The ear and perception of sound(Psychoacoustics)
General Physics VersionUpdated 2014July07
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Outline
A. Structure of the Ear
B. Perception of Loudness (Energy)
C. Perception of Pitch (Frequency)
D. References
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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
Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/place.html#c1
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Over 20,000 hair cells!
B. Perception of Loudness
1. Fechner’s law and decibel scale
2. Discrimination (jnd)
3. Threshold of hearing
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1. Which sounds half as loud as first?• Reference: http://www.phys.unsw.edu.au/jw/dB.html
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1b. Decibels: Fechner’s Law
• 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
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Gustav Theodor Fechner(1801-1887)
1c. Decibel Scale
• The decibel is a logarithmic scale
• A multiplicative factor of 10x in intensity is +10 db
• 0 db is threshold of hearing• 1 db is just noticeable difference• 15 db is a whisper• 60 db is talking• 120 db is maximum safe level• 150 db is jet engine (ear damage)• 180 db stun grenade
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==================Power Ratio dB___________________0.5 -31 02 +35 +710 1020 1350 17100 201000 3010000 40==================
21210 10
10m
W atts
IntensityLogdB
2a. JND: Just Noticeable Difference is 1dB• 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)• 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 thesquare of the pressure amplitudeMinimum ear can hear is 0.000,02 Pascals(Atmospheric pressure is 100,000 Pascal)
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3c Phon & Equal Loudness Level
The Fletcher-Munson curves are a way of mapping the dB of a pure tone to the perceived loudness level in phons.
17Hearing 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.
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
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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
• High Frequency Test
• http://audiocheck.net/audiotests_frequencycheckhigh.php
• Low Frequency Test
• http://audiocheck.net/audiotests_frequencychecklow.php
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2a. Pitch Discrimination
• At 1000 Hz, the “jnd” is about 1 Hz (0.1%)
• At 4000 Hz, the “jnd” is about 10 Hz (0.25%)
• Above 10,000 Hz, our discrimination is terrible.(Most music is in range of 30 to 4000 Hertz)
• We can distinguish approximately 5000 different tones
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2b. Beats• Two tones closer than 15 Hertz we hear as a “fused”
tone (average of frequencies) with a “beat”.
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Demo: http://www.phys.unsw.edu.au/jw/beats.html#sounds
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3. Combination Tones
• When tones are far enough apart we hear them as two distinct tones
• We also hear differenceand sum tones thatare not really there(Tartini Tones 1714)
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Demo: http://www.phys.unsw.edu.au/jw/beats.html#Tartini
D. References & Online Demos• 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/
Web-hearing-Shepard.htm
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D. Notes• Excluded SONE scale of hearing
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