The ear and perception of sound(Psychoacoustics)

Updated 2013Aug05

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Outline

A. Structure of the Ear

B. Perception of Pitch

C. Perception of Loudness

D. Timbre (quality of sound)

E. 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 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

C. 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==================

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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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D. Timbre

1. Waveforms and Timbre

2. Fourier Theory

3. Ohm’s law of acoustics

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1. Waveform Sounds

Different “shape” of wave has different “timbre” quality

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Sine Wave (flute)

Square (clarinet)

Triangular (violin)

Sawtooth (brass)

1b. Waveforms of Instruments

• Helmholtz resonators (e.g. blowing on a bottle) make a sine wave

• As the reed of a Clarinet vibrates it open/closes the air pathway, so its either “on” or “off”, a square wave (aka “digital”).

• Bowing a violin makes a kink in the string, i.e. a triangular shape.

• Brass instruments have a “sawtooth” shape.

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2a. Fourier’s Theorem

Any periodic waveform can be constructed from harmonics.

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Joseph Fourier1768-1830

2b. FFT: Fast Fourier Transform

• A device which analyzes any (periodic) waveform shape, and immediately tells what harmonics are needed to make it

• Sample output:tells you its mostly10 k Hertz, witha bit of 20k, 30k, 40k,etc.

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2c. FFT of a Square Wave

• Amplitude “A”

• Contains only odd harmonics “n”

• Amplitude of “n” harmonic is:

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Ab

n

bbn

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1

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2d. FFT of a Sawtooth Wave

• Amplitude “A”

• Contains all harmonics “n”

• Amplitude of “n” harmonic is:

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Ab

n

bbn

1

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2e. FFT of a triangular Wave

• Amplitude “A”

• Contains ODD harmonics “n”

• Amplitude of “n” harmonic is:

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?4

1

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Ab

n

bbn

3a. Ohm’s Law of Acoustics 31

• 1843 Ohm's acoustic lawa musical sound is perceived by the ear as a set of a number of constituent pure harmonic tones, i.e. acts as a “Fourier Analyzer”

Georg Simon Ohm (1789 – 1854)

Octave, in phase

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For example:, the ear does not really “hear” the combined waveform (purple above), it “hears” both notes of the octave, the low and the high individually.

3b. Ohm’s Acoustic Phase Law 32

• Hermann von Helmholtz elaborated the law (1863?) into what is often today known as Ohm's acoustic law, by adding that the quality of a tone depends solely on the number and relative strength of its partial simple tones, and not on their relative phases.

Hermann von Helmholtz(1821-1894)

The combined waveform here looks completely different, but the ear hears it as the same, because the only difference is that the higher note was shifted in phase.

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3c. Ohm’s Acoustic Phase Law 33

• Hence Ohm’s acoustic law favors the “place” theory of hearing over the “telephone” theory.

• Review:– The “telephone theory” of hearing (Rutherford,

1886) would suggest that the ear is merely a microphone which transmits the total waveform to the brain where it is decoded.

– The “place” theory” of hearing (Helmholtz 1863, Georg von Békésy’s Nobel Prize): different pitches stimulate different hairs on the basilar membrane of the cochlea.

E. Notes/References• 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• Fourier Applet (waveforms) http://www.falstad.com/fourier/

• http://www.music.sc.edu/fs/bain/atmi02/hs/index-audio.html

• Load Error on this page? http://www.music.sc.edu/fs/bain/atmi02/wt/index.html

• FFT of waveforms: http://beausievers.com/synth/synthbasics/

• Demos:• http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-

hearing-Shepard.htm

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