Transcript Ear_physics2703_2014jul07

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The ear and perception of sound
(Psychoacoustics)
General Physics Version
Updated 2014July07
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Outline
A.
B.
C.
D.
Structure of the Ear
Perception of Loudness (Energy)
Perception of Pitch (Frequency)
References
Introduction
Psychoacoustics
is the study of
subjective human perception
of sounds.
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A. The Structure of the Ear
The length of the auditory canal has been greatly exaggerated
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A.1 Outer Ear Amplifies Sound
Auditory canal is a resonator at approximately 2000 to 5000 Hertz.
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A.2 The Middle Ear
•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
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A.3 Inner Ear Senses Sound
Over 20,000 hair cells!
Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/place.html#c1
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B. Perception of Loudness
1. Fechner’s law and decibel scale
2. Discrimination (jnd)
3. Threshold of hearing
1. Which sounds half as loud as first?
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Reference: http://www.phys.unsw.edu.au/jw/dB.html
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1b. Decibels: Fechner’s Law
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• 1860 Fechner’s Law
• As stimuli are increased by
multiplication, sensations
increase by addition
(Sensation grows as the
logarithm of the stimulus)
• Example: A 10x bigger
intensity sound is “heard”
as only 2x bigger by the ear
Gustav Theodor Fechner
(1801-1887)
1c. Decibel Scale
• The decibel is a logarithmic scale
 Intensity 

dB  10 Log 10  12
 10 W atts 2 
m 

• A multiplicative factor of 10x in intensity is
+10 db
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•
•
•
•
•
0 db
1 db
15 db
60 db
120 db
150 db
180 db
is threshold of hearing
is just noticeable difference
is a whisper
is talking
is maximum safe level
is jet engine (ear damage)
stun grenade
==================
Power Ratio
dB
___________________
0.5
-3
1
0
2
+3
5
+7
10
10
20
13
50
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100
20
1000
30
10000
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==================
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2a. JND: Just Noticeable Difference is 1dB
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Reference: http://www.phys.unsw.edu.au/jw/dB.html
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2b Discrimination of Loudness
• jnd = “just noticeable difference”
• The ear’s “jnd” for Loudness is approximately 1 dB
• Or, sound must be 30% louder in intensity for us to just notice that
it is louder.
• 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
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2c. Smaller than JND (7% change)
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Reference: http://www.phys.unsw.edu.au/jw/dB.html
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3a. Threshold of Hearing & Age (Presbycusis)
Note “Sound Pressure dB” (or SPLdB) is approximately half
regular “energy” decibels (dB).
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3b. Hearing Threshold
• 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)
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3c Phon & Equal Loudness Level
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 Fletcher-Munson curves are a way of mapping the dB of a pure tone to the
perceived loudness level in phons.
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3d Steven’s “Phon”
• 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.
• 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
1. Range of Hearing
2. Pitch Discrimination and jnd
3. Combination tones
1a Range of Hearing
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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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
2a. Pitch Discrimination
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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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2b. Beats
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Two tones closer than 15 Hertz we hear as a “fused”
tone (average of frequencies) with a “beat”.
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401
400
403
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420
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440
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450
400
480
Demo: http://www.phys.unsw.edu.au/jw/beats.html#sounds
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3. 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
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D. References & Online Demos
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http://en.wikipedia.org/wiki/Weber-Fechner_law
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
• Demos:
• http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/We
b-hearing-Shepard.htm
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D. Notes
• Excluded SONE scale of hearing