Download Vocal Formants

DRANSFIELD’S Assignments for AP Physics
March 7—15
Today’s activities
For tomorrow
Snow day!
You’ve read chapter 12 by now,
right?
Long range, due
today
Monday
Troublesome problems?
Tuesday
(skinny)
Wednesda
y
(Block)
Thursday
(skinny)
Friday
(Block)
Monday
(skinny)
Tuesday
(Block)
Speed of sound in air Lab
1. Take notes on power (W), sound
intensity (W/m2), and intensity level
(dB).
2. Take notes on beats and the Doppler
Effect.
3. Take notes on demonstration of ULI
microphone and Fast Fourier
Transform program.
4. Finish speed of sound in air lab(informal, typed, partner lab due
Thursday. This should include: data,
data analysis including error analysis
and uncertainty, and a conclusion)
Troublesome problems?
Listen to and take notes on sound
demonstrations (dB, duck call, soprano).
Take notes on ear anatomy.
1. Troublesome problems?
2. Experiment: Determination of the
speed of sound in two metals. Semiformal report (limited background plus
data through conclusion) on one metal
from each partner due on Monday.
1. Experiment: Harmonic structure, the
physics of language and friendship.
Evaluation by quiz.
1. Troublesome Problems?
2. Lab Quiz
3. What’s the deal with Louie-Louie?
Reminder of help times: Blue 4b and G1b
Solve problems 8, 9, 10, 14, & 15
on p. 347.
Read handout: “Physics of Speech
and Song.”
Solve problems 11, 16, 36, 41 on
pp. 347-348.
Read handout: “Bekesy and Place
Theory.”
Solve problems 24, 25, 27, 29, & 34
on p. 348.
Solve problems 50—53 on p. 348.
Speed of sound in
air
Solve problems 67—70 on p. 370.
Read the first 5 sections of chapter
23.
Speed of sound in
metals
Non-relativistic Doppler Effect
The frequency heard by the observer is
given by the equation
 v  vo 
f ' f 

 v ve  ,
where f ' is the perceived frequency, f is
the frequency produced, v is the speed of
sound, vo is the speed of the observer,
and ve is the speed of the emitter. Use
the upper part of each double sign if the
distance between the source and observer
is decreasing.
Reminder of help times: Blue 4b and G1b
Georg von Bekesy and the
Place Theory of Pitch Perception
"The molder of the modern theory of basilar-membrane "resonance" is Georg von Bekesy. In 1928 Bekesy
was a communications engineer in Budapest, studying the mechanical and electrical adaptation of
telephone equipment to the demands of the human hearing mechanism. One day, in the course of a casual
conversation, an acquaintance asked him whether a major improvement would soon be forthcoming in the
quality of telephone systems. The idle remark started a chain of thought that eventually posed to Bekesy a
more fundamental question: "How much better is the quality of the human ear than that of any telephone
system?" His search for the answer has added volumes to our present-day knowledge of hearing."
"Bekesy studied the inner ear by building mechanical models of the cochlea- e.g., a metal tube filled with
water. Along the length of the tube ran a narrow slot covered by a stretched membrane, which served as
the basilar membrane of the model. When the fluid was set in motion, he observed, it caused a bulge which
swept like an undulating wave along the membrane. By adjusting the tension of the membrane along the
slot he was able to confine the biggest part of the bulge to a particular region on the membrane. The
undulation traveled down the length of the membrane, but its amplitude - the size of the bulge- varied with
position: the bulge was slight everywhere except in one area where it was large."
"He also detected the same wave movement in the cochlea itself. Using first animal ears and then the ears of
human cadavers, he carefully cut out the cochlea and bored a tiny opening in the bone. Working under a
microscope with "microtools" of his own invention (one pair of scissors had blades only a few thousandths
of an inch long), he laid open part of the basilar membrane. The cochlear fluid was drained and replaced
with a salt solution containing a suspension of powdered aluminum and coal. By scattering flashes of
intense light off the powder suspension, Bekesy was able to follow events within the interior of the
cochleas. Under the microscope he saw a bulging undulation sweep over the basilar membrane when a
sound was introduced into the cochlea. It was the same traveling wave he had seen coursing along the
artificial membrane of his model."
"From this work Bekesy evolved his traveling-wave theory: a sound impulse sends a wave sweeping along
the basilar membrane. As the wave moves along the membrane, its amplitude increases until it reaches a
maximum, then falls off sharply until the wave dies out. That point at which the wave reaches its greatest
amplitude is the point at which the frequency of the sound is detected by the ear. And as Helmholtz had
postulated, Bekesy found that the high-frequency tones were perceived near the base of the cochlea and the
lower frequencies toward the apex."
"No mammalian ear was beneath Bekesy's scrutiny. He observed the traveling wave in animals ranging
from mouse to elephant. In the early 1940s he read that an elephant had died in the Budapest zoo.
Immediately he went to the zoo to ask for the ears, but learned that the body had been sent to Budapest
University. The University authorities reported that they had shipped the huge carcass to a glue factory.
Finally, at the factory, he found the head still intact."
"That evening Bekesy sent his assistant to saw the portions of the skull containing the inner ears. The young
man proudly returned with two large ears and chunks of bone. But when Bekesy peered into the ear canals,
he found to his dismay that he could see clear through them; the prized inner ears were missing. Because
Reminder of help times: Blue 4b and G1b
an elephant's ear canal is about eight inches long, the assistant had not sawed in far enough. Bekesy sent
him back to the glue factory and this time he returned with the elephantine cochleas. To Bekesy's delight,
the traveling wave phenomenon was clearly visible in the elephant."
