Physics 1251 the science and technology of musical sound
Download
1 / 40

Physics 1251 - PowerPoint PPT Presentation


  • 317 Views
  • Updated On :

Physics 1251 The Science and Technology of Musical Sound Session 43 MWF Summary and Review Physics 1251 Session 43 MWF Summary and Review What is MP-3 and how does it do its “magic?”

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Physics 1251' - Jims


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Physics 1251 the science and technology of musical sound l.jpg

Physics 1251The Science and Technology of Musical Sound

Session 43 MWF

Summary and Review


Physics 1251 session 43 mwf summary and review l.jpg
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.


Physics 1251 session 43 mwf summary and review3 l.jpg
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


Physics 1251 session 43 mwf summary and review4 l.jpg
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.


Physics 1251 session 43 mwf summary and review5 l.jpg
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


Physics 1251 session 43 mwf summary and review6 l.jpg
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


Physics 1251 session 43 mwf summary and review7 l.jpg
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.


Physics 1251 unit 2 session 19 reverberation l.jpg
Physics 1251 Unit 2 Session 19 Reverberation

Intensity of Sound in a Room:

~ Io

I = Io‧ 10 –6 t / TR

t = ⅙ TR

~ 1/10 Io

Pressure

Amplitude

t = ⅓ TR

~ 1/100 Io

Time (ms)

http://hybrid.colorado.edu/~phys1240/sounds.html


Physics 1251 unit 2 session 19 reverberation9 l.jpg
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.

  • α is the absorptivity of the surface (in table)

    Se = α1 S1 + α2 S2 + α3 S3 + α4 S4 +…


Physics 1251 session 43 mwf summary and review10 l.jpg
Physics 1251 Session 43 MWF Summary and Review

The psychoacoustic response of the human ear is frequency dependent.


Physics 1251 unit 2 session 14 human perception loudness l.jpg
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)


Physics 1251 unit 2 session 14 human perception loudness12 l.jpg
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


Physics 1251 session 43 mwf summary and review13 l.jpg
Physics 1251 Session 43 MWF Summary and Review

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


Physics 1251 unit 2 session 16 wave properties propagation l.jpg
Physics 1251 Unit 2 Session 16 Wave Properties: Propagation

Intensity is Power per Unit Area

Why 1/r 2?

Area = 2/3π ‧ r 2

I = Power/Area

I2 = I1 (A1/A2)

I2 = I1 (r1 / r2) 2

A = ⅔π r 2

r


Physics 1251 unit 2 session 18 room acoustics l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

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

Reflection

Smooth Surface

Roughness ≲ λ


Physics 1251 unit 2 session 18 room acoustics16 l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

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

Refraction

V1 < V2


Physics 1251 unit 2 session 18 room acoustics17 l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

Diffraction

What happens when a wave “is partially obstructed?


Physics 1251 unit 2 session 18 room acoustics18 l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

Doppler Shift: Moving source

Lower f

Higher f

fobserver = fsource [v + vobserver] / [v – vsource]


Physics 1251 unit 2 session 18 room acoustics19 l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

Beats

f1

f2

In phase

Out of phase

fmean

fbeat


Physics 1251 unit 2 session 18 room acoustics20 l.jpg
Physics 1251 Unit 2 Session 18 Room Acoustics Propagation

Interference

Constructive

Destructive

Softer

Louder


Physics 1251 session 43 mwf summary and review21 l.jpg

Or pipers pipe? Propagation

Or Drummers drum

Or Fiddlers fiddle, too?

Physics 1251 Session 43 MWF Summary and Review

But why do Jingle Bells jingle, anyway?


Physics 1251 session 43 mwf summary and review22 l.jpg
Physics 1251 Session 43 MWF PropagationSummary and Review

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


Physics 1251 unit 2 session 22 strings guitar harp piano harpsichord l.jpg

L = Propagation2/₄ λ1

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 / λ1 = vstring / 2L

Node

Node

Antinode

λ1 /4

λ1 /4


Physics 1251 unit 2 session 22 strings guitar harp piano harpsichord24 l.jpg

L = Propagation4/₄ λ2

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

80/20The distance between neighboring nodes & antinodes is ¼ λ. [ “N-A d = ¼ λ” ]

