1. Sound 101: What is it, Why is it, Where is it?
Nikunj Raghuvanshi
University of North Carolina at Chapel Hill

2. University of North Carolina at Chapel Hill
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
University of North Carolina at Chapel Hill

3. University of North Carolina at Chapel Hill
Waves of what?
Air pressure
Compressions and Rarefactions
Wavelength (λ)
Compression
Rarefaction
University of North Carolina at Chapel Hill

4. 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 light’s 300,000,000 m/s. This has very interesting consequences
University of North Carolina at Chapel Hill

5. University of North Carolina at Chapel Hill
Frequency
What is frequency?
Given the wavelength, λ and the speed, c can you find the frequency, ν?
c = νλ
Humans can hear frequencies from 20 to 20,000 Hz Trivia: In music, the frequency doubles every octave
Range of wavelengths? (Use above formula)
University of North Carolina at Chapel Hill

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Phase
Wavelength()
pressure
p/2
Distance p 2p
Phase(q)
3p/2
Phase (q): Measures the progression of pressure at a point between a crest and a trough.
University of North Carolina at Chapel Hill

7. University of North Carolina at Chapel Hill
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
University of North Carolina at Chapel Hill

8. Loudness Source Pressure Loudness # of Times Greater Than TOH
Threshold of Hearing (TOH)
1*10-6
0 dB
100
Whisper
1*10-5
20 dB
101
Normal Conversation
1*10-3
60 dB
103
Busy Street Traffic
1*10-2.5
70 dB
103.5
Vacuum Cleaner
1*10-2
80 dB
104
Large Orchestra
6.3*10-1.5
98 dB
104.9
Front Rows of Rock Concert
1*10-0.5
110 dB
105.5
Threshold of Pain
1*100.5
130 dB
106.5
Military Jet Takeoff
1*101
140 dB
107
Instant Perforation of Eardrum
1*102
160 dB
108
Source:
University of North Carolina at Chapel Hill

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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
We talk about only production of sound, let the audio card do the propagation modeling
The University of North Carolina at Chapel Hill

10. Modeling surface vibration
Inertia Damping Elasticity Force
Mention about damping constants
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11. Where does Sound go?
All waves travel in much the same way (Ripples in a pond, sound, light, seismic waves etc.)
So how’s 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
out of phase: cancel
in phase: add 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
University of North Carolina at Chapel Hill

14. University of North Carolina at Chapel Hill
Overview
Background on Sound
Sound localization in humans
Sound localization for robots
Results
University of North Carolina at Chapel Hill

15. University of North Carolina at Chapel Hill
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
University of North Carolina at Chapel Hill

16. University of North Carolina at Chapel Hill
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.
University of North Carolina at Chapel Hill

17. 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)
University of North Carolina at Chapel Hill

18. 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 f<500 Hz (=69 cm)
Accurate for f>3000 Hz
University of North Carolina at Chapel Hill

19. 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
University of North Carolina at Chapel Hill

20. 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 f<1000 Hz
a). Peak 1 arrives properly in sequence at the two ears and there’s no confusion.
b). Peak 1 and 2 arrive closely at the ears and cause confusion
University of North Carolina at Chapel Hill

21. University of North Carolina at Chapel Hill
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
University of North Carolina at Chapel Hill

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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?)
University of North Carolina at Chapel Hill

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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?
University of North Carolina at Chapel Hill

24. University of North Carolina at Chapel Hill
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
University of North Carolina at Chapel Hill

25. University of North Carolina at Chapel Hill
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 >3000 Hz
ITD is useful for frequencies <1000 Hz
There is a front-back ambiguity using ITD and ILD alone which head motion resolves
University of North Carolina at Chapel Hill

26. University of North Carolina at Chapel Hill
Overview
Background on Sound
Sound localization in humans
Sound localization for robots
Results
University of North Carolina at Chapel Hill

27. 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
University of North Carolina at Chapel Hill

28. University of North Carolina at Chapel Hill
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”
University of North Carolina at Chapel Hill

29. University of North Carolina at Chapel Hill
Sound Localization
Start End
University of North Carolina at Chapel Hill

30. 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 = c*ITD
Solve for using above equation
University of North Carolina at Chapel Hill

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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 c=344 m/s is the speed of sound, is the velocity potential and is the laplacian
University of North Carolina at Chapel Hill

32. 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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33. 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
University of North Carolina at Chapel Hill

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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
University of North Carolina at Chapel Hill

36. 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:
University of North Carolina at Chapel Hill

37. University of North Carolina at Chapel Hill
Overview
Background on Sound
Sound localization in humans
Sound localization for robots
Results
University of North Carolina at Chapel Hill

38. Results: Accuracy of theoretical ILD
Curve: Theoretically computed ILD
Dots: Actual values measured from microphones
University of North Carolina at Chapel Hill

39. Results: Accuracy of theoretical IPD
Much more accurate than ILD
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40. Localization Performance
Sharp minima at small angles, not so sharp at large angles
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41. Localization Performance
IPD/ILD Algorithm Simple ITD-based algorithm
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42. Front-back ambiguity resolution
Symmetric
Without ambiguity resolution With ambiguity resolution
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43. Conclusion/Discussion
IPD/ITD is a much stronger clue than ILD. That’s 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.
University of North Carolina at Chapel Hill

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Video
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Thanks
Questions?
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Summary
Reflective environments, the precedence effect
University of North Carolina at Chapel Hill

47. Longitudinal vs. Transverse Waves
Sound is a longitudinal wave, meaning that the motion of particles is along the direction of propagation
Transverse waves—water waves, light—have things moving perpendicular to the direction of propagation
University of North Carolina at Chapel Hill