Learn about the physics of sound behind public speaking.

1. Physics of an Effective Public Speaker
PHYSICS 1204 / MUSIC 1466
Dr. Selby
John Scrugham
May 10, 2012

2. Scrugham,The Physics of Good Public Speaking, p.1
Introduction
It was with delight that one who remembers Edward Everett in his robes of rhetorical splendor;
who recalls his full-blown, high-colored, double-flowered periods; the rich, resonant, grave, far-
reaching music of his speech, with just enough of nasal vibration to give the vocal sounding-board
its proper value in the harmonics of utterance.
-Oliver WendellonAmerican politician and legendary orator, Edward Everett’s 1887
speech at Cambridge (Fillebrown 10)
Although Oliver Wendell gaveEdward Everett averbose and positive review of his
speaking, Wendell, and even many scientists1
in 1887, did not completely understand the physics
of why Everett sounded so great. Wendell did notice the beautiful sounds that were coming from
Everett’s throat and mouth, but he used words such as harmonics, vibrations, and resonance that
were not well understood at the time.Within a few years of Everett’s speech though, our
understanding of sound and physicsexpand rapidly with the help of great breakthroughs such as
Wallace Sabine’s research on architectural acoustics (1895) and Lord Rayleigh’s bookThe
Theory of Sound (1894). Over the course of the next century, our understanding of physics and
sound continued to exponentially grow. Now we canfully explain the harmonics, vibrations, and
resonance of Everett’s voice. More than merely explaining the voice of a 19th
century politician,
we have the power to manipulate the physics behind our voice so that we can become more
effective speakers.
While scientists have published research on speaking and physics, little research has been
published on the interplay between speaking and physics—i.e., how speakers can harness the
physics of their voices to become more effective speakers. I hope to provide that connection in
1
On the forefront of sound and physics research was Helmholtz’s published book On the Sensations of Tone as a
Physiological Basis for the Theory of Music (1863).

3. Scrugham,The Physics of Good Public Speaking, p.2
this paper. I will focus on two techniques—and the physics behind them—that effective speakers
can harness to deliver powerful speeches: you can achieve a heartier voice through vowel
darkening, pulling your larynx down, and by thickening your vocal chords; you can better project
you voice by tightening your vocal folds and by using belly breathing to achieve greater lung
volume.
Before delving in to the techniquesthat effective speakers employ, let’s look at how we
produce sound. The human instrument’sfirst part is the diaphragm which is a muscle under the
lungs that forces the lungs up and down: it is the driving force of the instrument. The lungs,
beyond giving us oxygen to sustain
life, serve as the energy source for
sound produce. The trachea and the
esophagusare tubes that connect the
lungs (energy source) to the vocal
folds (sound production) and have
little acoustic significance. Above
the esophagus, in the throat, lies the larynx which contains the vocal folds (Rossing337-339).
Figure1: The mechanisms of human sound (Rossing 337)

4. Scrugham,The Physics of Good Public Speaking, p.3
The vocal foldsare a muscular
tissue that vibrates if we achieve the
correct air pressure and tension in the
larynx. The vibration is depicted in the
graph on the next page where the V-shaped
openingopens and closes rapidly in sound
production. The V-shaped area between the
folds is called the glottis (Rossing 339).
The glottis is open when we are breathing
normally or when we make open consonants such as ―f‖ or ―sh.‖ The glottis is closed in times
like right before you cough. Lastly, and most importantly, the glottis can rapidly open and close,
which makes a buzzing sound in your throat. This occurs when you speak vowels and voiced
consonants. The frequency of your voice is determined by the buzzing sound of the vocal folds
(Wolfe).
However, we don’t talk in buzzes; we have the ability to speak smoothly. This is because
we have a filter above the vocal folds that is composed of the upper throat, mouth,tongue, lips,
and nasal cavity, which together round out the buzzing sound from the folds. All of these
partscome together as a ―resonance chamber‖and play an important role in creating good sound
(ibid). An example of a part not working correctly is when we have a stuffy nose. Our voice
changes because the resonance chamber is significantly decreased in size when mucus fills the
nasal cavity. Your voice is often flatter—or ―nasally‖.
Figure2: The vibration of the vocal folds (Wolfe)

