Auditory Perception
Rob van der Willigen
http://~robvdw/cnpa04/coll1/AudPerc_2007_P6.ppt
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Today’s goal
Understanding the perceptual scaling
of sound intensity: LOUDNESS
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Magnitude versus Loudness
Magnitude estimation
treats the perceiver as a
measuring instrument capable of
assigning numbers to sounds in
proportion to their loudness.
Equal loudness contours
summarize the intensity levels that
make tones of different
frequencies sound equal in
loudness.
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Magnitude versus Loudness
Loudness is a subjective
impression of the intensity of
sound
Loudness matching is adjusting
the loudness of one sound until it
is equivalent to the loudness of
another
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Humans versus the rest
Psychoacoustics
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Physical Dimensions of Sound
Amplitude
- height of a cycle
- relates to loudness
Wavelength (λ)
- distance between peaks
Phase (j )
- relative position of the peaks
Frequency (f )
- cycles per second
- relates to pitch
Psychoacoustics
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Acoustic Units of Sound Measurement
Psychoacoustics
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Physical parameters of sound waves: Sound Intensity
Sound Intensity (I) of a wave is the rate at which sound energy
flows through a unit area (A) perpendicular to the direction of travel:
Intensity  Pressure  Particle Velocity
Force Distance
Energy



Area
Time
Area  Time
Power
P[w]


Area
A[m 2 ]

Sound Pressure, P, is measured in watts [W=J/s]
A is measured in square meters [m2]
Psychoacoustics
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Sound Intensity: The Decibel scale
Sound Intensity Level:
Intensity threshold of
hearing I0 = 10-12 W/m2
Sound Pressure Level:

Pressure threshold of
hearing
P0 = 2 x 10-5 N/m2 = 20 mPa
Energy ratio
 I 
dB(SIL)  10log 10 
I 0 
Pressure ratio
2
P
P
dB( SPL)  10 log 10    20 log 10  
 P0 
 P0 
Psychoacoustics
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How does an acoustic sound level depend on
distance from the source?
Intensity (and pressure) is inverse
proportional for free field propagation.
At a distance 2r from the source, the area
enclosing the source is 4 times as large as the
area at a distance r.
NB. The power radiated remains the same
irrespective of the distance; consequently the
intensity, the power per area, must decrease.
Psychoacoustics
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Sound Intensity: Inverse square law
Sound intensity and the
inverse square law
A doubling of distance from the sound
source in the direct field will reduce the
"sound level” by 6 dB.
I 1 / I 2 = r2 2 / r1 2
I 

1
r2
That is, sound intensity level, I,
decreases by 6 dB per doubling of
distance from the source to 1/4 (25 %) of
the sound intensity initial value.
This will reduce the sound intensity I
(energy quantity) to 1/2² = 1/4 (25 %) and
the sound pressure p (field quantity) to 1/2
(50 %) of the the initial value.
Psychoacoustics
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Sound Pressure: 1/r law
Sound pressure p
and the inverse
distance law 1/r
In acoustics, the sound pressure of a
spherical wave front radiating from a
point source decreases by 50% as the
distance r is doubled, thus measured in
dB it decreases by 6.02 dB.
The behavior is not inverse-square, but
is inverse-proportional (blue-line).
Sound pressure decreases inversely as
the distance increases with 1/r from the
sound source.
Psychoacoustics
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Inverse square law versus Inverse distance law
The inverse square law 1/r2 shows the distance performance of
energy quantities. This relates to sound intensity or density.
The inverse distance law 1/r shows the distance performance of
field quantities. This relates to sound pressure / particle velocity /
particle displacement.
Energy quantities are proportional to squared field quantities:
Ip
2
Psychoacoustics
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The Physical Relationship between Intensity (I) & Pressure (po)
p02
1
I

 p02
r n 2  z
ris mass density or air 1.204 kg/m3 at 20o Celsius.
nis speed or air, 343.2 m/s, p0 zero-to-peak pressure amplitude.
z is acoustic impedance or air 413.2 kg/(s·m2) or 413.2 N·s/m3.
2
I 2p
 Ip 
  
