physics 1251 the science and technology of musical sound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 3Unit 3

Session 31 MWFSession 31 MWF

The Fundamentals of The Fundamentals of the Human Voice the Human Voice

Unit 3Unit 3

Session 31 MWFSession 31 MWF

The Fundamentals of The Fundamentals of the Human Voice the Human Voice

Physics 1251Physics 1251 Unit 3 Session 31Unit 3 Session 31 The Fundamentals of the Human The Fundamentals of the Human

VoiceVoice

What is the frequency of a palm pipe What is the frequency of a palm pipe at 20 C that is 500 mm long and at 20 C that is 500 mm long and has an internal diameter of 35 has an internal diameter of 35 mm? What are the first three mm? What are the first three audible harmonics?audible harmonics?A palm pipe is a stopped cylinder.A palm pipe is a stopped cylinder.

Therefore f Therefore f 11= v/4L= v/4L′; ′; L′ = 0.500 m+ 0.3 (0.035 m) = 0.5105L′ = 0.500 m+ 0.3 (0.035 m) = 0.5105

f f 11= 343/4(0.511) =85.75/0.511 =168 Hz. [E = 343/4(0.511) =85.75/0.511 =168 Hz. [E 33 +33 +33¢]¢]

ff33 = 3f = 3f11 = 3 (168) = 504 Hz. [B = 3 (168) = 504 Hz. [B44 + 35 + 35 ¢¢]]

ff55 = 5f = 5f11 = 5 (168) = 840 Hz. [G = 5 (168) = 840 Hz. [G5 5 ♯ ♯ + 19 + 19 ¢¢]]


VoiceVoice

11′ Lecture:′ Lecture:

• The vocal folds, located in the larynx, The vocal folds, located in the larynx, produce vibrations in the vocal tract.produce vibrations in the vocal tract.

• The vocal tract is a stopped air column The vocal tract is a stopped air column approximately 17 cm long. It resonates approximately 17 cm long. It resonates at a fundamental frequency of about 500 at a fundamental frequency of about 500 Hz.Hz.

• The shape of the vocal tract provides an The shape of the vocal tract provides an acoustic filter of the harmonics produced acoustic filter of the harmonics produced by the vocal folds.by the vocal folds.


VoiceVoice

Anatomy of the Human VoiceAnatomy of the Human Voice80/2080/20The vocal tract is the instrument The vocal tract is the instrument

of the of the human voice.human voice.

Vocal Tract:Vocal Tract:• Lungs—source of Lungs—source of airair

LungsLungs

• Trachea—wind pipeTrachea—wind pipe• Larynx—voice boxLarynx—voice box• Pharynx—mouth and Pharynx—mouth and nosenose

LarynLarynxx TracheTrache

aa

PharyPharynxnx


VoiceVoice

Anatomy of the Human VoiceAnatomy of the Human Voice80/2080/20The sound of the human voice originates in The sound of the human voice originates in

the larynx.the larynx.

LarynLarynxx

LarynLarynxx

OpenOpen


VoiceVoice

Anatomy of the Human VoiceAnatomy of the Human Voice80/2080/20The larynx (or voice box) contains the The larynx (or voice box) contains the

vocal folds.vocal folds.

LarynxLarynx

ClosedClosed

Vocal Vocal FoldsFolds


VoiceVoice

Anatomy of the Human VoiceAnatomy of the Human Voice80/2080/20The vocal folds rapidly open and close, The vocal folds rapidly open and close,

introducing pulsations of air into the vocal introducing pulsations of air into the vocal tract.tract.


Lower Vocal Lower Vocal TractTract


VoiceVoice

Video of Video of

LaryngoscopyLaryngoscopy


VoiceVoice

The Vocal Folds--FunctionThe Vocal Folds--Function80/2080/20The vocal folds are controlled by muscle The vocal folds are controlled by muscle

and actuated by air moving between them, and actuated by air moving between them, closing due to the Bernoulli Effect, closing due to the Bernoulli Effect, opening by tension.opening by tension.


PhonationPhonation

Air Air FlowFlow

When flow When flow is is interrupted interrupted folds open.folds open.