5. Scrugham,The Physics of Good Public Speaking, p.4
Now that we understand how humans produce sound, let’s look in to some things that
you can do to become a better speaker. Namely, creating a heartier voice and projecting a louder
voice.
A Heartier Voice
A heartier voice is a voice that is deep, rich, and resonates well. Examples include the
voice of a sports announcers and good actors. You can obtain a heartier voice by using vowel
darkening to decrease your formant frequencies and by dropping your larynx to create a richer
and lower pitch. You should strive for a heartier voice for two reasons.
First, your voice often sounds deeper and richer to yourself than it does to other people,
so it may not be as deep and rich as you think it may be.In a study, participants listened to
recordings of themselves speaking and were asked to compare the recorded voice to the voice
that they believed to have. The subjects perceive their voice in the recording as being higher-
pitched and less rich, both undesirable traits of good voice (Lundh25). We think that our voice is
deeper and richer than it actually is because when we talk,the eardrum, ossicles, and cochlea—
the places where sound is transferred from the sound air waves to electrical signals to the brain—
picks up on not only the sound outside (like they normally do) but also pick up on low-frequency
vibration through bone conduct (your check bones, skull, jaw) originating from your mouth and
throat (Wolfe). Our perceived voice is thus a combination of bone vibration and air vibration.
The second reason that you may want to gain a heartier voice is that there is a wealth of
research on the benefits of having a lower voice.For many years, men have dominated leadership
positions, so some scientist say that voices that sound more like a male leader (around 70-200
Hz) are perceived as being more effective(Campbell 160).While the discussion of why deeper
voices are perceived this way is outside the scope of this paper, the implications are that by

6. Scrugham,The Physics of Good Public Speaking, p.5
lowering your voice (in both pitch and tone quality) you can become a more effective speaker.
Men with lower-pitch voices are said to be stronger (Feinberg 562) and more socially dominant
(Gregory 525) and women are perceived to be socially dominant with deeper voices (Borkowska,
2011).
Our actions reflect our perceptions of people with lower voices: weprefer people with
lower voices to be our team leader, CEO, and even president (Campbell, 1960) (Kloftstad, 2012).
In a recent study conducted by Casey Kloftstad, it was found that people vote more often for
candidates with deeper voices. The research team played recordings of a person saying, ―I urge
you to vote for me this November‖ to participants. The team played two variations of this
recording: higher and lower pitched versions of the original statement. The lower pitched version
was shifted down about 20Hz and the higher pitched version shifted up 20Hz from the original.
The team asked the participants, ―if [the two people in the recordings] were running against each
other in an election, which one would you vote for?‖ Male and female participants selected male
and female leaders with lower voices more often than the higher-pitched voices even though it
was the same person speaking in both recordings (Klofstad).
Perhaps the most famous story of a leader lowering and darkening her tone of voice is
that of Margaret Thatcher and her rise to prime ministry. Her advisors, particularly her political
strategist Gordon Reece, wanted to train her to speak in a heartier voicein order to increase her
chance of winning the elections (Dunbar). Reece and the rest of the advisors most likely wanted
to change Thatcher’s voice in lieu of the consistent, and sometimes harsh, criticism. One such
criticism was delivered by television critic Clive James’ in The Observer during the 1973
elections:

7. Scrugham,The Physics of Good Public Speaking, p.6
The hang-up [with Thatcher] has always been the voice. Not the timbre so much as, well, the
tone—the condescending explanatory whine which treats the squirming interlocutors as an eight-
year-old child with personality deficiencies…She sounded like a cat sliding down a blackboard
(Clive).
Reece understood the need to change Thatcher’s voice, especially before the 1979 elections.
Luckily, Reece had a chance run-in with one of England’s best actors, Laurence Oliver, on a
train ride out of London. Reece asked if Oliver could help Thatcher to improve her vocal quality.
Oliver agreed to help and arranged lessons between Thatcher and his speech coach at the
National Theatre. After a year’s training, Thatcher lowered her voice by 46 Hzand darkened
many of her tones including her harsh, high shrills (Dunbar). It paid off. Not only did she win the
elections but critics also took a noticeable shift to enjoying her speaking. Charles Moore, the
author of Thatcher’s autobiography-in-process, noted that, ―soon the hectoring tones of the
housewife gave way to softer notes and smoothness.‖

