Download Sensitivity and Loudness

PSYC 60041 Auditory Science
Auditory Sensitivity &
Loudness
Chris Plack
Auditory Sensitivity & Loudness
• Learning Outcomes
– Understand how auditory sensitivity can be measured
– Understand what is meant by MAF and MAP
– Understand how and why threshold depends on
signal duration
– Understand how loudness is defined and quantified
– Understand how loudness is affected by hearing loss
– Understand the basic intensity sensitivity of the
human ear
dB SPL
We generally quantify sound by measuring its
pressure in Pascals (Pa = N/m2).
This is converted to a logarithmic scale: dB.
When the reference pressure of 20 mPa (or reference
intensity of 10-12 Watts/m2) is used to calculate
the level of a sound we call the measure dB
sound pressure level (or dB SPL):
dB SPL = 10 log10[I / (10-12 Watts/m2)]
or…
dB SPL = 20 log10[p / (2x10-5 Pa)]
(for reference, atmospheric pressure is 105 Pa)
Threshold of Audibility
Threshold of Audibility
A key role of the audiologist is to determine how
sensitive is an ear to sounds of different
frequencies.
Frequency specific stimuli
are used – sinusoids (“pure
tones”) – one single
frequency:
Measuring Threshold
The intensity of the sound can be adjusted to find
the smallest level required for detection –
threshold of audibility.
However our detection of a sound isn’t as simple as
just “yes I can hear it” or “no I can’t hear it.”
Sounds near threshold sometimes result in yes and
sometimes no for the same sound level.
Measuring Threshold
At each level there is a certain probability
associated with responding correctly (yes or
no depending on whether the sound is present
or not).
If we present several repeated presentations at each
level we can calculate the probability of a
correct response.
If we plot this probability against stimulus level we
have a “psychometric function.”
Measuring Threshold
Psychometric functions give a comprehensive
description of how detectability changes with
level. However, usually a certain probability is
chosen as the threshold (e.g. 50% or 75%
correct).
BSA audiometry procedure defines “threshold” as
the level corresponding to 50% correct
responses (for rising stimulus levels).
A listener with low threshold has high sensitivity.
Forced-Choice Task
For a PTA type task (yes/no) the probability of a correct
answer varies from 0% to 100%.
An alternative is to give two possible observation
intervals (usually indicated by lights).
The subject then has to indicate which interval
contained the signal – a two-interval, twoalternative forced choice (2I2AFC) task.
Here there is a 50% chance of guessing so the
psychometric functions run from 50% to 100%
with a certain value, say 75% correct, taken as the
threshold.
Psychometric Functions at
Different Frequencies
Other alternatives used in psychophysics (usually
automated) include:
3AFC, 33% chance of guessing correct
Threshold
Level
Adaptive tracking e.g. “2-down, 1-up” where two
consecutive correct responses are required
before the task gets harder and one wrong
before it gets easier:
trial number
Threshold of Audibility
Two basic methods have been used to define the
threshold of audibility:
Minimum audible field (MAF)
Minimum audible pressure (MAP)
Minimum Audible Field (MAF)
Absolute thresholds for free-field tones: presented
over a loud speaker in an anechoic
environment. Usually with listener facing
source 1 m away.
Binaural listening (both ears).
Listener removed and calibrated microphone placed
at the position of listener’s head to calibrate
sound field.
Calibration doesn’t account for torso, head, and
outer-ear diffraction effects which are there in
the actual measurements.
MAF
Free-field threshold of hearing
120
100
dB SPL
80
60
40
20
0
-20
10
100
1000
Frequency (Hz)
10000
100000
Minimum Audible Pressure (MAP)
Sound usually delivered by headphones.
Monaural measurements.
Thresholds described in terms of SPL at listener’s
tympanic membrane.
SPL measured at eardrum using probe-microphone
placed very close to eardrum.
Head diffraction and ear canal resonance effects not
taken into account in the threshold
measurements.
MAF vs. MAP
The MAP measured with headphones is typically 5-10
dB higher than binaurally measured MAF.
2-3 dB of this difference can be accounted for by the
use of two ears rather than one.
MAF includes the effect of reflections from the
listener’s head and shoulders; measuring MAP
with headphones does not.
MAF includes ear-canal resonance, MAP does not.
It is also likely that physiological noise “trapped” in the
ear-canal by the headphones also contributes to
this difference at low frequencies (Moore, 2012).
Ear canal resonance at 3-4 kHz results in an
increase in SPL at the ear-drum relative to that
measured with the head removed (MAF).
With MAP the SPL is already measured at the
ear-drum, so the ear canal resonance effect is
removed.
Auditory Sensitivity
20-20,000 Hz is the range of frequencies over which the
human ear is generally accepted to “hear” sounds.
The ear is most sensitive over the 1-6 kHz range.
At 1 kHz, normal threshold is about 0 dB SPL or 20 μPa.
