Sound of Music How It Works Session 2 Resonance: Building Musical Sounds

OLLI at Illinois Spring 2020 Ocarina (Helmholtz Resonator) Lena Leclaire 2012 Legend of Zelda Medley D. H. Tracy Course Outline

1. Building Blocks: Some basic concepts 2. Resonance: Building Musical Sounds 3. Hearing and the Ear 4. Musical Scales 5. Musical Instruments 6. Singing and Musical Notation 7. Harmony and Dissonance; Chords 8. Combining the Elements of Music

2/4/2020 Sound of Music 2 4 Visual Analyzer Demo

Whistle

0 100 200 300 400 500 600 700 800 900 1000 Hz 2/4/2020 Sound of Music 2 5 Sound As Compression Waves

Frequency f

Wavelength λ

Speed of Sound vS (velocity)

2/4/2020 Sound of Music 2 6 Simple Harmonic Oscillator

Imgur.com

James Dodd: You-Tube 2/4/2020 Sound of Music 2 7 Tuning Fork

Slo-Motion Video

Michigan Tech YouTube 9/11/2014

2/4/2020 Sound of Music 2 8 Resonators can be excited by well-timed nudges

2/4/2020 Sound of Music 2 9 How can we make Sine Waves?

• Simple Harmonic Oscillators do it

Circular Projection Simple Mass on e.g. Tuning e.g. Rotational Pendulum Spring Fork Crank Mechanism

• Electronics can also do it

2/4/2020 Sound of Music 2 10 Helmholtz Resonators

Ear hole

Herman von Helmholtz 1821-1894

Port

2/4/2020 Sound of Music 2 11 Helmholtz Resonators

Air in neck

Air at Inside Air atmospheric compressed pressure

Microphone

2/4/2020 Sound of Music 2 13 Helmholtz Resonator

Speaker

147 Hz Resonance Helmholtz Resonator

Microphone

Electronic Sine Wave Generator

2/4/2020 Sound of Music 2 14 Ever experience a Whump-Whump in your car when a rear window is cracked open?

2/4/2020 Sound of Music 2 15 Ever experience a Whump-Whump in your car when a rear window is cracked open?

2/4/2020 Sound of Music 2 16 Resonators Using Strings and Pipes

2/4/2020 Sound of Music 2 17 Resonators Using Strings and Pipes

Anne Sullivan playing Siciliana (Respighi)

2/4/2020 Sound of Music 2 18 Resonators Using Strings and Pipes

Prelude in C Major (Bach): Brian of the LDS [ Liahona.net]

2/4/2020 Sound of Music 2 19 Resonators Using Strings and Pipes

2/4/2020 Sound of Music 2 20 2 Traveling Waves Combine… To Form a Standing Wave

Node Anti-node

D Russell Penn State 2/4/2020 Sound of Music 2 24 Standing Waves in Air

L R

2/4/2020 Sound of Music 2 26 Q: How Do We Make Standing Waves? A: Reflections at a Boundary

“Hard” “Soft”

Anti- Node

Node

Reflection is upside down! Reflection is not inverted!

D Russell Penn State 2/4/2020 Sound of Music 2 28 Q: How Do We Make Standing Waves? A: Reflections at a Boundary

Displacement “Hard” “Soft”

Anti- Node

Node

Reflection is upside down! Reflection is not inverted!

D Russell Penn State 2/4/2020 Sound of Music 2 29 Q: How Do We Make Standing Waves? A: Reflections at a Boundary

Displacement “Hard” “Soft”

Anti- Node

Node

Reflection is upside down! Reflection is not inverted!

D Russell Penn State 2/4/2020 Sound of Music 2 30 Partial Reflection

D Russell Penn State 2/4/2020 Sound of Music 2 32 The Monochord

Length

2/4/2020 Sound of Music 2 34 Mersenne’s Laws of Strings L

1588-1648

T 

Frequency f depends on Length L, Tension Force T, and String Mass/length :

• f0  1 / L inversely proportional to length

• f0  T proportional to square root of tension

• f0  1 /  inversely proportional to square root of mass per unit length (‘fatness’)

2/4/2020 Sound of Music 2 35 Possible Pure String Modes

f Fundamental 2 Nodes ; 1 Antinode 2f 3 Nodes ; 2 Antinodes

4 Nodes ; 3 Antinodes 3f Harmonics

5 Nodes ; 4 Antinodes 4f

6 Nodes ; 5 Antinodes 5f

IVSR

2/4/2020 Sound of Music 2 38 Try to Launch the Fundamental Mode:

Sine shape But we actually pluck a triangle …

We could carefully pull the string into a half-sine wave and then suddenly let it go….

2/4/2020 Sound of Music 2 39 Try to Launch the Fundamental Mode:

Sine shape But we actually pluck a triangle …

We could carefully pull the string into a half-sine wave and then suddenly let it go….

2/4/2020 Sound of Music 2 40 Try to Launch the Fundamental Mode:

Plucked String in Slo-Mo

Dan Russell, Kettering/Penn State (2011)

2/4/2020 Sound of Music 2 41 The First Electric Monochord?