Second Harmonic

f2 = vstring / λ2 = vstring / L

Node

Node

Node

Antinode

Antinode

λ2 /4

λ2 /4

λ2 /4

λ2 /4


Physics 1251 unit 3 session 30 the timbre of wind instruments l.jpg

6f PropagationO

5f1

6f1

5f1

5fO

5f1

4f1

4fO

4f1

3f1

3fO

3f1

3f1

2f1

2fO

2f1

fO

f1

f1

f1

f1

Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments

Comparison of Wind Instruments

f

Pedal Tone

fo =

(1+ξ)v/4(L+c)

L

f1 = v/2L

f1 = v/4L

f1 = v/2(L+c)

Other Woodwinds

Flute

Clarinet

Brass

c


Physics 1251 unit 3 session 30 the timbre of wind instruments26 l.jpg
Physics 1251 Unit 3 Session 30 PropagationThe Timbre of Wind Instruments

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(L+c)

Stopped Combination Ap – Np fn = nf0f0= (1+ξ)v/4(L+c)

Comparison of Wind Instruments (cont’d.)

fo =

(1+ξ)v/4(L+c)

L

f1 = v/2L

f1 = v/4L

f1 = v/2(L+c)

Other Woodwinds

Flute

Clarinet

Brass

c


Physics 1251 unit 3 session 32 the singing voice l.jpg
Physics 1251 Unit 3 Session 32 PropagationThe 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


Physics 1251 unit 3 session 32 the singing voice28 l.jpg
Physics 1251 Unit 3 Session 32 PropagationThe Singing Voice

Harmonics align with Formants

Singers’ Formant

Formants and Singing

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


Physics 1251 unit 3 session 33 percussion l.jpg

Surface density Propagationσ

Surface Tension S

Physics 1251 Unit 3 Session 33 Percussion

The Modes of Oscillation of an (Ideal) Clamped Membrane

Mode: (0,1)

f0 1 = x0 1 /(π d) ‧ √(S/ σ)

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


Physics 1251 unit 3 session 33 percussion30 l.jpg
Physics 1251 Unit 3 Session 33 PropagationPercussion

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


Physics 1251 unit 3 session 33 percussion31 l.jpg
Physics 1251 Unit 3 Session 33 PropagationPercussion

80/20The timbre of an instrument’s sounds depends on its vibration recipe.

fn = n f1

Pitched

Amplitude

f1

2f1

3f1

4f1

fn m = xn m f1

Unpitched

Amplitude

f01

Frequency


Physics 1251 unit 3 session 34 percussion with pitch l.jpg

f Propagationn = n f1

Pitched

Amplitude

f1

2f1

3f1

4f1

fn m = xn m f10

Unpitched

Amplitude

f01

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


Physics 1251 unit 3 session 34 percussion with pitch33 l.jpg
Physics 1251 Unit 3 Session 34 PropagationPercussion with Pitch

Free Ends

Bending Modes in Bars:

f1= 1.133 fo

f2= 3.125 fo

f3=6.125 fo

fo∝ h/L2

.224 L


Physics 1251 session 43 mwf summary and review34 l.jpg
Physics 1251 Session 43 MWF PropagationSummary and Review

What is musical sound?

Harmonics are the key.


Physics 1251 unit 2 session 21 scales and strings l.jpg

Propagation

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 d’Arezzo: “gamma ut→gamut” • Solfeggio

G is “Do” in the G-scale


Physics 1251 unit 2 session 20 musical scales l.jpg

Propagation

440 Hz

A4

G3

C3

F3

B2

E3

A2

D3

Physics 1251 Unit 2 Session 20 Musical Scales

Musical Notation

G4

D5

A5

C6

G5

F4

C5

F5

B4

B5

E4

D4

A4

E5

C4

F2

B3

E2

A4

D2

G2

C2


Physics 1251 unit 2 session 20 musical scales37 l.jpg
Physics 1251 Unit 2 Session 20 Musical Scales Propagation

Harmonics! The harmonics must be “in tune” to avoid beats.

Why does this work?

3 rd

5 th

Octave

Unison

Frequency


Physics 1251 session 43 mwf summary and review38 l.jpg
Physics 1251 Session 43 MWF PropagationSummary and Review

What is special about the harmonics used in standard music?

Microtonalists say “nothing!”

http://www.io.com/~hmiller/music/warped-canon.html


Physics 1251 unit 4 session 41 computer music l.jpg
Physics 1251 Unit 4 Session 41 PropagationComputer 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.


Physics 1251 unit 4 session 41 computer music40 l.jpg
Physics 1251 Unit 4 Session 41 PropagationComputer 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

    8:00 – 10:00 am Room 102


ad