 2 2
2
I rms 
Ip
n
n

1
2
Ip
Psychoacoustics
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The Decibel scale
Since sound measuring instruments respond to sound pressure the
"decibel" is generally associated with sound pressure level.
Sound pressure levels quantify in decibels the intensity of given
sound sources. Sound pressure levels vary substantially with distance
from source, and also diminish as a result of intervening obstacles
and barriers, air absorption, wind and other factors.
Sound Pressure Level (SPL): 20 × log(p/p0) = 10 × log(p/p0)²,
where p0 = 2×10-5 N/m2.
p = root mean square sound pressure (N/m2)
The usual reference level p0 is 20×10-6 N/m2.
Psychoacoustics
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The Decibel scale
"Threshold of audibility'' or the minimum pressure fluctuation detected by
the ear is less than 10-9 of atmospheric pressure or about 20×10-5 N/m2
(pascal) at 1000 Hz.
"Threshold of pain'' corresponds to a pressure 106 times greater, but still
less than 1/1000 of atmospheric pressure.
Because of the wide range, sound pressure measurements are made on a
logarithmic scale (decibel scale).
Sound power levels are connected to the sound source and are
independent of distance. Sound powers are indicated in decibel.
Lw = 10 × log (P / P0) where: P0 = reference power (W).
The usual reference level is 10-12 W, calculated from
p0 = 20 micropascal, which is the lowest sound persons of excellent
hearing can discern.
Sound power is measured as the total sound power emitted by a source in
all directions in watts (joules / second). Sound power levels do not vary
with distance from source.
Psychoacoustics
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The Decibel scale
NB. 1 Pa = 1 N/m2 ≡ 94 dB
1 bar = 105 Pa
Psychoacoustics
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The Decibel scale
Psychoacoustics
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The Decibel scale
0 dB = Threshold of Hearing ≡ TOH
10 dB = 10 times more intense than TOH
20 dB = 100 times more intense than TOH
30 dB = 1000 times more intense than TOH
An increase in 10 dB means that the intensity of the sound increases
by a factor of 10
If a sound is 10x times more intense than another, then it has a sound
level that is 10 times x more decibels than the less intense sound
An increase of 6 dB represents a doubling of the sound pressure
An increase of about 10 dB is required before the sound subjectively
appears to be twice as loud.
The smallest change of the pressure level we can hear is
about 3 dB
Psychoacoustics
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Counting Decibels
Sound Intensity level of super imposed sources:
L1
10
SIL.[dB]  10log(10  10
L2
10

LN
10

 10 )  10log 10
N 1
where L1, L2, …, Ln are SIL [dB]
LN
10
Psychoacoustics
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Sound Density
When dealing with noises, it is advantageous to use density instead of
sound intensity e.g., the sound intensity within a bandwidth of 1 Hz.
The logarithmic correlate of the density of sound intensity is called
sound intensity density level,
usually shortened to density level, LE.
LE  SIL 10log10(f /Hz)[dB]
For white noise, l and SIL are related by the equations given above where
Δf represents bandwidth of the sound.
 I 
SIL  10log 10 [ dB]
I 0 
Psychoacoustics
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Physical parameters of sound waves: Noise Density
sound intensity density level
 E 
LE  10 log 10 [ dB]
E 0 
sound energy density

