Sound 101: What is it, Why is it, Where is it?

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Sound 101 What is it, Why is it, Where is it?

• Nikunj Raghuvanshi

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What is Sound?

• Waves, Particles? If waves, in what medium?
• Not an obvious answer in the 19th century
• Interesting read A short history of bad
  acoustics, M.C.M. Wright, The Journal of the
  Acoustical Society of America (JASA), 2006
• Now we do know the answer Waves in air

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Waves of what?

• Air pressure
• Compressions and Rarefactions

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How fast does sound travel?

• Newton did it first (As everything else)
• But, he made a mistake (Not a cyborg, after all)
• Laplace corrected that
• Accepted value today c 343 m/s (770 m.p.h) at
  room temperature
• Compare this to lights 300,000,000 m/s. This has
  very interesting consequences

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Frequency

• What is frequency?
• Given the wavelength, ? and the speed, c can you
  find the frequency, ??
• c ??
• Humans can hear frequencies from 20 to 20,000
  HzTrivia In music, the frequency doubles every
  octave
• Range of wavelengths? (Use above formula)

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Phase
Wavelength(?)
pressure
Distance
p
2p
Phase(q)
3p/2

• Phase (q) Measures the progression of pressure
  at a point between a crest and a trough.

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Loudness

• What range of sound amplitudes (pressure) can we
  hear?
• A huge, huge range (100,000,000 pressure
  levels)The human ear is an amazing organ
• Loudness measured in log scale (deciBels),
• Loudness, dB 20 log(p/p0) p0 is the
  threshold of hearing

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Loudness
Source Pressure Loudness of Times Greater Than TOH
Threshold of Hearing (TOH) 110-6 0 dB 100
Whisper 110-5 20 dB 101
Normal Conversation 110-3 60 dB 103
Busy Street Traffic 110-2.5 70 dB 103.5
Vacuum Cleaner 110-2 80 dB 104
Large Orchestra 6.310-1.5 98 dB 104.9
Front Rows of Rock Concert 110-0.5 110 dB 105.5
Threshold of Pain 1100.5 130 dB 106.5
Military Jet Takeoff 1101 140 dB 107
Instant Perforation of Eardrum 1102 160 dB 108
Source http//www.glenbrook.k12.il.us/gbssci/Phys
/Class/sound/u11l2b.html
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Why is sound produced?

• A vibrating surface creates pressure fluctuations
• Pressure waves are sensed by ear as sound
• Pressure fluctuation surface velocity

Vibration
Pressure Wave
Perception
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Modeling surface vibration

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Where does Sound go?

• All waves travel in much the same way (Ripples in
  a pond, sound, light, seismic waves etc.)
• So hows sound different?
• Coherent (Interference)
• Wavelength (Diffraction)
• Speed (Transient phenomena observable)

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Interference

• The resultant pressure at P due to two waves is
  simply their sum
• Phase is crucial

A
P
in phase add
out of phase cancel
B
signal A
signal B
A B
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Diffraction

• A wave bends around obstacles of size approx.
  its wavelength, i.e. when ? s
• P will have appreciable reception only if there
  is a good amount of diffraction
• This is the reason sound gets everywhere

?
s
?
P
s
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Overview

• Background on Sound
• Sound localization in humans
• Sound localization for robots
• Results

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Before we start

• This is a different connotation of localization
  than the one used in motion planning
• Sound localization is much easier if the number
  of sound sensors is large, by measuring the
  inter-arrival time difference between neighboring
  sensors
• There have been numerous such approaches
• However, the localization performance of humans
  clearly shows that just two ears are sufficient
• The work I discuss is the first one to
  effectively use just two sensors to accurately
  find the direction to the sound source

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Sound Localization
The sound localization facility at Wright
Patterson Air Force Base in Dayton, Ohio, is a
geodesic sphere, nearly 5 m in diameter, housing
an array of 277 loudspeakers. Listeners in
localization experiments indicate perceived
source directions by placing an electromagnetic
stylus on a small globe.
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Sound Localization ILD

• Idea A sound source on the right will be
  perceived to have more intensity at the right ear
• Head casts an acoustical or sound shadow
• The difference of the intensities at the two ears
  is the Interaural Level Difference (ILD)

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Sound Localization ILD

• The ILD depends on the angle as well as frequency
• Different frequencies diffract differently
• In general, higher frequencies diffract less,
  leading to a sharper shadow and higher ILD
• Assume head has dia 17 cm
• ILD becomes useless for flt500 Hz (?69 cm)
• Accurate for fgt3000 Hz

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Sound Localization ITD

• Idea Sound has longer path for farther ear (d),
  and hence takes more time to reach it
• This too depends on both the angle and frequency
  of sound
• Measured as the Interaural Time Difference (ITD)

d
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ITD Range of usefulness

• If the signal is periodic (eg. Pure tone), ITD is
  useless if the path difference is much greater
  than the wavelength
• For human head size, ITD is useful for flt1000 Hz

a). Peak 1 arrives properly in sequence at the
two ears and theres no confusion. b). Peak 1
and 2 arrive closely at the ears and cause
confusion
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Finding the ITD

• Use a pattern matcher to check position of
  MAXIMUM similarity
• Independent sound signals g(t) h(t) are slid
  across each other (Sliding Window)
• Correlation vector is returned showing delay
  between the signals g(t) h(t) i.e. the ITD

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Front-back ambiguity

• The theory of humans using only ITD and ILD has a
  big hole. The formulation has inherent symmetry
  which creates front-back ambiguity (points 2 and
  3 in figure)
• ITD and ILD for 2 and 3 will be identical (right?)