8. Scrugham,The Physics of Good Public Speaking, p.7
So how exactly did Thatcher rid herself of the shrill and
high pitch of her voice? Let’s take a step back and look at how we
produce pitch, specifically vowel sounds. We have the ability to
make sound by vibrating the vocal folds so that they rapidly open
and close. The frequency at witch these folds vibrates determines
the pitch of the voice (Wolfe). The first sound spectrum that you
see on the right is a chart of the frequencies produced from the
vocal chordsand their relative strength.As you may recall, the
―resonance chamber‖ above the larynx filters the buzzing sound
that is produced from the vocal chords. The amount and how it
filters depends on how you position each part of the chamber
(Rossing 340). For example, sing ―ah.‖ Now, sing ―ee.‖ Notice
how on the ―ee,‖ you pull your tongue up, make your mouth
smaller, and move your lips back. The shape that your ―resonance
chamber‖ takes on the ―ee‖ versus the ―ah‖ makes significantly
different sounds because the intensity of different harmonics differs with each shape. This is
exemplified in the second graph. The shape of the ―resonance chamber‖ resonates with some
frequencies found in the first graph (high peaks of resonance) and ―filters‖ other frequencies that
do not resonant well with that shape (valleys between the high peaks). The frequencies that
resonate the most (the peaks) for a certain resonance chamber shape are called the formants.
Lastly, the vowel sound that reaches an audience carries the original frequencies produced by the
vocal chords with the relative intensities determined by the resonance chamber (third graph).
Figure 3: Filtering of vocal fold
frequencies and the presence of
formants (Selby Lecture 32, Slide
20)

9. Scrugham,The Physics of Good Public Speaking, p.8
You can produce different sounds that have different formant frequencies as we saw in
―ah‖ versus an ―ee.‖ In fact, all vowels have a different ―frequency envelope‖—or shape of
formants. Vowels with the first formant (the first peak of high resonant intensity) in the lower
frequency rangesare said to be darker vowels.
You don’t have to always use darker vowels to have a darker and richer timbre. To create
a darker, richer timbre, youcan lower the frequency of your first formant artificially; this is called
vowel darkening (Selby Lecture 33). To do this, push your tongue back towards your throat
while still allowing air to come up from the vocal tract. Back vowels, or dark vowels, are created
this way (Lewis 47).The graph on the right illustrates
what happens if you were to darken an ―ah.‖ The first
formant in a normal ―ah‖ lies at 700 Hz as seen in the
first chart. By pushing your tongue further back
when sounding the ―ah,‖ you shift the first formant
down to 300 Hz as exemplified in the second graph.
Notice that the frequencies present (represented by
the vertical lines) remain the same in both graphs.
Thus, pitch remains constant, yet the tone quality
changes. This occurs because with vowel darkening, we are not altering our vocalfolds; rather,we
are changing the shape of the resonance chamber at the end of the human instrument.
The second way to create a heartier voiceis topull the larynx down. This lengthens the
vocal tract and widens the pharynx. Let’s first look at what happens when we lengthen the vocal
tract. As you may recall, the larynx (the voice box) holds the vocal folds and can move up and
down. When you lower your larynx, you lower the position of your vocal folds, lengthen the
Figure 4: Vowel darkening (Selby Lecture 33, Slide
19)

10. Scrugham,The Physics of Good Public Speaking, p.9
pharynx (the area above the larynx), and subsequently lengthen your vocal tract (Wolfe). The
physics behind lower our voice by lengthening our vocal tract is as follows. Below is the
equation2
for a standing wave in an open-closed pipe3
Frequency=
Velocity of Sound= 354 m/s at 37°C (which is the temperature of the air in our throats)
The average resting vocal tract length for an adult male is 16.9 cm.4
Using this as our length (L),
we can solve for the frequency that the resting larynx would naturally produce.
Frequency= =523.67Hz
Let’s say you drop you’re your larynx down 1 cm so that the total length of your vocal tract is
now 17.9cm, what would happen to the frequency of your voice?
Frequency = =494.4Hz
The frequency of your voice dropped 29.3 Hz from 523 Hz to 494 Hz by lowering the larynx
1cm. Margaret Thatcher was able to lower her voice by 46Hz which means, if we hold all other
factors constant, that through training, she was able to hold her larynx 1.9 cm lower than it was
before training (Dunbar)!
The second thing that lowering the larynx does is that it widens your pharynx. This
lowers your fourth formant frequency which creates richer sound.In a study, it was found that in
the production of vowels, better-than-normal male voices have a fourth formant that is lower
than worse-than-normal male voices. A better-than-normal (BNQ) voice was determined by a
group of linguistics PhD students on qualities such as richness of voice, strength of sound, and
2
To simplify, I eliminated the modes from the equation, so that we can only solve for the fundamental frequency
of the system. I understand that n=1,3,5,… (only odd modes present in this system).
3
The human vocal tract is an open-closed pipe. The vocal folds start the closed open of the system and the moutt
is the open side.
4
Goldstein, U.G. (1980) An articulatory model for the vocal tracts of growing children. Ph.D. dissertation,
Massachusetts Institute of Technology, Cambridge, MA.

