Copyright 2004 Ken Greenebaum Introduction to Interactive Sound Synthesis Lecture 2: Fundamentals Ken Greenebaum

Copyright 2004 Ken Greenebaum Physics of Sound These are the fundamentals These are the fundamentals Not just abstract theory to forget Not just abstract theory to forget We are going to revisit these principals again and again: We are going to revisit these principals again and again: 3D spatialization -Speed of sound, Attenuation, Doppler 3D spatialization -Speed of sound, Attenuation, Doppler Additive synthesis - Wave interference Additive synthesis - Wave interference Physical modeling - Wave propagation Physical modeling - Wave propagation More! More!

Copyright 2004 Ken Greenebaum Sound Propagation We will review the highlights We will review the highlights Questions from the reading? Questions from the reading?

Copyright 2004 Ken Greenebaum Sound Propagation Sound is a periodic compression and rarefaction of a medium Sound is a periodic compression and rarefaction of a medium Usually air at atmospheric pressure Usually air at atmospheric pressure Sound can not propagate in a vacuum Sound can not propagate in a vacuum Hollywood got it wrong Hollywood got it wrong Caused by physical interaction: Caused by physical interaction: Impact, friction or displacement Impact, friction or displacement

Copyright 2004 Ken Greenebaum Sound Propagation Sound is a periodic compression and rarefaction of a medium Sound is a periodic compression and rarefaction of a medium

Copyright 2004 Ken Greenebaum Sound Propagation Longitudinal propagation in a slinky Longitudinal propagation in a slinky Longitudinal displacement Longitudinal displacement Wave Propagates

Copyright 2004 Ken Greenebaum Sound Propagation Transverse wave on surface of water: Transverse wave on surface of water:

Copyright 2004 Ken Greenebaum Sound Propagation Transverse wave on surface of water Transverse wave on surface of water Vertical displacement shown in cross section: Vertical displacement shown in cross section: λ wavelength amplitude surface of water trough crest Wave Propagates

Copyright 2004 Ken Greenebaum Sound Propagation Transverse waves Transverse waves On surface of water On surface of water Inside solids Inside solids Not possible in Not possible in Liquids Liquids Gas Gas (require a restoring force such) (require a restoring force such)

Copyright 2004 Ken Greenebaum Sound Propagation Transverse waves restoring force Transverse waves restoring force On surface of water -air pressure/gravity On surface of water -air pressure/gravity In solids -shear In solids -shear

Copyright 2004 Ken Greenebaum Sound Propagation Waves in the ground are earthquakes! Waves in the ground are earthquakes! Longitudinal waves – primary waves Longitudinal waves – primary waves Transverse waves – secondary waves Transverse waves – secondary waves These waves propagate at different rates These waves propagate at different rates

Copyright 2004 Ken Greenebaum Sound Propagation Spherical spreading is primary source of attenuation Spherical spreading is primary source of attenuation Sound waves propagate omnidirectionally in concentric rings (like an onion) Sound waves propagate omnidirectionally in concentric rings (like an onion) Energy falls off proportionally to the area of the spherical shell (wavefront) Energy falls off proportionally to the area of the spherical shell (wavefront) Inversely proportional to the square of the distance Inversely proportional to the square of the distance I=P/(4πr 2 ) I=P/(4πr 2 ) Intensity I, P power at source, r distance from source Intensity I, P power at source, r distance from source

Copyright 2004 Ken Greenebaum Sound Propagation Spherical spreading predicts rapid sound intensity falloff not experienced in real life Spherical spreading predicts rapid sound intensity falloff not experienced in real life Due to reflections from walls Due to reflections from walls Ever present ground Ever present ground Simulations need to modify the coefficients for the environment Simulations need to modify the coefficients for the environment Similar to the modification of the light falloff equations in computer graphics Similar to the modification of the light falloff equations in computer graphics

Copyright 2004 Ken Greenebaum Sound Propagation Spherical spreading only represents omnidirectional radiators Spherical spreading only represents omnidirectional radiators Many radiators exhibit dipole dispersion Many radiators exhibit dipole dispersion An infinitely large dipole (speaker cone) would have no dispersion An infinitely large dipole (speaker cone) would have no dispersion

Copyright 2004 Ken Greenebaum Sound Propagation Absorption due to frictional loss is another source of attenuation Absorption due to frictional loss is another source of attenuation Losses depend on frequency Losses depend on frequency Greatest losses in high frequencies Greatest losses in high frequencies Also dependent on: Also dependent on: Humidity Humidity Temperature Temperature Atmospheric Pressure Atmospheric Pressure

Copyright 2004 Ken Greenebaum Sound Propagation Speed of sound Speed of sound 340 meters per second (750 MPH) if 340 meters per second (750 MPH) if One atmosphere One atmosphere 0 degrees Celsius 0 degrees Celsius No humidity No humidity Speed increases with temperature Speed increases with temperature Much faster in solids Much faster in solids

Copyright 2004 Ken Greenebaum Sound Propagation Sound is affected by: Sound is affected by: Reflection Reflection Interference Interference Refraction Refraction Diffraction Diffraction Doppler Shift Doppler Shift

