Physics 1251 The Science and Technology of Musical Sound

1
Physics 1251The Science and Technology of
Musical Sound

• Session 43 MWF
• Summary and Review

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Physics 1251 Session 43 MWF Summary and
Review

• What is MP-3 and how does it do its magic?

• MP-3 is a three (3) layer compression algorithm
  that was adopted as a standard by the Motion
  Picture Experts Group (MPEG).
• Audio data is transformed to a frequency
  spectrum
• A masking filter is applied
• The residual data is encoded in a more efficient
  code.

3
Physics 1251 Session 43 MWF Summary and
Review

• MIDI is a control protocol that can make the
  sound card in our PC play music.
• http//www.rememberjosie.org/carols
• MIDI coded Christmas Carols

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Physics 1251 Session 43 MWF Summary and
Review

• 1' Lecture
• This course contains approximately 275 essential
  facts and concepts.
• There are 31 significant equations.
• The sensation of sound depends on
  psychoacoustical phenomena as well as the
  frequency spectrum or the vibration recipe.
• Musical sound is characterized by a harmonic
  series.
• Strings, pipes, the voice and percussion, all
  achieve sound according to their individual modes
  of oscillation.

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Physics 1251 Session 43 MWF Summary and
Review

• Computer based music exploits novel tonal
  possibilities.
• www.research.ibm.com/mathsci/cmc/do_lamentations1.
  htm
• Lamentation for Jerusalem
• For solo Saxophone and DMIX
• By Daniel V. Oppenheim

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Physics 1251 Session 43 MWF Summary and
Review

• What one hears can be objectively characterized
  by a time-dependent Vibration Recipe or the
  Frequency Spectrum (Fourier Spectrum)

Log(Amplitude) dB
Frequency Hz
7
Physics 1251 Session 43 MWF Summary and
Review

• The acoustic properties of the room affect the
  time dependence of the vibration recipe.
• The reverberation time is an important property
  of a room.

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Physics 1251 Unit 2 Session 19 Reverberation

• Intensity of Sound in a Room

Io
I Io ? 10 6 t / TR
t ? TR
1/10 Io
Pressure Amplitude
t ? TR
1/100 Io
Time (ms)
http//hybrid.colorado.edu/phys1240/sounds.html
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Physics 1251 Unit 2 Session 19 Reverberation

• 80/20The Sabine Equation
• I Io ? 10 6 (t/TR)
• TR 0.16 V/Se
• V is the volume of the room.
• Se is the effective surface area of the walls
  S1 , floor S2 and ceiling S3 (in sabin) etc.
• a is the absorptivity of the surface (in table)
• Se a1 S1 a2 S2 a3 S3 a4 S4

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Physics 1251 Session 43 MWF Summary and
Review

• The psychoacoustic response of the human ear is
  frequency dependent.

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Physics 1251 Unit 2 Session 14 Human
Perception Loudness

• Fletcher- Munson Diagram
• Fletcher and Munson (1933) J. Acoust. Soc. Am. 5,
  82-108

130
120
110
100
90
SIL (dB)
80
70
60
50
40
30
20
10
Loudness (phon)
Frequency (Hz)
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Physics 1251 Unit 2 Session 14 Human
Perception Loudness

• The Density
• of Hair Cells (HC)
• varies with distance
• from the stapes.

Fewer HC
More HC
Fewer HC
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Physics 1251 Session 43 MWF Summary and
Review

• The character of sound depends on physical
  acoustical phenomena as well.

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Physics 1251 Unit 2 Session 16 Wave
Properties Propagation

• Intensity is Power per Unit Area
• Why 1/r 2?
• Area 2/3p ? r 2
• I Power/Area
• I2 I1 (A1/A2)
• I2 I1 (r1 / r2) 2

A ?p r 2
r
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Physics 1251 Unit 2 Session 18 Room Acoustics

• When the surface is smooth we have specular
  (mirror-like) reflection.

Reflection
Smooth Surface Roughness ? ?
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Physics 1251 Unit 2 Session 18 Room Acoustics

• Refraction occurs when a wave enters a medium
  that has a different velocity?

Refraction
V1
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Physics 1251 Unit 2 Session 18 Room Acoustics

• What happens when a wave is partially obstructed?

Diffraction
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Physics 1251 Unit 2 Session 18 Room Acoustics
Doppler Shift Moving source
Higher f
Lower f
fobserver fsource v vobserver / v
vsource
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Physics 1251 Unit 2 Session 18 Room Acoustics
Beats f1 f2
In phase
Out of phase
fmean
fbeat
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Physics 1251 Unit 2 Session 18 Room Acoustics
Interference
Constructive
Destructive
Softer
Louder
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Physics 1251 Session 43 MWF Summary and
Review

• But why do Jingle Bells jingle, anyway?

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Physics 1251 Session 43 MWF Summary and
Review

• The Normal Modes of Oscillation determine the
  frequencies present in the radiated sound.

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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• A Standing Wave results from interference of
  counter-reflecting waves.

Fundamental Mode
f1 vstring / ?1 vstring / 2L
Node
Node
Antinode
?1 /4
?1 /4
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Physics 1251 Unit 2 Session 22 Strings
Guitar, Harp, Piano Harpsichord

• 80/20The distance between neighboring nodes
  antinodes is ¼ ?. N-A d ¼ ?