11. Scrugham,The Physics of Good Public Speaking, p.10
resonance of the voice (Bele 570).To be an effective speaker, we should strive to lower our
fourth formant.
To achieve a lower fourth formant frequency, the pharynx has to be widened because it
naturally creates many high harmonics when vibrating with a small opening. When an average
male talks, the pharynx’s fourth formant resonates at 3,500 Hz (Bele 574). When we widen the
pharynx, longer wave lengths have the ability to form in that area, thus decreasing the frequency
and lowering the fourth formant. To support this claim, let’s look at the equation that drives this
assumption: velocity is proportional to frequency times wavelength, v = ƒ λ. When we widen our
pharynx, the wavelength (λ) increases. Since we aren’t changing the speed of our breath (v), in
order for the equation to stay balanced, the frequency (ƒ) must decrease proportionally to
wavelength. By widening the pharynx, we are able to drop the frequency of the fourth formant
by on average 200Hz (579), which contributes to darker and richer sounds, much like how vowel
darkening lowers the first formant frequency.
In the study though, the better voiceshad naturally wider pharynxes, but you can
artificially widen the pharynx by lowering your larynx.To widen your pharynx, you need to
achieve the same motion as if you were just about to swallow. When you are about to swallow,
you lower your larynx, which pulls down of the pharynx and widens it to let food down the
throat. Once you achieve the same action of swallowing, hold the larynx down but don’t
swallow. Now, produce sound with this set up and your fourth formant frequency will be lower
and your voice will sound richer.
Lastly, you can make your vocal
chords thicker to create a heartier voice.
Figure5: Thick versus thin vocal chords in first 3 phases of vibration
cycle (Rossing 387)

12. Scrugham,The Physics of Good Public Speaking, p.11
Let’s look at how vocal folds interact with air passing through your throat first. Looking at the
chart below, the folds on the left are the thick folds and the folds onthe right are thin folds. The
chart depicts the first 3 steps in a cycle of the folds flipping up and down when producing sound.
Notice how the thick vocal folds close completely for longer than for thin vocal folds. Because
the thick folds stay closed for longer than they are open during the cycle, the sound pressure
created is non-sinusoidal5
, and thus produces a richer timbre (Rossing 384-386).
To achieve thick vocal folds, flex the folds so that the muscles contract and bulge (similar
to how your muscles flare up with flexing during lifting heavy objects). You will know that you
your vocal chords are thick when you feel significant vibration in the chest register. This is
called your ―chest voice.‖
A Louder Voice
By projecting your voice, your audience will be able to more easily hear your message. If
an audience can hear and interpret the words of your message, you can be a more successful
speaker. To get a louder voice, you can use belly breathing and use a voice with strong high
harmonics.
Research has been conducted on the positives of speaking louder. Jean Krause wanted to
understand how a person can communicate as clearly as possible to people who are hearing
impaired. She analyzed how the volume of read statements affects listener comprehension. Two
groups of participants were set up: a reader and an audience member who washearing impaired.
The readers were instructed to read ten sentences. The team then normalized the loudness of the
5
Sinusoidal sound is a pure sound that comes from a sine wave. It has one tone with no other harmonics present.
On the contrary, when air is passed across the thick vocal folds, the resulting pressure wave is a non-sinusoidal.
High harmonics then capture the “roughness” that a non-sinusoidal wave has (such as a square wave or saw-
toothed wave).