At this sound level the tympanic membrane is vibrating
through a distance less than a tenth the diameter of
a hydrogen atom…
Auditory Sensitivity – Low Frequencies
The true limit of low frequency hearing is about 20 Hz.
Below this the necessary sound level is so intense that
it may actually be felt rather than heard.
Also, low frequency sounds may be detected by higher
frequency distortion components rather than the
low-frequency components themselves.
Auditory Sensitivity – High Frequencies
The upper frequency limit of hearing is about 20 kHz.
Young children can often hear tones as high as 20
kHz.
However, for most adults the threshold rises rapidly
above 15 kHz.
dB Hearing Level (HL)
If we turn the threshold graph upside down and plot
the normal threshold of hearing as a straight
line, we can obtain a new scale: dB HL (hearing
level).
0 dB HL represents average normal hearing at all
frequencies.
Threshold of Hearing (dB HL)
-20
0
dB HL
20
40
60
80
100
100
1000
Frequency (Hz)
10000
dB Sensation Level (SL)
dB sensation level is the number of decibels above
a person's threshold for a given signal.
E.g. a person has a 1 kHz pure-tone threshold of 40
dB SPL, a 1 kHz tone is presented at 60 dB
SPL…
…the tone is at 20 dB SL, i.e. 20 dB above the
person's threshold.
Signal Duration and Threshold
All these threshold values apply for relatively long
signals (~500 ms plus).
If we are interested in how signal duration affects
signal threshold we can either:
Keep the signal power constant.
or
Keep the signal energy constant.
Power = Energy/Time.
Signal Duration and Threshold
Constant energy: power is decreased as duration increases
power
time
Constant power
power
time
Signal Duration and Threshold
Thresholds plotted
relative to the
threshold for a
duration of 1024 ms:
Signal Duration and Threshold
Above about 250-500 ms the threshold changes little.
Below about 250 ms the power must be increased as
the tone is made shorter.
Signal Duration and Threshold
Below about 250-300 Hz we can approximate the ear as
a constant energy detector (only approximately).
A 10 fold decrease in duration requires a 10 dB
increase in power to maintain detection:
10 dB increase in power = 10-fold increase
i.e. 10 log10(10/1) = 10 dB
For sounds with durations below 10 ms much larger
increases in power are required.
Implications in audiometry – presentations of 1-3 s
duration.
Temporal Integration
This process has been modelled as “temporal
integration.”
A signal must contain a critical amount of energy to be
detected.
If the signal is short it must have a higher intensity
(power) to be detected.
If the signal is longer a lower power is required.
Once a critical duration (about 300 ms) is reached the
integration is complete. If the total energy is below
that required then the sound isn’t detected.
Temporal Integration
power
Integration time
time
Loudness
Loudness
Loudness is the sensation (i.e., a subjective
attribute) related to the intensity of a sound.
Loudness is a perceptual characteristic, not a
physical characteristic of a sound (such as
amplitude, intensity etc.).
Measurement of Loudness
Two main methods of quantifying loudness:
Loudness matching - adjust level of target sound so
that it matches loudness of comparison sound.
Loudness scaling – present target sound and ask
subject to assign numerical value to loudness
(magnitude estimation), or to adjust loudness of
sound to match a given number (magnitude
production).
Loudness Matching Example
The test tone and a 1 kHz tone presented alternately.
Listener is asked to adjust the level of the test tone until
the two sounds are perceived as being equally loud.
Procedure is repeated with test tones of different
frequencies and a fixed level reference tone.
Repeated for different level reference tones.
Equal-Loudness Contours
Equal-loudness contours can be mapped out: any two
points on a given contour are perceived as having
the same loudness. Loudness level in phons is level
(in dB SPL) of 1-kHz reference tone that appears
equally loud.
E.g. sounds equal in loudness to a 40-dB SPL 1-kHz pure
tone have a 40 phon loudness level etc.
Equal-Loudness Contours
Loudness Level in Phons
Loudness Scales
On the basis of loudness scaling methods Stevens
(1957) suggested that for sounds above 40 dB
SPL loudness (L in sones) was a power function
of intensity (I) such that:
L = kI0.3 (where k is a constant)
What does this mean?
Loudness function is not linear, but is compressive.
A 10-fold increase in intensity (+10 dB) approximates
to a doubling in loudness.
10 dB increments:
BM Response Growth
The healthy BM shows a shallow, compressive,
growth with level for a tone at CF.
80 dB input range is squashed into a 20 dB output
range:
80
f = CF, compressive
response
BM Velocity (dB)
70
60
50
40
30
10 kHz
8 kHz
3 kHz
20
10
0
0
10
20
30
40
50
60
70
Level (dB SPL)
80
90 100 110 120
Loudness & BM Nonlinearity
The shallow growth of loudness with level is a direct
consequence of the compressive BM response
function.
In fact, loudness in sones is approximately
proportional to the square of BM velocity (in other
words, loudness is proportional to the intensity of
BM vibration).
Loudness Recruitment
Effects of Cochlear Hearing Loss:
Loudness Recruitment
Dysfunction of OHCs leads to loss of active
mechanism that produces compression.