Copyright 2004 Ken Greenebaum Sound Propagation Reflection Reflection Sound bounces off surfaces Sound bounces off surfaces Angle of incidence equals angle of reflection Angle of incidence equals angle of reflection 45° angle of incidence45° angle of reflection

Copyright 2004 Ken Greenebaum Sound Propagation Interference Interference Constructive interference Constructive interference Peak+Peak=Larger peak Peak+Peak=Larger peak Destructive interference Destructive interference Peak+Trough cancel out Peak+Trough cancel out 2 waves of same frequency phase matched will add 2 waves of same frequency phase matched will add 2 waves of same frequency 180° out of phase cancel 2 waves of same frequency 180° out of phase cancel 2 waves of similar frequency create beat (guitar tuning) 2 waves of similar frequency create beat (guitar tuning) Complex interaction in other situations Complex interaction in other situations We will return to this with additive synthesis We will return to this with additive synthesis

Copyright 2004 Ken Greenebaum Sound Propagation Interference visualization with GNUPlot Interference visualization with GNUPlot set xrange [-3:3] set xrange [-3:3] set samples set samples plot sin(10*x) plot sin(10*x) plot sin(10*x)+sin(10*x)Constructive plot sin(10*x)+sin(10*x)Constructive plot sin(10*x)+sin(10*x+pi)Destructive plot sin(10*x)+sin(10*x+pi)Destructive plot sin(10*x)+sin(10.5x)Beat plot sin(10*x)+sin(10.5x)Beat

Copyright 2004 Ken Greenebaum Sound Propagation Refraction Refraction Bending of sound waves as sound moves between different density media Bending of sound waves as sound moves between different density media Consider a car running onto Consider a car running onto the shoulder

Copyright 2004 Ken Greenebaum Sound Propagation Diffraction Diffraction Effect of a wave re-radiating from an obstruction (like a window) Effect of a wave re-radiating from an obstruction (like a window)

Copyright 2004 Ken Greenebaum Sound Propagation Doppler Shift Doppler Shift Speed of sound source affects the frequency of sound perceived Speed of sound source affects the frequency of sound perceived Expanded Wavelength Direction of Travel Compressed Wavelength

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!" We will review the highlights We will review the highlights Questions from the reading? Questions from the reading?

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ People mean many things by loud: People mean many things by loud: It’s keeping me awake -> I can hear it It’s keeping me awake -> I can hear it It’s giving me a headache -> I can clearly hear it It’s giving me a headache -> I can clearly hear it I can’t hear you over the music I can’t hear you over the music My ears are ringing from it -> It’s physically painful My ears are ringing from it -> It’s physically painful

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ Most people don’t quantify or measure loudness Most people don’t quantify or measure loudness Make it louder/softer Make it louder/softer It was loud/quiet It was loud/quiet Almost no devices have calibrated volume Almost no devices have calibrated volume Almost no devices specify their loudness Almost no devices specify their loudness How loud is your doorbell, car horn, file alarm, etc.? How loud is your doorbell, car horn, file alarm, etc.?

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ Humans are able to perceive a wide range of sound pressure levels Humans are able to perceive a wide range of sound pressure levels Nominal air pressure is 1 bar (14.7 PSI) Nominal air pressure is 1 bar (14.7 PSI) Threshold of perception: microbar Threshold of perception: microbar Threshold of pain/damage: 200 microbars Threshold of pain/damage: 200 microbars Tremendous (Million fold) ratio between perception and pain Tremendous (Million fold) ratio between perception and pain (Eustachian tubes allow adaptation to large slow changes in pressure) (Eustachian tubes allow adaptation to large slow changes in pressure)

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ We measure volume in SPL dbA We measure volume in SPL dbA Million fold ratio Million fold ratio Human response is roughly logarithmic Human response is roughly logarithmic A sound must be 10x as powerful to be perceived as twice as loud A sound must be 10x as powerful to be perceived as twice as loud Hard to make things quiet -> 90% as intense to be ½ as loud! (eventually blend into noise floor) Hard to make things quiet -> 90% as intense to be ½ as loud! (eventually blend into noise floor) log10 relationship log10 relationship

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ 1 dB SPL -Just noticeable difference 1 dB SPL -Just noticeable difference A VERY important concept for optimization A VERY important concept for optimization 3 dB SPL -Generally noticeable 3 dB SPL -Generally noticeable 6 dB SPL -Easily noticed 6 dB SPL -Easily noticed 10 dB SPL -Twice as loud 10 dB SPL -Twice as loud

Copyright 2004 Ken Greenebaum Sound Pressure Levels: "Mine Goes to 11!“ Human hearing is more sensitive to some frequencies than others Human hearing is more sensitive to some frequencies than others This sensitivity changes based on This sensitivity changes based on Loudness of sound Loudness of sound Age of listener Age of listener Fletcher-Munson equal loudness curves Fletcher-Munson equal loudness curves

Copyright 2004 Ken Greenebaum Reading Audio Anecdotes Audio Anecdotes Sound Pressure Levels: "Mine Goes to 11!“ Sound Pressure Levels: "Mine Goes to 11!“

Copyright 2004 Ken Greenebaum Next class: Sound Pressure Continued… Sound Pressure Continued…