VoiceVoice

The Vocal FoldsThe Vocal Folds80/2080/20The pressure waveform produced by the The pressure waveform produced by the

action of the vocal folds is an action of the vocal folds is an asymmetrical sawtooth, rich in harmonics.asymmetrical sawtooth, rich in harmonics.

80/2080/20The fundamental frequency of the voice is The fundamental frequency of the voice is determined by the properties of the vocal determined by the properties of the vocal folds, not the vocal tract.folds, not the vocal tract.Vocal Folds snap Vocal Folds snap openopen

are pulled shut by are pulled shut by air flowair floware pulled shut by are pulled shut by air flowair floware pulled shut by are pulled shut by air flowair floware pulled shut by are pulled shut by air flowair floware pulled shut by are pulled shut by air flowair flow


VoiceVoice

Resonances of Vocal TractResonances of Vocal Tract

ff11 = v/4L = 353/(4 = v/4L = 353/(4 ‧ 0.17) = ‧ 0.17) = 519 Hz 519 Hz ff3 3 = 3f = 3f1 1 , f, f5 5 = 5f= 5f11 … …

LL≈ 17 ≈ 17 cmcm

80/2080/20The Vocal Tract is a “lossy” stopped pipe The Vocal Tract is a “lossy” stopped pipe ~17 cm long with a fundamental frequency of ~17 cm long with a fundamental frequency of ~500 Hz. ~500 Hz.

v =343 + 0.6(37-20) v =343 + 0.6(37-20) =353 m/s=353 m/s~500 ~500

HzHz ~1500 ~1500 HzHz ~2500 ~2500

HzHz


VoiceVoice

Formants of Vocal TractFormants of Vocal Tract

ff11 = v/4L = 353/(4 = v/4L = 353/(4 ‧ 0.17) = ‧ 0.17) = 519 Hz 519 Hz ff3 3 = 3f = 3f1 1 , f, f5 5 = 5f= 5f11 … …

LL≈ 17 ≈ 17 cmcm

80/2080/20The Vocal Tract filters the spectrum The Vocal Tract filters the spectrum generated by the vocal folds; the frequency generated by the vocal folds; the frequency filter is called the filter is called the FormantFormant..

Amplitude

Amplitude

FrequencyFrequency

FormantFormant


VoiceVoice

SpeechSpeech• 80/2080/20The individual units of speech are The individual units of speech are

called called phonemes.phonemes.• The classes of (English) phonemes are:The classes of (English) phonemes are:

• Unvoiced PlosivesUnvoiced Plosives‒ p, t, soft k (c, q, x) ‒ p, t, soft k (c, q, x) • Voiced Plosives‒ b, d, gVoiced Plosives‒ b, d, g• Fricatives‒ f, v, thFricatives‒ f, v, th• Sibilants‒ s (c) , z, sh, zh, jSibilants‒ s (c) , z, sh, zh, j• Liquids‒ l, rLiquids‒ l, r• Nasals‒ m, n, ngNasals‒ m, n, ng• Semi-vowelsSemi-vowels‒ w, y‒ w, y• VowelsVowels‒ a, e, i, o, u‒ a, e, i, o, u


VoiceVoice

Spectrogram of Human SpeechSpectrogram of Human Speech


VoiceVoice

80/2080/20The shape of the Vocal Tract The shape of the Vocal Tract determines the frequency of the determines the frequency of the Formants.Formants.

““ah”ah”

““eh”eh”

““oh”oh”

““oo”oo”


VoiceVoice

Summary:Summary:• The vocal folds, located in the larynx, The vocal folds, located in the larynx,

produce vibrations in the vocal tract.produce vibrations in the vocal tract.

• The vocal tract is a stopped air column The vocal tract is a stopped air column approximately 17 cm long, that approximately 17 cm long, that resonates at ~500, 1500 and 2500 resonates at ~500, 1500 and 2500 Hz.Hz.

• The shape of the vocal tract provides The shape of the vocal tract provides an acoustic filter, called the formant, an acoustic filter, called the formant, that modifies the amplitude of the that modifies the amplitude of the harmonics produced by the vocal folds.harmonics produced by the vocal folds.

physics 1251 the science and technology of musical sound

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