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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400403

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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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