1. Copyright 2004 Ken Greenebaum Introduction to Interactive Sound Synthesis Lecture 23:Physical Modeling III/ambience Ken Greenebaum

2. Copyright 2004 Ken Greenebaum And then there were 3 Three Classes left! Three Classes left! Wrap-up physical modeling Wrap-up physical modeling Discuss ambience/spatialization Discuss ambience/spatialization Final Review/Discussion Final Review/Discussion

3. Copyright 2004 Ken Greenebaum Readings Audio Anecdotes: Audio Anecdotes: Listening to Nature Listening to Nature Optional Optional Using FLAVOR Bitstream Representation Using FLAVOR Bitstream Representation

4. Copyright 2004 Ken Greenebaum Physical modeled string: Example 1 How does this sound? How does this sound?

5. Copyright 2004 Ken Greenebaum Physical modeled string: Example 1 Not thrilling? Not thrilling? Why? Why?

6. Copyright 2004 Ken Greenebaum Physical modeled string: Example 2 Sound more realistic? Sound more realistic? Why? Why?

7. Copyright 2004 Ken Greenebaum Example 2 Similar model but: Similar model but: Have two strings for each note Have two strings for each note ‘Pluck’ strings with a sawtooth plus ‘Pluck’ strings with a sawtooth plus Delay lines initialized with random noise for brightness and variety Delay lines initialized with random noise for brightness and variety Low-pass filter used to Low-pass filter used to model hi-freq losses model hi-freq losses Resonant filter used to Resonant filter used to model body of instrument model body of instrument

8. Copyright 2004 Ken Greenebaum Violin Expand this model to include Expand this model to include Model of bow friction Model of bow friction To model (simple) violin To model (simple) violin

9. Copyright 2004 Ken Greenebaum Standing Waves in Tubes Acoustic tubes can be modeled Acoustic tubes can be modeled in a similar way using standing waves in a similar way using standing waves Displacement is replaced by pressure Displacement is replaced by pressure

10. Copyright 2004 Ken Greenebaum Tube example Slap end of this tube Slap end of this tube Sound like a plucked string? Sound like a plucked string?

11. Copyright 2004 Ken Greenebaum Ideal Tube Moving piston in tube Moving piston in tube Acts much like displacement of spring Acts much like displacement of spring Air pressure in tube: Air pressure in tube: Same as string displacement… Same as string displacement… P (x,t ) = P l (t +x /c )+P r (t –x /c) P (x,t ) = P l (t +x /c )+P r (t –x /c)

12. Copyright 2004 Ken Greenebaum Jug’a’lug Air filled containers have strong resonances Air filled containers have strong resonances Bottles, Jugs, etc. Bottles, Jugs, etc. Called Helmholtz resonators Called Helmholtz resonators

13. Copyright 2004 Ken Greenebaum Helmholtz resonator Intuitively resonant Frequency Decreases with: Intuitively resonant Frequency Decreases with: Smaller opening Smaller opening Longer neck Longer neck Larger volume Larger volume Consider: Consider: Wine bottle Wine bottle Musical instruments Musical instruments

14. Copyright 2004 Ken Greenebaum Helmholtz resonator We can model this system as: We can model this system as: Piston Piston Moving in a pipe Moving in a pipe Connected to a air reservoir Connected to a air reservoir Provided no standing waves (small reservoir) Provided no standing waves (small reservoir) Which is our spring model Which is our spring model Spring force replaced by Spring force replaced by Pressure * change in volume Pressure * change in volume Cross section of piston * length of displacement Cross section of piston * length of displacement

15. Copyright 2004 Ken Greenebaum Helmholtz resonator Where Where f : Resonant frequency of vessel f : Resonant frequency of vessel V : Volume of the vessel V : Volume of the vessel L : Length of pipe (neck) L : Length of pipe (neck) r : Radius of pipe (neck) r : Radius of pipe (neck)

16. Copyright 2004 Ken Greenebaum Ubiquitous model Many instruments may be modeled as: Many instruments may be modeled as: Linear resonator Linear resonator Modeled by filters Modeled by filters all-pole resonators (waveguides) all-pole resonators (waveguides) Driven by Driven by Single point, nonlinear oscillator Single point, nonlinear oscillator

17. Copyright 2004 Ken Greenebaum Nonlinear oscillator Models: Models: Reed of clarinet Reed of clarinet Lips of trumpet player Lips of trumpet player Jet of the flute Jet of the flute Bow-string friction of violin Bow-string friction of violin

18. Copyright 2004 Ken Greenebaum Example 3 Wind Instrument Clarinet block diagram: Clarinet block diagram:

19. Copyright 2004 Ken Greenebaum Problem: Stiffness For stiff systems For stiff systems Metal Bar Metal Bar Propagation speed varies with frequency Propagation speed varies with frequency Simple constant c Simple constant c Replaced with frequency dependent fn Replaced with frequency dependent fn c (f ) c (f )

20. Copyright 2004 Ken Greenebaum Piano Piano strings have weak stiffness Piano strings have weak stiffness All-pass filter added to waveguide to model freq. dependent speed of sound All-pass filter added to waveguide to model freq. dependent speed of sound All-pass filter designed to have: All-pass filter designed to have: No change in gain No change in gain Frequency dependent phase delay Frequency dependent phase delay

21. Copyright 2004 Ken Greenebaum Rigid Bars Such as in a xylophone Such as in a xylophone Can’t efficiently be modeled with single waveguide & all-pass filter Can’t efficiently be modeled with single waveguide & all-pass filter Instead banded waveguides are used Instead banded waveguides are used Waveguides models speed of sound near each significant vibration mode Waveguides models speed of sound near each significant vibration mode