13. Scrugham,The Physics of Good Public Speaking, p.12
sentences of all of the readers and created a louder and softer version of the statement which was
15 dB apart. An audience memberthen listened to the recording and wrote down what they heard.
Krause found that the audience understood 53% of the words in the loud speech whereas only
43% of the words in conversational speech were understood (Krause 2172). While the hearing
impaired may benefit more from louder speaking, the implication for regular speech is that, in
general, it’s easier better understand someone when you can hear all the words that they are
saying.
First, we can speak louder by speaking in a pitch with strong frequencies which our ears
are most sensitive to. The loudness perceived by the audience varies acrossfrequencies. The
graph on the right shows that the
sensitivity of our hearing is poorest for
very low and very high frequency sound
(think about how hard it is to hear a dog
whistle). One line contour represents equal
loudness and frequency as perceived by
the human ear. Let’s use the bottom
contour (the solid line above the dotted
line) as an example. On the far left, the
contour line lies at a frequency of 50 Hz andloudness of 80 dBwhich creates a sound as sensitive
as 5000 Hz and loudness of 10dB which is the far right of the same contour line; a speaker can
just as effectively yell (80 dB) at 50 Hz as barely whispering (10 dB) at 5000 Hz(Rossing 108).
The volume that you choose to speak at is influenced by the frequency of your voice.
Choosing frequencies where our hearing is the most sensitive—1000 to 7000 Hz—will give the
Figure 6: Frequency and intensity of equal sensitivity sounds (Selby
Lecture 11, Slide 3)

14. Scrugham,The Physics of Good Public Speaking, p.13
speaker the greatest ability to produce a sound that has the most sensitivity to the audience’s ears
(Wolfe).
Although our ears are most sensitive at these ranges, humans cannot produce sound with
its fundamental frequency as high as 5000 Hz. Therefore, we must make sound with high
frequency 3rd
and 4th
formants to carry the sound far. We can produce high 3rd
and 4th
formants
by influencing the rate of glottal closure. When the V-shaped vocal folds shake faster, we can
produce higherharmonics that resonant in the vocal tract (Pinczower 447).
To increase the rate of your glottal closure, you can increase the tension of the vocal folds
so that when air goes by them, the speed at which they vibrate increases.When we increase the
tension, we increase the velocity that the glottal closure vibrates at as displayed in the following
equation:
V=
T = tension
= mass per unit length
Second, we can maximize the volume of our lungs to create louder sound.At normal
breathing, the sub glottal pressure6
is 100 N/m2
, yet we have the ability to fill our lungs to exert
up to 10,000 N/m2
in pressure when the glottis is closed. There is a direct relation between sub
glottal pressure and the maximum loudness you can produce with that pressure, so the more
volume in our lungs, the more pressure we can exert on the vocal folds and the louder we can
project our voice (Rossing 381).
6
The pressure that our lungs exert on the glottal area (the area below our vocal folds) is called the sub glottal
pressure.

15. Scrugham,The Physics of Good Public Speaking, p.14
So what techniques are there to get more air in the
lungs?Many singers use a technique called belly
breathing. They achieve higher lung volume through
belly breathing by lowering the diaphragm and pulling out
the walls of their abdomen as shown in Figure 7.
This creates a larger lung cavity to pull in air to
the lungs (Sunderg 284). Effective speakers have adapted the signer’s techniques of belly
breathing to ensure that they can project their voice during oration
(Marshall).
Belly breathing is preferable over chest breathing because it
allows more air to enter the lungs. In chest breathing, we elevate our
ribs to create more room in our lungs to breathe in. This is called
shallow breathing because we only use the top part of our lungs to
inhale and exhale the air that we need.
Figure 8 shows the potential volume that you can add to your
lungs by using belly breathing. The tidal volume is the volume during normal breathing and falls
between 2,400 and 2,800 cm3
; this is the volumefluctuation of our lungswhen we chest breath.
The inspiratory reserve volume is the volume we can fit in to our lungs (Rossing 382). With
belly breathing, we can maximize our use of the inspiratory reserve volume which gives us on
average 3000 cm3
more volume, nearly doubling the maximum volume that we can speak at
from chest breathing(Sundberg 290).
Figure 7: A human cross-section of belly breathing
(Rossing 380)
Figure 8: Lung volume modes (Rossing 382).

16. Scrugham,The Physics of Good Public Speaking, p.15
Conclusion7
We are able to be smarter about how we speak by understanding the underlying physics
of our voices. Because we know what makes sound, we can modify the mechanisms in a positive
way to create a voice that is both rich and loud, which is a voice that is more effective in
persuading individuals and getting them to trust you. Recall that you can achieve a heartier voice
through vowel darkening, pulling your larynx down, and by thickening your vocal chords; you
can project you voice better by tightening your vocal folds and by using belly breathing to
achieve greater lung volume. While I don’t promise that these tactics will lead you to presidency
or influence writers to publish wonderful prose about your speeches, I can ensure you that your
public speaking will greatly improve if you adapt and practice some of the tactics outlined.
7
In addition to my concluding remarks, I would also like to make it apparent of conflicting physics in the richer
voice and louder voice production. I know that a higher frequency produces a louder sound and that getting a
richer voice means making a lower sound. How can we get a higher and lower frequency at the same time? We
can’t; it’s a trade-off between the two. One work around is to use the tactics of gaining a heartier voice and use a
microphone to help you project your voice.