Second Harmonic
f2 vstring / ?2 vstring / L
Node
Node
Node
Antinode
Antinode
?2 /4
?2 /4
?2 /4
?2 /4
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Physics 1251 Unit 3 Session 30 The Timbre
of Wind Instruments

• Comparison of Wind Instruments

f
Pedal Tone
fo (1?)v/4(Lc)
L
f1 v/2L
f1 v/4L
f1 v/2(Lc)
Other Woodwinds
Clarinet
Flute
Brass
c
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Physics 1251 Unit 3 Session 30 The Timbre
of Wind Instruments

• Comparison of Wind Instruments (contd.)

Open Cylinder Np Np fn nf1 f1 v/2L
Stopped Cylinder Ap Np f2n-1
(2n-1)f1 f1 v/4L
Stopped Cone Ap Np fn nf1
f1 v/2(Lc)
Stopped Combination Ap Np
fn nf0 f0 (1?)v/4(Lc)
fo (1?)v/4(Lc)
L
f1 v/2L
f1 v/4L
f1 v/2(Lc)
Other Woodwinds
Clarinet
Flute
Brass
c
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Physics 1251 Unit 3 Session 32 The Singing
Voice

• Anatomy of the Human Voice
• 80/20The vocal folds comprise muscle, lamina
  propria and epithelium.

Cover
Body
Epithelium
Lamina Propria (3 layers)
Thyroarytenoid Muscle
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Physics 1251 Unit 3 Session 32 The Singing
Voice

• Formants and Singing

Harmonics align with Formants
Singers Formant

• Vowel modification shifts formats.
  Alignment of formants with harmonics
  intensifies pitch.
  Dilation of vocal tract causes
  Singers Formant.

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Physics 1251 Unit 3 Session 33 Percussion

• The Modes of Oscillation
  of an (Ideal) Clamped Membrane

Mode (0,1)
f0 1 x0 1 /(p d) ? v(S/ s) x0 1 2.405
Mode (1,1)
Mode (2,1)
f1 1 (x1 1 / x0 1) f0 1 x1 1 / x0 1 1.594
f2 1 (x2 1 / x0 1) f0 1 x2 1 / x0 1 2.136
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Physics 1251 Unit 3 Session 33 Percussion

• The Modes of Oscillation
  of a Clamped Membrane

Mode (0,1) xn m / x0 1 1
(1,1)1.594
(2,1)2.136
(0,2)2.296
(3,1)2.653
(1,2)2.918
(4,1)3.156
(2,2)3.501
(0,3)3.600
(5,1)3.652
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Physics 1251 Unit 3 Session 33 Percussion

• 80/20The timbre of an instruments sounds depends
  on its vibration recipe.

fn n f1
Pitched
Amplitude
f1
2f1
3f1
4f1
fn m xn m f1
Unpitched
Amplitude
f01
Frequency
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Physics 1251 Unit 3 Session 34 Percussion
with Pitch

• 80/20The task of producing pitch in a percussion
  instrument is an exercise in manipulating the
  overtones into a harmonic series.

Frequency
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Physics 1251 Unit 3 Session 34 Percussion
with Pitch

• Bending Modes in Bars

Free Ends

f1 1.133 fo f2 3.125 fo f36.125 fo fo ? h/L2
.224 L
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Physics 1251 Session 43 MWF Summary and
Review

• What is musical sound?

Harmonics are the key.
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Physics 1251 Unit 2 Session 21 Scales and
Strings

• What is a scale?
• Gamut Note G-Clef

?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
Do Re Mi Fa So La Ti Do
Do Re Mi Fa So La Ti Do
C-major
G-major
Guido dArezzo gamma ut?gamut Solfeggio G is
Do in the G-scale
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Physics 1251 Unit 2 Session 20 Musical Scales

• Musical Notation

?
?
?
?
?
?
?
?
?
?
?
D5
A5
C6
G4
G5
F4
C5
F5
?
B4
B5
E4
?
E5
D4
A4
?
?
?
?
?
?
?
?
?
?
C4
F2
B3
E2
A4
D2
G2
C2
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Physics 1251 Unit 2 Session 20 Musical Scales

• Why does this work?

Harmonics! The harmonics must be in tune
to avoid beats.
3 rd
5 th
Octave
Unison
Frequency
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Physics 1251 Session 43 MWF Summary and
Review

• What is special about the harmonics used in
  standard music?

Microtonalists say nothing!
http//www.io.com/hmiller/music/warped-canon.html
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Physics 1251 Unit 4 Session 41 Computer
Music

• Summary
• Read the vibration recipe.
• The vibration recipe happens because of the
  normal modes of the source.
• The normal modes of oscillation result from
  standing waves in the instrument.
• Sound is a longitudinal displacement/pressure
  wave that can be reflected, refracted,
  diffracted, interfered with, beat and Doppler
  shifted.

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Physics 1251 Unit 4 Session 41 Computer
Music

• Review Quiz
• Extra credit 1-2 points added to test average.
• Keep test and pick up key.
• Evaluate performance and develop review strategy
• Good luck!
• Final Exam Friday December 14, 2001
• 800 1000 am Room 102