.
(b) (1 point) volume velocity.
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No
Solution: Volume velocity refers to the number of air particles passing a particular point in unit time.
(c) (1 point) channel turbulence.
Solution: Channel turbulence refers to turbulence created by fast-moving air
moving through a narrow channel.
(d) (1 point) obstacle turbulence.
Solution: Obstacle turbulence refers to turbulence created by a an airstream
striking a physical obstacle.
7. (4 points) (Johnson 2011, page 168 #2.) The analysis of fricative acoustics presented
here assumed that the front and back cavities were not acoustically coupled, because
fricative constrictions are narrow. At what points in time during the production of a
fricative is is this assumption most likely to be wrong? And how would you expect the
acoustic coupling of the front and back cavities to affect the fricative spectrum?
Solution: The assumption is likely to be wrong at the beginning and end of a
friative when the constriction is not fully formed and so there is more of an opening
connecting the two cavities. During these stages of formation and release of the
fricative, back cavity resonances should become visible.
Chapter 8
8. (Johnson 2011, page 184, sufficient jargon.) Define the following terms.
(a) (1 point) phonation types.
Solution: There are three phonation types: breathy, creaky and modal. Articulatorily phonation type refers to they way the vocal folds are vibrating.
(b) (1 point) open quotient.
Solution: The open quotient refers to the proportion of time the glottis is open
in one glottal cycle.
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(c) (1 point) voice bar.
Solution: The voice bar refers to a low frequency band that appears in spectograms during the closure phase of voiced stops.
(d) (1 point) glottalized stops.
Solution: Glottalized stops refers to ejective sounds which are produced by
building the air pressure up behind the constriction by raising the larynx. They
have two release bursts: an oral one and a glottal one.
9. (4 points) (Johnson 2011, page 184, #4.) Do affricates have stop release bursts? How
might short rise time lead to decreased auditory salience of the release bursts in affricates?
Solution: Affricates have stop release bursts. The short rise time means the frication
noise would more quickly follow the noise from the burst, potentially covering it up.
This would make it more difficult to perceive the burst release itself.
633 only
Please answer the following questions on a separate piece of paper.
10. (2 points) Reetz and Jongman. page 181. #5
11. (3 points) Reetz and Jongman. page 181. #6
12. (3 points) Reetz and Jongman. page 206. #1
13. (2 points) Johnson Chapter 8, page 148, #5.
14. (2 points) Reetz and Jongman, Chapter 9, page 207, #6.
15. (2 points) Reetz and Jongman, Chapter 9, page 207. #7.
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