E  E 0 10
LE
10
[J / m 3 ]
pJ 
12 J 
E 0  1 3  10  3 
m 
m 
Psychoacoustics
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Physical parameters of sound waves: Power Spectrum Density
The Intensity Density Level of three types of NOISES:
Intensity density level [dB]
WHITHE NOISE
BROWN (RED) NOISE
Log Frequency [Hz]
GRAY NOISE
Psychoacoustics
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Physical parameters of sound waves: Power Spectrum Density
Power Spectral Density (PSD) is the
frequency response of a random or
periodic signal.
PSD shows the strength of the
variations per unit frequency as a
function of frequency.
The PSD is the average of the Fourier
transform magnitude squared, over a
large time interval.
It tells us how the average intensity is
distributed as a function of frequency.
Plot shows de PSD of white Noise
Psychoacoustics
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THE BELL DECODER
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
MAF
Minimum Audible Field thresholds
sound pressure level for pure tone at
absolute threshold in a free field tested in
a room, using loudspeakers, listening
binaurally, 1 meter from source SPL
calibrated using microphone,
with listener not present.
MAP
Minimum Audible Pressure thresholds
SPL at listener’s tympanic membrane
sound presented over headphones (monaural)
SPL estimated from the sound level in a test coupler attached to
earphone.
Differences in the two measures are due to some binaural
advantage, outer-ear filtering (mid frequencies), and
physiological noise (low frequencies).
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
Differences in the two measures are due to some binaural
advantage, outer-ear filtering (mid frequencies), and
physiological noise (low frequencies).
Psychoacoustics
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Auditory sensitivity: Hearing range (MAF)
Psychoacoustics
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Auditory sensitivity: upper limit
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
Hearing Level (dB HL)
Threshold of hearing, relative to the average of the normal
population.
For example, the average threshold at 1 kHz is about 4 dB SPL.
Therefore, someone with a threshold at 1 kHz of 24 dB SPL
has a hearing level of 24 - 4 = 20 dB HL.
Audiograms
Audiograms measure thresholds in dB HL, and are plotted “upsidedown”. Measurements usually made at octave frequencies from 250
Hz to 8000 Hz.
Threshold microstructure
Individuals show peaks and dips as large as 10 dB over very small
frequency differences (probably due to OHCs and “cochlear
amplifier”).
Psychoacoustics
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Auditory sensitivity: Audiometric curve (audiogram)
Plot A shows the threshold of hearing
or audibility curve for a patient with a
hearing loss (curve b) and a normal
curve (curve a).
Notice that the patient's threshold is
higher for every frequency above 128
Hz.
The normal audibility curve is usually
converted to a straight line at 0 dB
loss, and the patient's values are
plotted as deviations from the normal
values.
The result is a hearing loss curve b, as
shown in plot B.
Psychoacoustics
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Auditory sensitivity: Audiometric curve (hearing loss)
Psychoacoustics
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Auditory sensitivity: Audiometric curve (hearing loss)
Conduction loss stems from
damage to outer or middle ear
(areas involved in conduction of
sound energy to the inner ear).
Sensory/neural loss is
associated with damage to the
inner ear or auditory cortex.
Psychoacoustics
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Auditory sensitivity: Audiometric curve (hearing loss)
Blue lines in the audiogram indicate the hearing
loss as measured by air conduction, whereas pink
lines indicate the hearing loss as measured by
bone conduction.
Typically, in neural hearing loss (A), both
measures show the same pattern of loss.
Surgery is not indicated for this form of hearing
loss because the neural tissue probably cannot be
repaired, but some improvement in hearing is
possible with a hearing aid, depending upon the
nature of the damage.
The audiogram of a person with pure conduction
hearing loss (B). Here, bone conduction (pink) is
near normal, i.e., near 0 dB loss, but air conduction
is impaired (blue).
Notice that the air audiogram is nearly flat with
conduction hearing loss (B, pink), but there is a
differential loss, depending upon frequency, in
nerve hearing loss (B, blue).
Psychoacoustics
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Absolute thresholds: temporal integration
Audiometric thresholds and international
threshold standards are measured using
long-duration tones (> 500 ms).
Detectability of tones with a fixed level
decreases with decreasing duration,
below 300 ms.
IL is the minimum intensity which is an
( I  I L )  t  I Lt  I  t  I L  1  I L
t
effective long duration stimulus for the ear.
t represents the integration time of the
auditory system.
Thus, the auditory system does not simply
integrate stimulus time (Intensity x duration)
It may also vary with frequency.
Psychoacoustics
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Absolute thresholds: temporal integration
The absolute threshold for detecting sounds
is affected by duration
Up to a few hundred milliseconds the
threshold for detecting sounds decreases
(more sensitive) with increasing duration
Effect of duration on loudness
causes variability in the results
For a given intensity, loudness increases
with duration up to 100-200ms
( I  I L )  t  I Lt  I  t  I L  1  I L
t
Psychoacoustics
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Perceived Loudness: Equal-loudness Contours
The pressure, or intensity, of a sound wave is not solely
responsible for its loudness – frequency is also important.
1 kHz is used as a reference.
By definition, a 1-kHz tone at a
Intensity level of 40 dB SPL has a
loudness level of 40 phons.
Any sound having the same
loudness (no matter what its SPL)
also has a loudness level of 40
phons.
Equal-loudness contours are
produced using loudness
matching experiments
(method of adjustment or method
of constant stimuli).
Equal-loudness contours
Psychoacoustics
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SPL is not a measure of Perceived Loudness
Loudness is defined as
the attribute of auditory sensation in terms of which sounds can be
ordered on a scale extending from quiet to loud.
Two sounds with the same sound pressure level may not have the
same (perceived) loudness
A difference of 6 dB between two sounds does not equal a 2x increase
in loudness
Loudness of a broad-band sound is usually greater than that of a
narrow-band sound with the same (physical) power (energy content)
Psychoacoustics
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Perceived Loudness: Equal-loudness Contours
The pressure, or intensity, of a sound wave is not directly
related to its loudness – frequency is also important.
Psychoacoustics
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Perceived Loudness: phone
A unit of LOUDNESS LEVEL (L) of a given sound or noise can only be
derived from indirect loudness measurements
(see e.g., the Fletcher and Munson experiment)
If SPL at reference frequency of 1kHz is X dB – the corresponding equal
loudness contour is X phon line.
Phon units can’t be added, subtracted,
divided or multiplied.
60 phons is not 3 times louder than 20 phons!
The sensitivity to different frequencies is more
pronounced at lower sound levels than at higher.
For example: a 50 Hz tone must be 15 dB higher
than a 1 kHz tone at a level of 70 dB
Psychoacoustics
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Perceived Loudness: sound level meters
The shapes of equal-loudness
contours have been used to
design sound level meters
(audiometer).
At low sound levels,
low-frequency components
contribute little to the total
loudness of a complex sound.
Thus an A weighting is used to
reduces the contribution of lowfrequencies.
Psychoacoustics
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Perceived Loudness: A-weighting & sound level meters
A-weighting is only really valid for relatively quiet sounds and for pure tones as it
is based on the 40-phon Fletcher-Munson curves which represented an early
determination of the equal-loudness contour for human hearing.
Nevertheless, A-weighting would be a better match to the loudness curve if it fell
much more steeply above 10 kHz, and it is likely that this compromise came
about because steep filters were difficult to construct in the early days of
electronics.
Nowadays, no such limitation need exist.
If A-weighting is used without further band-limiting it is possible to obtain different
readings on different instruments when ultrasonic, or near ultrasonic noise is
present.
Accurate measurements therefore require a 20 kHz low-pass filter to be
combined with the A-weighting curve in modern instruments. This is defined in
IEC 61672 as A-U weighting and while very desirable, is rarely fitted to
commercial sound level meters.
Psychoacoustics
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Perceived Loudness: Masking
Auditory masking occurs when background noise makes sound
inaudible.
Broadband noise is contains energy at all audible frequencies.
Bandpass noise removes energy from the low- and highfrequency ends of the spectrum.
Psychoacoustics
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Loudness Scaling: Magnitude of perceptual change
I  dI 
dS 1 1