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Front-back ambiguity

• There is a simple way to break this symmetry
  move the head!
• This approach is used in the paper I discuss
  later
• Interestingly, a moving source alone may not be
  enough to break the ambiguity, its important to
  move the head
• But humans can do it without even moving, how?

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The HRTF

• There is no symmetry in reality because of the
  structure of the external ear and scattering by
  the shoulders and head
• The Head Related Transfer Function (HRTF)
  measures the amounts by which different
  frequencies are amplified by the head for
  different source positions
• This thing works well only when the sound is
  broad-band

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Summary

• Sound provides two cues ILD and ITD
• ILD measures the intensity difference between the
  two ears at a given point in time
• ITD measures the difference in arrival time for
  the same sound at the two ears
• ILD is useful for frequencies gt3000 Hz
• ITD is useful for frequencies lt1000 Hz
• There is a front-back ambiguity using ITD and ILD
  alone which head motion resolves

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Overview

• Background on Sound
• Sound localization in humans
• Sound localization for robots
• Results

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Sound Localization for robots

• The papers I will discuss
• A Biomimetic Apparatus for Sound-source
  Localization. Amir A. Handzel, Sean B. Andersson,
  Martha Gebremichael and P.S. Krishnaprasad. IEEE
  CDC 2003
• Robot Phonotaxis with Dynamic Sound-source
  Localization. Sean B. Andersson, Amir A. Handzel,
  Vinay Shah, and P.S. Krishnaprasad. IEEE ICRA
  2004

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Sound Localization

• As discussed, to resolve front-back ambiguity, we
  have two options
• Use a spherical head, and use head motion to
  resolve front-back ambiguity
• Use an asymmetric head and compute the HRTF and
  use that, like humans
• The first approach is much simpler and is the one
  used in this paper

• The head

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Sound Localization

• Start End

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A simple ITD-based method

• A much simpler method commonly in use
• Consider a distant source so that impinging wave
  is nearly planar
• Path difference between left and right is given
  by l(ABC), which is,
• By correlating the left and right sound signal,
  suppose the ITD is found, then a cITD
• Solve for using above equation

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The IPD-ILD algorithm

• Solve for scattering from a hard spherical head.
  This is a more realistic physical model
• Two microphones at the poles ( )
• Wave equation is given by,
• Where c344 m/s is the speed of sound, is the
  velocity potential and is the laplacian

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Mathematical Formulation

• Basic idea for solution Solve in spherical
  coordinates. The solution is well known, using
  separation of variables
• The only place where scattering from a hard
  sphere is invoked is to satisfy the following
  equation
• In the above, and are the incident
  potential (from source) and scattered potential
  (from sphere) respectively
• The solution has the following important
  properties
• Dependent only on the angle between source and
  receiver
• Independent of source distance can localize only
  the direction

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Mathematical Formulation

• It is assumed that the sound source, the center
  of the head and the ears are in the same plane,
  i.e. localization is performed only in the
  horizontal plane
• The pressure p, measured at a microphone is
• given by
• In the above, is the geometry and
  frequency-dependent phase-shift, and is the
  angular frequency ( )
• Its important to note that both A and depend
  on the frequency, , due to differential
  scattering

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The IPD and ILD

• The Interaural Phase Difference (IPD) is the same
  concept as the ITD, except it measures the phase
  difference rather than the time difference.
  Specifically,
• The IPD and ILD can be computed as,
• At given source angle , using these
  theoretical formulas, we may calculate IPD( )
  and ILD( )
• Our job is to invert this operation, given the
  IPD and ILD at different frequencies, we need to
  find

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Localization Metric

• Sample and store the values of IPD( , ) in a
  table
• Collect data from microphones and try to find
  closest theoretical curve
• Apply FFT to gather ILD and IPD values for
  different
• Distance metric L2 norm distance between
  predicted and observed IPD and ILD curves
• Final distance,
• Minimize over , to get source direction

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Resolving front-back ambiguity

• Even though IPD and ILD are the same for any two
  angles and , their derivatives
  with respect to , IPD and ILD are not
• Since IPD and ILD are theoretically known, their
  derivatives may be calculated, sampled and stored
  just like the IPD and ILD values
• The observed difference between the IPD values
  for two consecutive samples provides an
  approximation for IPD
• Define a similar L2-norm metric for IPD and ILD
  
• Augmented distance function to minimize

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Overview

• Background on Sound
• Sound localization in humans
• Sound localization for robots
• Results

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Results Accuracy of theoretical ILD

• Curve Theoretically computed ILD
• Dots Actual values measured from microphones

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Results Accuracy of theoretical IPD

• Much more accurate than ILD

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Localization Performance

• Sharp minima at small angles, not so sharp at
  large angles

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Localization Performance

• IPD/ILD Algorithm Simple ITD-based
  algorithm

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Front-back ambiguity resolution
Symmetric

• Without ambiguity resolution With
  ambiguity resolution

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Conclusion/Discussion

• IPD/ITD is a much stronger clue than ILD. Thats
  why the simple ITD algorithm also gives decent
  performance
• Overall they are the first ones to demonstrate a
  real working robot with good sound localization,
  so presumably this works well in practice
• The method is theoretically well-motivated, and
  shows that good localization can be achieved with
  just isotropic microphones
• They also claim that it works well in a
  laboratory environment with some noise (CPU fans
  etc.) and reflections from the walls etc.

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Video
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Thanks

• Questions?

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Summary

• Reflective environments, the precedence effect

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Longitudinal vs. Transverse Waves

• Sound is a longitudinal wave, meaning that the
  motion of particles is along the direction of
  propagation
• Transverse waveswater waves, lighthave things
  moving perpendicular to the direction of
  propagation