4. The Ear and the
Perception of Sound
(Psychoacoustics)
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Outline
A.
B.
C.
D.
Structure of the Ear
Perception of Loudness
Perception of Pitch
References
Updated May 13, 2012
Introduction
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A. The Structure of the Ear
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Psychoacoustics
is the study of
subjective human perception
of sounds.
The length of the auditory canal has been greatly exaggerated
A.1 Outer Ear Amplifies Sound
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A.2 The Middle Ear
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•The bones (ossicles)
of the middle ear form
a lever which
“amplifies” the
displacement by a
factor of 3x.
•The stirrup transfers
the force to the much
smaller area of the oval
window, resulting in 10
to 30 x increase in
pressure level
•Overall the sound is
amplified by as much
as 1000x or 30 dB
Auditory canal is a resonator at approximately 2000 to 5000 Hertz.
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A.3 Inner Ear Senses Sound
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B. Perception of Loudness
1. Discrimination of Loudness
2. The Phon (Equal loudness)
3. The Sone & Perceived Loudness
Over 20,000 hair cells!
Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/place.html#c1
1a. JND: Just Noticeable Difference is 1dB
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1c. Smaller than JND (7% change)
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1b Discrimination of Loudness
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Reference: http://www.phys.unsw.edu.au/jw/dB.html
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jnd = “just noticeable difference”
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The ear’s “jnd” for Loudness is approximately 1 dB
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Or, sound must be 30% louder in intensity for us to just notice that
it is louder.
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This depends somewhat on frequency (pitch) and loudness
(intensity). We have trouble distinguishing changes in loudness
for very the very loud or the very soft sounds
2a. Threshold of Hearing & Age (Presbycusis)
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Reference: http://www.phys.unsw.edu.au/jw/dB.html
Note “Sound Pressure dB” (or SPLdB) is approximately half
regular “energy” decibels (dB).
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2a. Hearing Threshold
2b Phon & Equal Loudness Level
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Hearing Threshold changes with frequency. The “Phon” scale is a
frequency-adjusted decibel scale based upon perception. Hence 0 Phon is
always the threshold, and 10 Phon “sounds” like its 10 dB louder.
• The ear can hear as small as 10-12 Watts/m2
(one trillionth of a watt per square meter)
( 0.000,000,000,001 Watt/m2 )
• Example: you might be able to hear someone talking
half a mile away under ideal circumstances
• Intensity is proportional to the
square of the pressure amplitude
Minimum ear can hear is 0.000,02 Pascals
(Atmospheric pressure is 100,000 Pascal)
The Fletcher-Munson curves are a way of mapping the dB of a pure tone to the
perceived loudness level in phons.
2c Steven’s “Phon”
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3a. Sone Scale (Steven’s Power Law)
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• Ear is found NOT to exactly follow Fechner’s
logarithmic law (i.e. decibel scale).
• Stanley Smith Stevens (1906–1973)
proposes “Phon”, which matches
dB at 1000 Hertz.
Phon = 40 + 10 Log 2 (Sone )
• 0 Phon is the threshold of hearing,
which is adjusted for frequency
(for example, at 100 Hertz,
0 Phon is equivalent to 35 dB)
• Perception of loudness is also frequency dependent.
– 1000 Hertz: 10 dB is perceived as 10 phon
– 100 Hertz: 10 dB is perceived as 16 phon
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C. Perception of Pitch
1936 Stevens proposes the “Sone” scale is
closer to perceived loudness (2 Sones will
“sound” to the ear as if it is twice as loud as 1
Sone)
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A multiplicative factor of 2x in Sone
corresponds to 10 Phon.
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10 people singing will only appear to be 2x as
loud as a soloist!
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1/16 Sone
0.17 Sone
4 Sone
256 Sone
2048 Sone
is threshold of hearing
is a whisper
is talking
is maximum safe level
is jet engine (ear damage)
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Phon
Sone
____________________
0
0.0625
10
0.125
20
0.25
30
0.5
40
1
50
2
60
4
70
8
80
16
90
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1a Range of Hearing
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1. Range of Hearing
2. Pitch Discrimination and jnd
3. Uncertainty Principle
Humans can hear from 16 to 20,000 Hertz
(In terms of music, this is about 10 octaves)
Piano only goes from 27.5 to 4186 Hertz
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1c. Test your Hearing
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1b Test Hearing
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High Frequency Test
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http://audiocheck.net/audiotests_frequencycheckhigh.php
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Low Frequency Test
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http://audiocheck.net/audiotests_frequencychecklow.php
http://www.phys.unsw.edu.au/jw/hearing.html
2a. Pitch Discrimination
2b. Beats
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At 1000 Hz, the “jnd” is about 1 Hz (0.1%)
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At 4000 Hz, the “jnd” is about 10 Hz (0.25%)
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Above 10,000 Hz, our discrimination is terrible.
(Most music is in range of 30 to 4000 Hertz)
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We can distinguish approximately 5000 different tones
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Two tones closer than 15 Hertz we hear as a “fused”
tone (average of frequencies) with a “beat”.
400
401
400
403
400
410
400
420
400
440
400
450
400
480
Demo: http://www.phys.unsw.edu.au/jw/beats.html#sounds
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2c. Combination Tones
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When tones are far enough apart we hear them as two
distinct tones
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We also hear difference
and sum tones that
are not really there
(Tartini Tones 1714)
Demo: http://www.phys.unsw.edu.au/jw/beats.html#Tartini
3a. Pitch Uncertainty
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The longer time you have ∆T to measure
a tone, the smaller your uncertainty in its
frequency ∆f
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Uncertainty Equation: ∆f ∆T ∼ 1
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So to distinguish a 400 and 401 Hertz
tone you would need 1 second
http://www.phys.unsw.edu.au/jw/uncertainty.html
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3b. Pitch & Amplitude
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Tones above 2000 Hz appear to increase in
pitch with increase in dB
Tones below 2000 Hz appear to decrease in
pitch with increase in dB
At 4000 Hz, increases 20 cents /30 dB (14%)
At 1000 Hz, decreases 10 cents/30 db (7%)
*An octave (doubling of frequency) is divided into 1200 cents.
The ear can discriminate a frequency difference of about 5
cents, so these effects are small!
D. Notes/References
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http://en.wikipedia.org/wiki/Phon
http://en.wikipedia.org/wiki/Sound_pressure_level
http://en.wikipedia.org/wiki/Weber-Fechner_law
http://en.wikipedia.org/wiki/Stevens%27_power_law
http://www.sfu.ca/sonic-studio/handbook/Sone.html
http://www.phys.unsw.edu.au/jw/dBNoFlash.html
http://www.phys.unsw.edu.au/jw/uncertainty.html
http://www.phys.unsw.edu.au/jw/beats.html
http://audiocheck.net/audiotests_frequencycheckhigh.php
http://audiocheck.net/audiotests_frequencychecklow.php
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Demos:
http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Webhearing-Shepard.htm
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