Week 2 – Sound and Hearing

Mark Huckvale

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Last Week

• Human spoken language re-uses mammalian anatomy and physiology for vocalisation and hearing to create a communication system of complexity beyond any other animal.

• The form of speech is thus contingent on the nature of our vocal apparatus, our hearing, our cognition and our social structures.

• Speech science seeks explanations for the form of spoken language through study of the processes of speaking, listening, language acquisition and language evolution.

• Speech Science is an experimental science that sits at the crossroads of many other disciplines; it has developed its own explanatory models which have in turn been developed into many practical technologies.

• The Speech Chain is a simple model of spoken communication that highlights the transformation of an intention in the mind of the speaker to an understanding of that intention in the mind of the listener through processes that involve the Grammatical Code, the Phonological Code, articulation, sound, hearing and perception.

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Psychoacoustics

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What you perceive depends on how your senses operate

Physical character of sound

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Pressure variations in air

• Any moving or vibrating body affects local air pressure

• These fluctuations in pressure propagate away from the source (at high speed)

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Pressure variations in air

•Pressure variations propagate through the air in all directions

•As they travel they diminish in size

•Note that the air itself does not move

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Perceptual character of sound

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Pitch

Terms to describe sound

Subjective terms for sound

Loudness “Quantity of sound”

Pitch “Melody of sound”

Timbre “Quality of sound”

Loudness, Pitch and Timbre are the three basic dimensions of our perception of sounds.

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Loudness

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Pressure (Pa)

Loudness

Loud

Quiet

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Pressure (Pa)

Loudness

small change in pressure large change in loudness

large change in pressure small change in loudness

Loud

Quiet

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Matching Pressure to Loudness

200Pa

150Pa

100Pa

50Pa

0Pa

Painful

Very Loud

Loud

Moderately Loud

Moderate

Quiet

Very Quiet

Just Audible

Silence 16

Weber’s Law

The increase in stimulus size necessary to produce a just noticeable difference is a constant fraction of the stimulus size:

∆𝑆 ∝ 𝑆 ∆𝑆 = 𝑘. 𝑆

k = “Weber fraction”

Ernst Heinrich Weber 1795 - 1878

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Linear vs. Exponential Series

2 3 4 5 6 7

2 4 8 16 32 64

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Scale of JND

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Add 5 Add 5% Powers of 1.05

100 100 1001.050

105 105 1001.051

110 110 1001.052

115 116 1001.053

120 122 1001.054

125 128 1001.055

130 134 1001.056

100+5*N 1001.05N

Linear Series

Exponential Series

Linear vs. Exponential Series

• In a linear series, each step is a constant size

0 2 4 6 8

(add 2)

• In an exponential series, each step is a constant multiplying factor

1 2 4 8 16

(multiply by 2)

• We can convert an exponential series back to a linear series using logarithms

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Logarithms

• Logarithms are a way of saying – “Ten to the power of what is this number?”

• For example: log10(100) – Ten to the power of what is 100?

– Ten to the power of two is 100

– Therefore log10(100) is 2.

• Logarithms convert numbers into powers of 10

The logarithm of x

is some number y where

10y is equal to x 22

Practice with Logarithms

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Logarithms Connect

• Logarithms convert an exponential series into a linear series:

x= 1 10 100 1000 10000

log(x)= 0 1 2 3 4

• So if the property we want to measure changes exponentially, the logarithm of that value will change linearly.

• Loudness is like this.

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decibels

• Decibels (dB) are a standard log-ratio scale dB = 20.log10(test/reference)

• Ideal for situations where we are interested in exponential change rather than linear

• Say we have a change from 100units to 150units

dB = 20.log10(150/100) = 3.52dB

• Same as change from 200units to 300units dB = 20.log10(300/200) = 3.52dB

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decibel Scale

• 1 decibel (1dB) = change of 1.12

• 6 decibels (6dB) = change of 2

• 20 decibels (20dB) = change of 10

• 1Pa increased by 6dB => 2Pa

• 10Pa increased by 20dB => 100Pa

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Practice with decibels

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Loudness vs. dB

Pressure (dB re 20Pa)

Loudness

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Loudness vs. dB

Loudness

Smallest noticeable change ~ 1dB

More like a linear relationship

Pressure (dB re 20Pa) 29

Matching dB to Loudness

Painful

Very Loud

Loud

Moderately Loud

Moderate

Quiet

Very Quiet

Just Audible

Silence

200 Pa 140dB

20 Pa 120dB

2 Pa 100dB

0.2 Pa 80dB

0.02 Pa 60dB

0.002 Pa 40dB

0.0002 Pa 20dB

0.00002 Pa 0dB

<0.00002 Pa <0dB

decibels measured w.r.t. 20Pa 30

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Pitch

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Repetition Frequency (Hz)

Pitch

High

Low

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Repetition Frequency (Hz)

Pitch

High

Low

small change in frequency large change in pitch

large change in frequency small change in pitch

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• Concert pitch ‘A’ = 440Hz

• Middle ‘C’ = 262Hz

• One octave = 2 × frequency

• One semitone = 1.06 × frequency

699 587 494 392 330

‘A’ = 440Hz

‘C’ = 262Hz

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Notice how the change in frequency from one note to the next (one semitone) is about ×1.06 (e.g. note 71 to 72 is 523.25/493.88 = 1.059).

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Timbre

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Auditory system

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KEMAR 47

Auditory Transduction

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Conclusions

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Big Ideas Today

• Sounds are tiny, rapid fluctuations in atmospheric pressure that propagate rapidly away from physical vibrations in air.

• The subjective dimensions of sound are loudness, pitch and timbre which are (non-linearly) related to the physical sound properties of amplitude, repetition frequency and spectrum

• Loudness perception is seen to follow Weber's law, in which perceptual responses are proportional to the logarithm of stimulus size.

• Our hearing is extremely sensitive to small sound pressure variations - and may easily be damaged by loud sounds.

• Auditory sensations are determined by how sound travels through the ear and how it is converted to nerve firing in the cochlea.

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Lab Session

• Just Noticeable Differences. This is a listening experiment in which we will measure your sensitivity to small changes in loudness, pitch and timbre.

• Pitch & Repetition Frequency. You will use a program that measures the repetition frequency of sounds and reports the values in Hertz and in musical notation.

• Sound Localisation. You will hear some sounds recorded using a special binaural recording technique that preserves the features that help localise them in space.

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