There are several clues you could use:

1
Localization

• There are several clues you could use
• arrival time
• phase lag (waves are out of sync)
• sound shadow (intensity difference)- sound is
  louder at ear closer to sound source

2
Localization

• What are some problems or limitations?

3
Localization

• Low frequency sounds arent attenuated by head
  shadow

Sound is the same SPL at both ears
Left Ear
Right Ear
Compression Waves
4
Localization

• High frequency sounds have ambiguous phase lag

Left Ear
Left Ear
Right Ear
Right Ear
Two locations, same phase information!
5
Localization

• These cues only provide azimuth (left/right)
  angle, not altitude (up/down) and not distance

Left Ear
Right Ear
Azimuth
6
Localization

• Additional cues

7
Localization

• Additional cues

Head Related Transfer Function Pinnae modify
the frequency components differently depending on
sound location
8
Localization

• Additional cues

Room Echoes For each sound, there are 6 copies
(in a simple rectanguluar room!). Different
arrival times of these copies provide cues to
location of sound relative to the acoustic space
9
Localization

• What would be the worst case scenario for
  localizing a sound?

10
Pitch and Music
11
Pitch

• Pitch is the subjective perception of frequency

Period - amount of time for one cycle
Frequency - number of cycles per second (1/Period)
Air Pressure
time -gt
12
Pitch

• Pure Tones - are sounds with only one frequency

f 400 hz
f 800 hz
13
Tone Height

• Tone Height is our impression of how high or low
  a sound is
• but theres something more to our impression of
  how something sounds than just its tone height

14
Chroma

• Tone Chroma is the subjective impression of what
  a tone sounds like
• Notes that have the same Chroma sound similar

500 Hz
400 hz
800 Hz
15
Chroma

• Tones that have the same Chroma are octaves apart

16
Chroma

• chroma is best represented as a helix
• chroma repeats every octave
• tones with the same chroma are above or below
  each other on a helix

17
Chroma

• Tones that are octaves apart have the same chroma
  
• one octave is a doubling in frequency

18
Chroma

• frequency is determined (in part) by location of
  stimulation on the basilar membrane

19
Chroma

• frequency is determined (in part) by location of
  stimulation on the basilar membrane
• but that relationship is not linear (its
  logarithmic)

20
Chroma

• doublings of frequency map to equal spacing on
  the basilar membrane

21
Pure Tones are Very Rare in Nature!

• What are real sounds composed of?

22
Pure Tones are Very Rare in Nature!

• What are real sounds composed of?
• Virtually all sounds are composed of several (or
  many) frequencies all going at once

23
Pure Tones are Very Rare in Nature!

• What are real sounds composed of?
• Virtually all sounds are composed of several (or
  many) frequencies all going at once
• Extra frequencies are called harmonics

24
What are harmonics?
imagine a guitar string
up
position
down
25
What are harmonics?
imagine a guitar string
up
position
down
26
What are harmonics?
But more than one frequency can fit between the
end points
up
position
time -gt
down
27
What are harmonics?
In fact many frequencies can be superposed.
f0
up
f2
position
time -gt
down
f1
28
What are harmonics?
Superposition of two (or more) frequencies yields
a complex wave with a fundamental frequency
29
The Missing Fundamental

• Your brain so likes to track the fundamental of a
  set of harmonics that it will perceptually fill
  it in even when it is absent

missing fundamental