"For his studies of the traveling wave, Georg von Bekesy received the Nobel Prize in 1961. His incredible
delicate and elegant experiments had traced sound to the very threshold of sensation. ..."
Excerpt from "Sound and Hearing", Stevens, S. S., & Warshofsky, Fred, eds., Time-Life Books, NY, 1965.
p. 54
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Physics of Speech and Song
The Voice Mechanism
The voice mechanism involves the lungs and diaphragm as the power
source, and the larynx, pharynx, mouth and nose. At the base of the
short tubular larynx are the vocal folds, commonly called the vocal
cords. The larynx opens into the pharynx during speech or singing,
and is covered by the epiglottis during swallowing. The vocal tract
acts as a resonator with frequencies which can be modulated by the
articulators, forming the vocal formants which make vowel sounds
recognizable.
Voice Articulators
In order to produce distinguishable voice sounds, like vowel sounds, the
vocal mechanism must control the resonances of the vocal tract which
produce the characteristic vocal formants. If the vocal tract is considered to
be a cavity resonator, then it can be seen that the position of the tongue, the
area of opening of the mouth, and any changes which affect the volume of the
cavity will retune the resonance.
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Forming the Vowel Sounds
The vocal resonances are altered by the articulators to form distinguishable vowel sounds. The peaks in the
vowel spectra are called vocal formants. Note the prominent role of the tongue in this process. The jaw
position and lips also play a major part.
The sketches at left above are adapted from Gunnar Fant's "Acoustic theory of speech production" and are
reportedly sketches taken from x-rays of the head during the production of these sounds. These are the
vowels classified as IPA [a], [i], and [u] and roughly correlate with the vowels represented in the spectra
from Benade. The emphasis should be on "roughly" since I don't know how close the correlation is. The
intent here is to illustrate the role of the articulators and to point to the fact that their action has a major
influence on the harmonic content of the voiced sounds. The normal ear is able to clearly distinguish those
differences.
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Vocal Formants
The term formant refers to peaks in the harmonic spectrum of a complex sound which arise from some sort
of resonance of the source. Because of their resonant origin, they tend to stay essentially the same when the
frequency of the fundamental is changed. Formants in the sound of the human voice are particularly
important because they are essential components in the intelligibility of speech. For example, the
distinguishability of the vowel sounds can be attributed to the differences in their first three formant
frequencies. Producing different vowel sounds amounts to retuning these formants within a general range of
frequencies. Benade suggests the following ranges of frequencies for the formants of a male voice:
1st formant 150-850 Hz
2nd formant 500-2500
Hz
3rd formant 1500-3500
Hz
4th formant 2500-4800
Hz
The process of articulation determines the frequencies of the vocal formants. Sundberg has identified
portions of the vocal anatomy which he associates with the formant frequencies. The jaw opening, which
constricts the vocal tract toward the glottal end and expands it toward the lip end, is the deciding factor for
the first formant. This formant frequency rises as the jaw is opened wider. The second formant is most
sensitive to the shape of the body of the tongue, and the third formant is most sensitive to the tip of the
tongue.
Same Vowel, Different Pitch
To explain how the ear can recognize a vowel sound as
the same vowel, even though it is sounded at different
pitches, the idea of vocal formants is invoked. This is data
from Benade showing that an "Ah" vowel involves a
similar envelope of harmonics when sounded at different
frequencies.
Reminder of help times: Blue 4b and G1b
AP Physics
Name __________________________
Harmonic Structure
1. a. Find the frequency of the second and fourth harmonics of a sound of frequency 440 Hz.
2nd ________________
4th ________________
b. Four hundred forty hertz is the frequency of A, the note to which an orchestra tunes. What is the
musical interval from the fundamental to the second harmonic and from the second harmonic to the
fourth harmonic? [Hints: The answer is the same for both intervals. Musical intervals include thirds,
fourths, fifths, and octaves.]
________________
2. Why do you think I am making a big deal out of the differences in vowel sounds?
The next three questions are based on the graphs on this and the following pages. Two people and three
vowels are depicted. Each person says two of the vowels. Another vowel is pronounced by only one of
the people.
Sample A, peak frequency = 344 Hz
.
Sample B, peak
frequency = 526
Hz
Sample C, peak
frequency =
1031 Hz
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Sample D, peak frequency = 215 Hz
Sample E, peak frequency = 773 Hz
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3. Only one of these vowel sounds is one that you studied in lab. Which one is it? How do you know?
4. Look at sample E. When the sound is too loud for Logger Pro, the highest peaks look like they have
been “folded over,” that is, the highest peaks show up as craters in the tops of the crest. The amount by
which the voltage exceeded the scale is subtracted from the maximum voltage displayed (4 volts). For
the first peak in this sample, the greatest voltage is a little over 5 volts, but it shows up as a little less than
3 volts. It should be pointing up. The next little jag that points down should also be pointing up, and has
a peak voltage of about 4.7 volts. I’ve drawn a crude correction for the peak that starts the second cycle
of the waveform.
What sample represents the same vowel sound as Sample E? How do you know?
5. These graphs represent varying voltages at different frequencies, which is precisely the same information
the brain gets from your ear via the auditory nerve. How is your brain able to recognize the voices of
your family, friends, and acquaintances?
6. Telephones do not transmit the full range of frequencies that we can hear, but only from about 300 to
3400 Hz. One result is that people sound different on the phone than they do in person. For which sound
would you have the most trouble recognizing who was speaking? Explain your reasoning.
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