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Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

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Page 1: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Applied PsychoacousticsLecture 4: Loudness

Jonas Braasch

Page 2: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Definition Loudness

Loudness is the quality of a sound that is the primary psychological correlate of physical intensity. Loudness is also affected by parameters other than intensity, including: frequency bandwidth and duration.

Page 3: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

How can we measure loudness

• We can present a sinusoidal tone to our subject and ask them to report on the loudness.

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Scales of Measurement

nominal ordinal interval ratioNon-numeric scale

Scale with greater than, equal and less than attributes, but indeterminate intervals between adjacent scale values

equal intervals between adjacent scale values, but no rationale zero point

Scale has a rationale zero point

e.g., color, gender

e.g., rank order of horse race finalist

e.g., the difference between 1 and 2 is equal to the difference of 101 and 102e.g., Temperature in Fahrenheit

e.g., the ratio of 4 to 8 is equal to the ratio of 8 to 16.

e.g., Temperature in Kelvin.

Page 5: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Measuring loudness in phon

• At 1 kHz, the loudness in phon equals the sound pressure level in dB SPL.

• At all other frequencies the loudness the corresponding dB SPL value is determined by adjusting the level until the loudness is equally high to the reference value at 1kHz (so-called equal loudness curves or Fletcher-Munson curves).

• Loudness measured in Phon is based on an ordinal scale

Page 6: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Typical goal of our measurement

• Determine the relationship between a physical scale (e.g., sound intensity) and the psychophysical correlate (e.g., loudness)

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Measurement Methods

• method of adjustment or constant response– The subject is asked to adjust the stimulus

to a fulfill certain task (e.g., adjust the stimulus to be twice as loud).

• method of constant stimuli – Report on given stimulus (e.g., to what

extent it is louder or less loud then the previous stimulus).

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Equal loudness curve

Detection threshold

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Loudness in Sone

• Stevens proposed in 1936 to measure loudness on a ratio scale in a unit he called Sone. He defined 1 Sone to be 40 phons. The rest can be derived from measurements.

Do you have an idea how he could have done it?

Page 11: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

1. Measure the Sone scale at 1 kHz

e.g., by asking the subject to adjust the level of the sound stimulus (1-kHz sinusoidal tone) such that it is twice, 4 times … as loud as the Reference stimulus at 1 Sone (40 phons).

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Relationship between Sones and Phons

At 1-kHz this is also the psychometric function between Sone and dB SPL

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2. Measure the Sone scale at all other frequencies

• The easiest way is to follow the equal loudness contours. If they are labeled with the correct Sone value at 1 kHz, they are still valid.

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2 Sone

1 Sone

4 Sone8 Sone16 Sone

32 Sone

64 Sone

Equal loudness curve

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Psychometric Function

Page 16: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Stevens’ Power Law

Stevens’ was able to provide a general formula to relate sensation magnitudes to stimulus intensity:

S = aIm

• Here, the exponent m denotes to what extent the sensation is an expansive or compressive function of stimulus intensity.

• The purpose of the coefficient a is to adjust for the size of the unit of measurement.

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Examples for Steven’s Power Law

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Examples for Steven’s Power Law Exponents

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… and now in the log-log space

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An introduction to Signal Detection Theory

Let us come back to our initial example of determining the Absolute Threshold of Hearing, but this time we choose a constant stimulus approach.

How can we do it?

Page 21: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Measuring the ATH one more time

• For example, we can present the stimulus at different levels ask the subject each time whether he or she perceived an auditory event or not.

• We might naively assume that our psychometric function will look like this:

Page 22: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Measuring the ATH one more time

Sound pressure levelNum

ber

of c

orre

ct r

espo

nses

[%

]

Hearing threshold100%

0%

… would be nice, but in reality

Page 23: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

… it looks like this

Log-normalized stimulus intensity (e.g, sound pressure level)

Prob

abil

ity

for

corr

ect r

espo

nse

50 % threshold

75 % threshold

In signal detection theory, we explain this variation with internal noise in the central nervous system

Page 24: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Definition of the correct response

hit miss

False alarm Correct reject

Positive responseNegative response

Stimulus present

Stimulus not present

Sometimes it is better to rather accept a false alarm (e.g., fire detector) while other times it is better to accept a miss (e.g., non-emergency surgery cases)

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Just noticeable differences (JNDs)

• Is the smallest value of a stimulus variation (e.g., sound intensity) that we are able to detect.

• A classic example is the work of Fechner measuring the JNDs for lifting different weights

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Weber-Fechner’s Law• In one of his classic experiments, Weber gradually increased the

weight that a blindfolded man was holding and asked him to respond when he first felt the increase. Weber found that the response was proportional to a relative increase in the weight. That is to say, if the weight is 1 kg, an increase of a few grams will not be noticed. Rather, when the mass is increased by a certain factor, an increase in weight is perceived. If the mass is doubled, the threshold is also doubled. This kind of relationship can be described by a differential equation as,–

• where dp is the differential change in perception, dS is the differential increase in the stimulus and S is the stimulus at the instant. A constant factor k is to be determined experimentally.

• Integrating the above equation gives–

• where C is the constant of integration, ln is the natural logarithm.• To determine C, put p = 0, i.e. no perception; then

– • where S0 is that threshold of stimulus below which it is not

perceived at all.• Therefore, our equation becomes

– • The relationship between stimulus and perception is logarithmic

Page 27: Applied Psychoacoustics Lecture 4: Loudness Jonas Braasch

Fechner’s indirect scales

0 sensation units (0 JND of sensation)stimulus intensity at absolute detection threshold

1 sensation unit (1 JND of sensation)stimulus intensity that is 1 difference threshold above absolute threshold

2 sensation units (2 JND of sensation)stimulus intensity that is 1 difference threshold above the 1-unit stimulus

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Fechner’s Law

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Determination whether difference is perceivable

Internal response to stimulus #1, e.g., perceived loudness

Internal response to stimulus #2

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Receiver Operating Characteristic (ROC)

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Discriminability index: d’=ms-mm/(), if s=m

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Excitation pattern for 1-kHz sinusoid

from Delgutte

•An excitation pattern for a 1-kHz Sinusoid with a level of 70-dB SPL.•The data was calculated from the response of several single neurons. •For each neuron, the SPL was recorded that was needed to receive the same discharge rate compared to the discharge rate for the reference condition (1-kHz, 70 dB SPL).•The thick line plots the resulting level of the CF tone for many neurons. Of course, for neurons with a CF of 1 kHz, the level has to be 70 dB, because here the CF is identical to the reference frequency. The further the CF is apart from the reference frequency, the lower the SPL that is needed to excite the neuron with similar discharge rate, because the neuron becomes less sensitive to excitation at 1 kHz. •The thin curve describes the threshold SPL for many neurons at their CF (Bump at 3 kHz not clear).

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Zwicker loudness model

N=N’mm=1

24Overall loudness

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dB (A), roughly 35 phons

dB (B)

dB (C)

Equal Loudness Contours

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Frequency weighting for dBA and dBC

from: Salter, Acoustics, 1998

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from: W. J. Cavanaugh, Acoustics-General Principles, 1988

Typical Exterior Sound Sources

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from: W. J. Cavanaugh, Acoustics-General Principles, 1988

Different Weighting Schemes

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Relative Subjective Changes

Cavanaugh & Wilkens, Architectural Acoustics, 1998

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