17. WORKS CITED
Atkinsons, Max. Our Masters' Voices: Language and Body Language of Politics, Routledge,
1984. Print.
Bele, I V. ―The speakerʼs formant.‖Journal of Voice 20.4 (2006) : 555–578.
Borkowska, B., and B. Pawlowski. 2011 ―Female voice frequency in the context of dominance
and attractiveness perception.‖ Anim. Behav. 82 (2011), 55–59.
Campbell, A., P.Converse,W. Miller,and D. Stokes. The American voter. Chicago, IL: University
of Chicago Press.1960. Print.
Clive, James. The Observer (London).9 February 1975, 119–120.
Dunbar, Polly. "How Laurence Olivier gave Margaret Thatcher the voice that went down in
history". Daily Mail (London). (30 October 2011). Web.Retrieved May 8,
2012.<http://www.dailymail.co.uk/news/article-2055214/How-Laurence-Olivier-gave-
Margaret-Thatcher-voice-went-history.html>
Fillebrown, Thomas. Resonance in Singing and Speaking. Boston: Oliver Ditson, 1911.
Ebook.<http://www.gutenberg.org/files/19138/19138-h/19138-h.htm>
Feinberg, D. R., Little, A. C., Burt, D. M. andPerrett, D L. ―Manipulations of fundamental and
formant frequencies influence the attractiveness of human male voices.‖Anim. Behav. 69
(2005): 561–568. Print.
Gregory, S. ―Sounds of power and deference: acoustic analysis of macro social constraints on
micro interaction.‖Sociol.Perspect. 37 (1994): 497–526. Print.
Klofstad, Casey A., Rindy C. Anderson, and Susan Peters.―Sounds like a winner: voice pitch
influences perception of leadership capacity in both men and women.‖Proceedings of the
Royal Society.B (2012).Print.
Krause, Jean C. and Louis D.Braida―Investigating alternative forms of clear speech: the effects
of speaking rate and speaking mode on intelligibility.‖J AcoustSocAm.5.1 (2002): 2165–
2172.Print.
Lewis, D. and J. Tiffin.―A psychophysical study of individual differences in speaking
ability.‖Arch. Speech 1(1934): 43-60.Print.
Lundh, Lars-Gunnar, et al. ―Social Anxiety is Associated with a Negatively Distorted Perception
of One's Own Voice. Cognitive Behaviour Therapy 31.1 (2002):25-30. Print.

18. Marshal, Lisa B. Communications consultant. http://publicspeaker.quickanddirtytips.com/How-
To-Breathe.aspx
Pinczower, R. and J. Oates.―Vocal Projection in Actors: The Long-Term Average Spectral
Features That Distinguish Comfortable Acting Voice From Voicing With Maximal
Projection in Male Actors.‖J. Voice 19 (2005): 440-453. Print.
Rossing, Thomas, Richard Moore, and Paul Wheeler.The Science of Sound.3rd edition. New
York: Addison Wesley, 2002.
Seymour, Harry N. ―Attributes of loudness, pitch and rate among male children.‖Journal of
Communication Disorders. 8. 2 (1975): 97–104. Print.
Selby, Kathy. Physics of Musical Sound (PHYS 1204/ MUSIC 1466).Cornell University. Ithaca.
2012 Spring Semester. Lecture.
Sundberg,J. , R. Leanderson, C. von Euler, and E. Knutsson. ―Influence of body posture and
lung volume on subglottal pressure control during singing.‖Journal of Voice,5. 4 (1991):
283-291.Print.
Wolfe, Joe, MaevaGarnier, and John Smith. "Voice Acoustics: An Introduction." To the Science
of Speech and Singing.University of New South Wales, 2009.Web. 13 Apr. 2012.
<http://www.phys.unsw.edu.au/jw/voice.html>.
Weinberg, Ashley.The Psychology of Politicians. Cambridge University Press, 2012. Print.