22. Copyright 2004 Ken Greenebaum Dimensional models Our models thus far are 1 dimensional Our models thus far are 1 dimensional Multi-dimensional models required to model Multi-dimensional models required to model Membranes Membranes Plates Plates

23. Copyright 2004 Ken Greenebaum Consider 2-dimensional mass- spring model Modeled at each point: Modeled at each point: Density (mass per unit area) Density (mass per unit area) Tension Tension Thickness Thickness Displacement Displacement Sum of bidirectional X and Y traveling waves Sum of bidirectional X and Y traveling waves

24. Copyright 2004 Ken Greenebaum 2D Mass Spring Model Pretty expensive to calculate for: Pretty expensive to calculate for: High resolution High resolution Large area Large area

25. Copyright 2004 Ken Greenebaum 2D Mass Spring Model Benefits: Benefits: Accurately model actual object Accurately model actual object Vibration modes modeled Vibration modes modeled Important for: Important for: Inhomogeneous media Inhomogeneous media Media with unusual boundary Media with unusual boundary Jagged edge Jagged edge Unusual shape Unusual shape

26. Copyright 2004 Ken Greenebaum 3D Models An extension of 2D models An extension of 2D models Computationally expensive: Computationally expensive: Assuming: Assuming: 44.1K samples/s 44.1K samples/s Sound traveling at 1100’/s Sound traveling at 1100’/s Spatial sampling requires 0.3” resolution Spatial sampling requires 0.3” resolution 3D wave junction requires 12 adds and a multiply 3D wave junction requires 12 adds and a multiply Perry’s 3 gallon jug would take: Perry’s 3 gallon jug would take: 800 in 3 jug requires 30,000 3D wave junctions 800 in 3 jug requires 30,000 3D wave junctions

27. Copyright 2004 Ken Greenebaum Modal Synthesis 3D modeling is required for 3D modeling is required for Unusual shapes Unusual shapes Utmost accuracy/correctness Utmost accuracy/correctness Fortunately this is not always required Fortunately this is not always required Sometimes we just want to ‘rich’ responses and can use Modal Synthesis Sometimes we just want to ‘rich’ responses and can use Modal Synthesis

28. Copyright 2004 Ken Greenebaum Modal Synthesis May be used for May be used for Solid objects such as Solid objects such as Bottles, swords, crowbars Bottles, swords, crowbars Excited by Excited by Tapping, scraping Tapping, scraping

29. Copyright 2004 Ken Greenebaum Modal Synthesis Replaces N-dimensional model with Replaces N-dimensional model with Small number of damped harmonic oscillators Small number of damped harmonic oscillators Model the vibration modes of the actual object Model the vibration modes of the actual object

30. Copyright 2004 Ken Greenebaum Determining the modes A modal for any object A modal for any object May be defined as having May be defined as having N modes N modes At K locations At K locations The hard part is determining these! The hard part is determining these!

31. Copyright 2004 Ken Greenebaum 3 ways to determine the Model Care to guess? Care to guess?

32. Copyright 2004 Ken Greenebaum Building a Model Computationally Can model the object mathematically Can model the object mathematically Solve for the modes Solve for the modes

33. Copyright 2004 Ken Greenebaum Building a Model Experimentally Systematically bang on physical object Systematically bang on physical object At sampled locations At sampled locations With discrete forces With discrete forces Determine modes with spectral analysis Determine modes with spectral analysis

34. Copyright 2004 Ken Greenebaum Building a model Creatively Tune parameters to suite tastes Tune parameters to suite tastes

35. Copyright 2004 Ken Greenebaum Exciting a Modal Model Once a Modal Model exists Once a Modal Model exists Any function can be used to excite it: Any function can be used to excite it: Impulse Impulse Collision Collision Noise model Noise model Scraping/Rolling Scraping/Rolling Actual Signals! Actual Signals! Kees & Pai used a microphone Kees & Pai used a microphone

36. Copyright 2004 Ken Greenebaum Modal Modeled Engine Can model an auto engine Can model an auto engine Resonant object Resonant object Models everything that is vibrating Models everything that is vibrating Explosions Explosions Reciprocating parts Reciprocating parts Resonant exhaust Resonant exhaust Model excited with 4-part sound Model excited with 4-part sound Models strokes of internal combustion engine: Models strokes of internal combustion engine: Intake, Compression, Combustion, Exhaust Intake, Compression, Combustion, Exhaust

37. Copyright 2004 Ken Greenebaum Modal Modeled Engine Intake: sound of aspiration (on carbureted engine) Intake: sound of aspiration (on carbureted engine) Enveloped white noise Enveloped white noise Compression: compression of gas/fuel mixture Compression: compression of gas/fuel mixture Silent Silent Combustion: Explosion inside of metal (low pass filter) Combustion: Explosion inside of metal (low pass filter) Enveloped burst of 1/f noise Enveloped burst of 1/f noise Exhaust: Rapid expansion of gas Exhaust: Rapid expansion of gas White noise enveloped to decay quickly White noise enveloped to decay quickly

38. Copyright 2004 Ken Greenebaum Modal Engine Model N cylinder engine modeled by N cylinder engine modeled by Adding modeled output Adding modeled output 2pi/n degrees out of phase 2pi/n degrees out of phase

39. Copyright 2004 Ken Greenebaum Modal Engine Speed Excitation rate proportional to RPM Excitation rate proportional to RPM Resonances vary depending on load Resonances vary depending on load Can make engine ‘miss’ occasionally Can make engine ‘miss’ occasionally Replace a cylinder’s combustion stroke w/silence randomly Replace a cylinder’s combustion stroke w/silence randomly