Hence, loudness grows much more rapidly with
increasing sound level than normal (loudness
recruitment).
Response Functions
The shallow response growth, and sensitivity, goes away if the
cochlea is in a poor physiological condition:
Gain ≈ 50 dB
Ruggero et al. (1997)
Loudness Recruitment
5
Normal
Loudness Rating
4
Cochlear Loss
3
2
1
0
0
20
40
60
Level (dB SPL)
80
100
Binaural Loudness Matching
For listeners with a unilateral loss, recruitment in the
impaired ear can be measured by loudness
matching with the good ear.
Medium-level tones in the impaired ear may sound as
loud as low-level tones in the normal ear.
However, the same high-level tone might be judged
equally loud in the normal and impaired ears.
Loudness Scaling
Similar results can be obtained for loudness scaling
experiments.
In this experiment, listeners had to rate the loudness of
sounds on a five-point scale (1 = “very soft”, 5 =
“very loud”).
dashed lines
indicate normal
hearing
S1 and S2 both
show
recruitment
S3 shows no
recruitment conductive loss?
Temporal Masking Curves
Masker
Interval
2.2 kHz
4 kHz
4 kHz
Time
Frequency
Frequency
Masker Level (dB SPL)
Signal
Masker-Signal Interval (ms)
A given increase in masker-signal interval has a
larger effect on the masker level required at
medium masker levels:
(dB)
BM
BM Velocity
Velocity (dB)
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Masker
Level (dB
Sound Pressure
LevelSPL)
(dB)
80
90
100
Masker Level (dB SPL)
Temporal Masking Curves
Masker-Signal Interval (ms)
Masker Level (dB SPL)
Temporal Masking Curves
Masker-Signal Interval (ms)
2.2-kHz Masker Level (dB SPL)
Derived basilar-membrane input/output function:
4-kHz Masker Level (dB SPL)
Response functions at 4 kHz derived from TMCs for normalhearing listeners (Plack et al., 2004, JASA 115, p. 1684):
Response functions at 4 kHz derived from TMCs for listeners
with mild-to-moderate cochlear loss:
2200-Hz Masker Level (dB SPL)
Fit linear regression functions to estimate the slope of the
response function and the gain of the cochlear amplifier:
Slope = 0.13 dB/dB
Gain = 53 dB
4000-Hz Masker Level (dB SPL)
Strong relation between the amount of hearing loss and the
maximum gain of the cochlear amplifier:
No clear relation between the amount of hearing loss and the
maximum compression exponent:
Mild-to-moderate cochlear hearing loss:
Normal
Impaired
Moderate-to-severe cochlear hearing loss:
Normal
Impaired
Calculation of OHC and IHC loss:
OHC loss = loss of gain
Normal
Impaired
IHC loss = HL - OHC loss
Correcting for Loudness Recruitment
If the sound is simply amplified for the impaired
listener, say by 40 dB, then low-level sounds
would be audible, but high level sounds would be
unbearably loud!
To overcome this, the signal needs compression (to
reduce the dynamic range) as well as
amplification.
This can restore a normal dynamic range, and normal
growth of loudness with level.
Linear
TOO
LOUD
peak clipping
LOUD
Intense
Moderate
LOUD
QUIET
QUIET
Weak
Normal
Impaired
Compression
LOUD
Intense
Moderate
LOUD
QUIET
QUIET
Weak
Normal
Impaired
Correcting for Loudness Recruitment
The same degree of hearing loss may not be present at
all frequencies.
Different degrees of amplification and compression
may be required at different frequencies to enable
speech sounds to be heard comfortably.
Hence multi-band compression in digital (and some
analogue) hearing aids.
Intensity Discrimination
Detection of Intensity Changes
Intensity discrimination - two or more separate sounds presented
successively, one more intense than the others, and the
listener indicates which was the more intense:
Intensity Discrimination for
Wideband Noise
Smallest detectable intensity change is approximately
a constant fraction of the stimulus intensity.
I.e. DI/I is roughly constant.
An example of Weber’s law (DI/I is often referred to as
the Weber fraction).
Weber’s Law
Weber's law - the smallest detectable change in a
stimulus is proportional to the magnitude of that
stimulus.
In dB, the smallest detectable change in level is given by:
DL = 10 log10[(I+DI)/I]
The value of DL is about 0.5 - 1 dB for wideband noise.
Holds from about 20 dB above threshold to about 100 dB
above threshold for wideband noise.
Intensity Discrimination for Pure Tones
For pure tones (sinusoids), Weber's law does not hold.
DI/I decreases with increasing I.
This is referred to as the "near miss to Weber's law."
Auditory Sensitivity & Loudness
• Learning Outcomes
– Understand how auditory sensitivity can be measured
– Understand what is meant by MAF and MAP
– Understand how and why threshold depends on
signal duration
– Understand how loudness is defined and quantified
– Understand how loudness is affected by hearing loss
– Understand the basic intensity sensitivity of the
human ear