k
dI
I
I/I  constant
Fechner assumed that a JND for
a faint reference sound produces
the same difference in sensation
as does the JND for a loud
reference.
Measure of loudness: sensation
intensity (S) in JND units
As it turned out, this assumption
is not valid, as shown by
Stevens (1957) he simply asked
subject to asses supra-threshold
stimuli.
Psychoacoustics
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Louness Scaling: Stevens’ Power law
Another function relating
Loudness S in sones to stimulus
intensity in I:
S  aI
=0.3
m
The exponent m describes
whether sensation is an expansive
or compressive function of
stimulus intensity.
The coefficient a simply adjusts for
the size of the unit of
measurement for stimulus intensity
threshold above the
1-unit stimulus.
Psychoacoustics
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Auditory sensitivity: JND
Smallest detectable change in sound level equals
0.3-2dB for a wide range of levels and types of sound
A value of 0.5-1dB for wideband noise – holds from about
20dB to 100dB above threshold – JND increases for
sounds close to absolute threshold
For pure tones the JND for loudness varies slightly with
frequency (best 1-4 kHz) and may improve at higher
sound levels
Psychoacoustics
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Loudness Scaling
Psychoacoustics
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Loudness Scaling: sone vs. phon
SONE: a unit to describe the comparative
loudness between two or more sounds.
One SONE has been fixed at 40 phons at any
frequency (40 phon curve).
2 sones describes sound two times LOUDER
than 1 sone sound.
A difference of 10 phons is sufficient to
produce the impression of doubling loudness,
so 2 sones are 50 phons.
L  k ( p  p0 )
4 sones are twice as loud again, viz. 60 phons.
0.6
p is the base pressure of a sinusoidal stimulus, po is its absolute threshold.
Psychoacoustics
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Predicting Loudness
Currently, predictors of loudness are only successfully for sound stimuli
extending over many seconds.
Note that the dBA scale does not include bandwidth influences on loudness
(etc.).
It is better than the dB SPL scale, but far away from human perception
Psychoacoustics
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Neural Coding of Loudness
Neural Coding related to the perception of loudness:
Increase in sound level:
increased BM movement
leads to increased firing rates in the neurons of
the auditory nerve
spread of activity to adjacent neurons
the summation of neural activity across different
frequency channels – critical bands
Psychoacoustics
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Neural Coding of Loudness
Individual neurons are
sensitive to a limited range
of intensities (blue vs red)
But different neurons are
responsive to different
intensity ranges
Neurons respond to nonpreferred frequencies at high
enough intensities