Tristan Andreas (YouTube 2012)

Yuri Landman (YouTube 2011)

2/4/2020 Sound of Music 2 42 The Monochord

8 foot Electric Monochord Demo

2/4/2020 Sound of Music 2 43 Organ Pipe – One Closed End

Air Displacement Pressure

Fundamental Mode 퐿 = 휆Τ4

Third Harmonic 퐿 = 3Τ4 휆

Fifth Harmonic 퐿 = 5Τ4 휆

2/4/2020 Sound of Music 2 44 Illustration of Wave Reflection at Open End of Pipe

(Animation) 2/4/2020 Sound of Music 2 45 Open End of Pipe

Open Particle Organ Displacement  Pipe: 9th Harmonic

Pressure 

2/4/2020 Sound of Music 2 Dan Russell Penn State 46 Resonant Cavities: Augmenting Sounds

Helmholtz Irregular Pipes Resonators Resonators P Port 휆1 = 4퐿 1 Neck 3 Non-uniform Pipe • Overtones not integer 5 multiples unless “Spherical” conical Volume • Example: Saxophone

휆1 = 2퐿 1

• Mainly has fundamental 2 resonance • Typically lower frequency than a pipe of similar length 3

2/4/2020 Sound of Music 2 50 Closed vs. Open Pipe (Pressure Modes)

Closed One End Open Both Ends Clarinet , e.g. Flute, e.g.

fC fO =2fC

3fC 2fO

5fC 3fO

2/4/2020 Sound of Music 2 52 Open Pipe 5.6 ft

Demo

2fO

3fO

2/4/2020 Sound of Music 2 54 Closed Pipe 5.6 ft

Demo

3fC

5fC

2/4/2020 Sound of Music 2 55 Open Pipe (Bent 4.7ft)

Demo: Not Carried Out

2fO

3fO

2/4/2020 Sound of Music 2 56 2/4/2020 Sound of Music 2 57 Air Column Instrument Examples

Open Cylinder Flute

Closed Cylinder Clarinet

Conical Oboe

2/4/2020 Sound of Music 2 58 Air Column Instrument Examples

2 ft

Open Cylinder Flute o  4 ft P

Closed Cylinder Clarinet

o  8 ft Conical Oboe

o  4 ft

2/4/2020 Sound of Music 2 59 What About Timbre?

2 ft

Open Cylinder Flute o  4 ft P

Closed Cylinder Clarinet

o  8 ft Conical Oboe

o  4 ft

2/4/2020 Sound of Music 2 60 Comparison of Standing Wave Modes

Open Cylinder Pipe Closed Pipe Conical Pipe

(No Even 2 fo Harmonics)

3 fo

(No Even 4 fo Harmonics)

Same Length, Fundamental Frequency, and Harmonics J Wolfe, University of New South Wales 2/4/2020 Sound of Music 2 61 More Complex Resonators

Common Characteristic: Modes are generally not harmonics of Fundamental

2/4/2020 Sound of Music 2 62 Singing Prayer Bowl

2/4/2020 Sound of Music 2 63 Resonant Vibrational Modes of a Wine Glass

Marty33 2009 YouTube 2/4/2020 Sound of Music 2 Wine Glass Resonance in Slow Motion 65 Benjamin Franklin’s Glass Harmonica (1761)

Stick/Slip on rotating glass bowls

Thomas Bloch, Paris Music Museum 2007

2/4/2020 Sound of Music 2 66 ? 67 th 4 ? rd rd 3 ? nd 2

0.0 317 Hz Hz 317 1882, 1882, 17 tons Sound of Music Music of2 Sound Apparent Frequency: Apparent St. Paul’s Cathedral St. Paul’s Great Paul Bell Paul Great 2/4/2020 Vibrating Bars

2.76 fo

5.40 fo

8.93 f Dan Russell o (Penn State)

Open University [GB]

2/4/2020 Sound of Music 2 68 Drumheads: Two Dimensional Membranes

2/4/2020 Sound of Music 2 69 Fundamental Mode of a Drumhead (0,1)

D Russell Penn State

2/4/2020 Sound of Music 2 70 The (0,2) Drumhead Mode

Nodal Line

Outer Edge Always a Nodal Line

f = 2.295 f0 D Russell Penn State

2/4/2020 Sound of Music 2 71 The (1,1) Drumhead Mode

Symmetric: No net air volume change under the f = 1.593 f drumhead 0 D Russell Penn State

2/4/2020 Sound of Music 2 72 More Drumhead Modes

0,1 1,1 2,1 3,1

f 2.653 f 0 1.593 f0 2.135 f0 0

0,2 1,2 2,2 3,2

2.296 f0 2.918 f0 3.501 f0 4.060 f0

0,3 4,1 5,1

2 4 3.600 f0 3 3.156 f0 3.652 f0 2/4/2020 Sound of Music 2 73 What you’re hearing…

2/4/2020 Sound of Music 2 74 Measured Sound Spectrum of 12” Tom Drum

(1,1) UIUC Physics Course 193/406 (2007) (1,1)

(0,1) Struck at Center Struck Halfway Out (2,1) “Lug Tone” (0,2)

0 100 200 300 400 500 600 700 800 900 1000 Frequency (Hz)

2/4/2020 Sound of Music 2 76 Room Modes

A Resonant Frequency: Sound 74.88 Hz Pressure

Different Surfaces of Equal Room Loudness

Masacoustics.it Comsol.com

2/4/2020 Sound of Music 2 77 Longitudinal Room Modes “Organ Pipe” 8’ modes 25’ 10’

Resonant Modes for 25 x 10 x 8 foot Rectangular Room 22.5 Hz 45 Hz 67.5 Hz

0 20 40 60 80 100 120 140 160 180 200 Resonant Frequency (Hz)

10’

2/4/2020 25’ Sound of Music 2 78 Course Outline

2/4/2020 Sound of Music 2 79